Which is one of the binomial factors of the polynomial x^3+3x-2x-8?
a. x-1
b. x+1
c. x-2
d. x+2
Answers
Answer:
x+2
Step-by-step explanation:
A factor of a polynomial can be thought of as the value of x at which the polynomial is equal to zero.
So, you can use the values in the options given and put them in the polynomial from the question.
for example: try, part a) x-1, here x=1 since the factor is x-1=0
put this value in the polynomial to see if it results to zero.
[tex](1)^3 + 3(1)^2 - 2(1) - 8\\ -6[/tex]
so this isn't the answer.
now try, part d) x + 2, here, x = -2
[tex](-2)^3 + 3(-2)^2 - 2(-2) - 8\\ 0[/tex]
you'll see this is the factor!
Answer:
d. x+2
Step-by-step explanation:
The question is essentially asking which of -2, -1, 1, 2 is a zero of the polynomial. All of them are plausible, because all are factors of -8, the constant term.
So, we don't have much choice but to try them. That means we evaluate the function to see if any of these values of x make it be zero.
±1:
The value 1 is easy to substitute for x, as it makes all of the x-terms equal to their coefficient. Essentially, you add all of the coefficients. Doing that gives ...
1 +3 -2 -8 = -6
Similarly, the value -1 is easy to substitute for x, as it makes all odd-degree terms equal to the opposite of their coefficient. Here, ...
f(-1) = -1 +3 -(-2) -8 = -4
Neither one of these values (-1, +1) is a zero of the polynomial, so choices A and B are eliminated.
__
(x-2):
To see if this is a factor, we need to see if x=2 is a zero. Evaluation of a polynomial is sometimes easier when it is written in Horner form:
((x +3)x -2)x -8
Substituting x=2, we get ...
((2 +3)2 -2)2 -8 = (8)2 -8 = 8 . . . not zero
This tells us there is a zero between x=1 and x=2, but that is not what the question is asking.
__
(x+2):
We can similarly evaluate the function for x=-2 to see if (x+2) is a factor.
((-2 +3)(-2) -2)(-2) -8 = (-4)(-2) -8 = 0
Since x=-2 makes the function zero, and it makes the factor (x+2) equal to zero, (x+2) is a factor of the polynomial.
So, the factor (x+2) is a factor of the given polynomial.
_____
I find that a graphing calculator answers questions like this quickly and easily. If you're allowed one, it is a handy tool.
Related Questions
Before school, Janine spends 1/10 hour making her bed, 1/5 hour getting dress, and 1/2 hour eating breakfast. What fraction of an hour does she spend doing these activities?
Answers
Answer:
4/5
Step-by-step explanation:
This is a long-winded way to ask you the sum of the three fractions:
1/10 + 1/5 + 1/2
= 1/10 + 2/10 + 5/10 = (1 +2 +5)/10 = 8/10
= 4/5
Janine spends 4/5 hour doing morning activities.
Suppose you begin a job with an annual salary of $32,900. Each year you are assured of a 5.5% raise. What its the total amount that you can earn in 15 years? A) $34,815 B) $51,751 C) $737,245 D) $1,682,920
Answers
Answer: the total amount that you can earn in 15 years is $737245. Option C
Step-by-step explanation:
You receive an annual salary of $32,900 and each year, you are assured of a 5.5% raise. Assuming there was no raise, you get 100% of your previous salary each year. With a raise of 5.5%, you will get 100 + 5.5 = 105.5% of your previous salary for each year. This is a geometric progression and we want to determine the sum of 15 terms(15 years).
The formula for the sum of terms in a geometric progression is
Sn = [a(r^n - 1)]/ r - 1
Sn = sum of n terms
a = the first term
n = number of terms
r = common ratio
From the information given,
a = 32900
n = 15
r = 105.5/100 = 1.055
S15 = [32900(1.055^15 - 1)] / 1.055 - 1
S15 = [32900(2.23247649 - 1)] / 0.055
S15 = 32900 × 1.23247649) / 0.055
S15 = 737245.0277
S15 = $737245
A person standing cloes to the edge on the top of a 200-foot building throws a baseball vertically upward. The quadratic functions(t)=-16t^2+64t+200models the ball's height above the ground, s(t), in feet, t seconds after it was thrown.A) After how many seconds does the ball reach it's maximum height? What is the maximum height?B) How many seconds does it take until the ball finally hits the ground?C) Find s(0) and describe what this means. D) Use your res ults from parts (a) through (c) to graph the quadratic function . Begin the graph with t = 0 and end with the value oft for which the ball hits the ground.
Answers
Answer:
Part (A): it would take 2 seconds to reach maximum height of 264 foot.
Part (B): Ball will hit the ground in about 6.1 seconds
Part (C): S(0) represents the initial height of the base ball or the baseball was thrown at a height of 200 ft.
Step-by-step explanation:
Consider the provided function.
[tex]s(t)=-16t^2+64t+200[/tex]
Part (A) After how many seconds does the ball reach it's maximum height? What is the maximum height?
The coefficient of t² is a negative number, so the graph of the above function is a downward parabola.
From the given function a=-16, b=64 and c=200
The downward parabola attain the maximum height at the x coordinate of the vertex. [tex]x=\frac{-b}{2a}[/tex]
Substitute the respectives.
[tex]x=\frac{-64}{2(-16)}=2[/tex]
Substitute x=2 in the provided equation.
[tex]s(t)=-16(2)^2+64(2)+200=264[/tex]
Hence, it would take 2 seconds to reach maximum height of 264 foot.
Part (B) How many seconds does it take until the ball finally hits the ground?
Substitute s(t)=0 in the provided equation.
[tex]-16t^2+64t+200=0[/tex]
Use the formula [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] to find the solutions of the quadratic equation.
[tex]t=\frac{-64+\sqrt{64^2-4\left(-16\right)200}}{2\left(-16\right)}\\t=\pm\frac{4+\sqrt{66}}{2}\\t\approx-2.1\ or\ 6.1[/tex]
Reject the negative value as time can't be a negative number.
Hence, ball will hit the ground in about 6.1 seconds
Part (C) Find s(0) and describe what this means.
Substitute x=0 in the provide equation.
[tex]s(0)=-16(0)^2+64(0)+200[/tex]
[tex]s(0)=200[/tex]
S(0) represents the initial height of the base ball or the baseball was thrown at a height of 200 ft.
Part (D) Use your results from parts (a) through (c) to graph the quadratic function.
Use the starting points (0,200), maximum point (2,264) and the end point (6.1,0) in order to draw the graph of the function.
Connect the points as shown in figure.
The required figure is shown below.
A consumer products company relies on direct mail marketing pieces as a major component of its advertising campaigns. The company has three different designs for a new brochure and want to evaluate their effectiveness, as there are substantial differences in costs between the three designs. The company decides to test the three designs by mailing 5,000 samples of each to potential customers in four different regions of the country. Since there are known regional differences in the customer base, regions are considered as blocks.
Answers
Answer:
What is the question?????
A bag contains only 3 blue disks, 3 green disks, and 4 orange disks. If 3 disks are selected at random from the bag, what is the probability that 1 of the disks will be green and 2 of the disks will be orangeA) 1/30
B) 1/20
C) 3/40
D) 1/10
E) 3/20
Answers
Answer:
E= 3/20
Step-by-step explanation:
Number of blue disk= 3
Number of green disk= 3
Number of orange disk= 4
Total number of disk = 3+3+34
= 10
Let B represent blue disk
Let G represent green disk
Let O represent orange disk
If three disk are selected at random, the possible outcome of one green disk and two orange disks are
OOG, OGO, GOO
Pr(OOG) = Pr(O1) * Pr(O2) * Pr(G3)
= 4/10 * 3/9 * 3/8
= 36/720
= 1/20
Pr(OGO) = Pr(O1) * Pr(G2) * Pr(O3)
= 4/10 * 3/9 * 3/8
= 36/720
= 1/20
Pr(GOOG) = Pr(G1) * Pr(O2) * Pr(O3)
= 4/10 * 4/9 * 3/8
= 36/720
= 1/20
Pr(total) = Pr(OOG) + Pr(OGO) + Pr(GOO)
= 1/20 + 1/20 + 1/20
= 3/20
In a random sample of 81 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3408 with a standard deviation of $2565. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. The lower bound is $ nothing. (Round to the nearest cent as needed.) The upper bound is $ nothing. (Round to the nearest cent as needed.) Interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. Choose the correct answer below.
a. One can be 90% confident that the mean additional tax owed is less than the lower bound
b. One can be 90% confident that the mean additional tax owed is between the lower and upper bounds
c. One can be 90% confident that the mean additional tax owed is greater than the upper bound.
Answers
Answer:
B. One can be 90% confident that the mean additional tax owed is between the lower and upper bounds.
Step-by-step explanation:
Given:
n= 81
[tex]\bar{x}=3408[/tex]
[tex]\sigma= 2565[/tex]
Solution:
A confidence interval, in statistics, refers to the probability that a population parameter will fall between two set values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. A confidence interval can take any number of probabilities, with the most common being a 95% or 99% confidence level.
Confidence interval = [tex]\bar{x} \pm z * \frac{\sigma}{\sqrt{n}}[/tex]
To Find the z value:
Degree of freedom = n-1
=>81- 1
=> 80
Significance level = 1- confidence level
=>[tex]\frac{(1-\frac{90}{100})}{2}[/tex]
=>[tex]\frac{(1-0.90)}{2}[/tex]
=> [tex]\frac{0.1}{2}[/tex]
=>0.05
using this value In T- Distribution table we get
z = 1.645
Substituting the values we have,
confidence interval = [tex]3408\pm 1.645 * \frac{2565}{\sqrt{81}}[/tex]
confidence interval = [tex]3408\pm 1.645 * \frac{2565}{\sqrt{9}}[/tex]
confidence interval = [tex]3408\pm 1.645 * 285[/tex]
confidence interval = [tex]3408\pm 468.825[/tex]
confidence interval= (2939.18, 3876.83)
To construct a 90% confidence interval for the mean additional amount of tax owed for estate tax returns, we need to use a z-score and the formula CI = x ± z * (σ/√n), where CI is the confidence interval, x is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size. Plugging in the values from the problem, we can calculate the lower and upper bounds of the confidence interval.
Explanation:To construct a 90% confidence interval for the mean additional amount of tax owed for estate tax returns, we can use the formula:
CI = x ± z * (σ/√n)
where CI is the confidence interval, x is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
Plugging in the values from the problem, we have:
x = $3408
σ = $2565
n = 81
Using a z-score table or a statistical calculator, we can find that the z-score corresponding to a 90% confidence level is approximately 1.645.
Substituting these values into the formula, we get:
CI = $3408 ± 1.645 * ($2565/√81)
Simplifying the expression, we have:
CI = $3408 ± 1.645 * $285
Calculating the upper and lower bounds of the confidence interval, we get:
Lower bound = $3408 - 1.645 * $285 = $2977.82
Upper bound = $3408 + 1.645 * $285 = $3838.18
Therefore, the 90% confidence interval for the mean additional amount of tax owed for estate tax returns is approximately $2977.82 to $3838.18.
Interpreting the confidence interval, we can say that we are 90% confident that the true mean additional amount of tax owed for estate tax returns falls within this range.
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A cardboard box without a lid is to be made with a volume of 44 ft3. Find the dimensions of the box that requires the least amount of cardboard.
Answers
Answer:
x = 3.53 ft
y - 3.53 ft
z = 3.53 ft
Step-by-step explanation:
given details
volume = 44 ft^3
let cardboard dimension is x and y and height be z
we know that area of given cardboard without lid is given as
A = xy + 2xy + 2yz
xyz = 44 ft^3
To minimize area we have
A = xy + 2x (44/xy) + 2y(44/xy)
A = xy + (44/y) + (44/x)
we have
[tex]Ax = y - \frac{44}{x^2}[/tex]
[tex]0 = yx^2 = 44[/tex]................1
[tex]Ay = x - \frac{44}{y^2}[/tex]
[tex]0 = x - \frac{44}{y^2}[/tex]
[tex]xy^2 = 44[/tex] ..............2
from 1 and 2
[tex]yx^2 = xy^2[/tex]
xy(y-x) = 0
xy = 0 or y = x
from geometry of probelem
x ≠ 0 and y ≠ 0
so y = x
x^3 = 44
x = 3.53 ft = y
z = 44/xy = 3.53
To find the dimensions of the box that requires the least amount of cardboard, we need to minimize the surface area of the box. Since it doesn't have a lid, the box will have an open top. Let's call the length of the box 'x' and the width and height 'y'. The dimensions of the box that requires the least amount of cardboard are x = 44 ft and y = 0 ft.
Explanation:To find the dimensions of the box that requires the least amount of cardboard, we need to minimize the surface area of the box. Since it doesn't have a lid, the box will have an open top. Let's call the length of the box 'x' and the width and height 'y'.
The volume of the box is given as 44 ft3, so we have the equation x * y * y = 44.
To minimize the surface area, we can differentiate the surface area function with respect to x or y, set it equal to zero, and solve for the corresponding variable.
Let's differentiate the surface area function with respect to x to find the critical point:
0 = 2y2 + 2xy * dy/dx
Since the box has an open top, the length, x, cannot be zero. Therefore, we can solve the equation 2y2 + 2xy * dy/dx = 0 for dy/dx. This gives us:
dy/dx = -y/x
Now, we can substitute this into the equation for the surface area:
S = x * y2 + 2xy * dy/dx
Simplifying, we get:
S = x * y2 - 2y2
To find the critical point, we set the derivative equal to zero:
0 = y2 - 2y2
0 = -y2
Since y is squared, it cannot be negative. Therefore, the only possible critical point is when y is zero, which means the dimensions of the box are x = 44 ft and y = 0 ft.
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At the end of the year a library reported 32books lost or stolen and 24 books were sent out for repair if the Library originally had 1219 books how many were left on the shelves or in circulation
Answers
Answer:
The number of books left on shelves or in circulation is 1,163 .
Step-by-step explanation:
Given as :
The total number of Books in the Library = 1219
The number of lost or stolen books = 32
The number of books sent fro repair = 24
Now, Let The number of books left on shelves or in circulation = x
So,
The total number of Books in the Library = The number of lost or stolen books + The number of books sent fro repair + The number of books left on shelves or in circulation
I.e 1219 = 32 + 24 + x
Or, 1219 = 56 + x
Or, x = 1219 - 56
∴ x = 1,163
Hence The number of books left on shelves or in circulation is 1,163 Answer
Answer: Number of books in circulation or left on the shelf is 1163
Step-by-step explanation:
At the end of the year, 32 books were reported to be lost or stolen and 24 books were sent out for repair. This means that the number of books not in circulation is the sum of the number books that was lost or reportedly stolen and the number of books that were sent out for repair.
Therefore,
Number of books not in circulation = 32+24 = 56
The Library originally had 1219 books.
The number of books left on the shelves or in circulation will be total number of books initially - number of books not in circulation. This becomes
1219 - 56 = 1163 books
blake buys paperback from the used bookstore for $ 5 . 5 . Natalie purchased an annual membership to the same bookstore for $ 35 35 so she can buy paperbacks at a discounted price $ 2.50 2.50 each. How many books would Natalie and Blake have to buy this year for their spending at the bookstore to be the same? What would their total cost be? Evaluate
Answers
Answer:
Step-by-step explanation:
1:22
Answer:
Step-by-step explanation:
so
b buys a paperback for 5.5, while after natalie purchases 35.35 for membership- her books are 2.50
blake paid 5.5
nat paid 37.85
lets see how many books blake has to pay to reach 37.85 shall we?
5.5*22=121
2.5*35=87.5
35.35+87.5=122.85
i dont think its possible
]An electrician charges $40 for each hour he works plus a $125 service charge. The total charge for a recent job was $1,205. Which equation could be used to determine the number of hours, h, that the electrician worked on the job
Answers
Answer:
40h+125=1205
Step-by-step explanation:
He is paid $40 for an unknown amount of hours which in this case would be considered as (h) plus a 125 service charge. Overall, he was paid $1205
DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data is displayed.
Poisoned rats 12.207 16.869 25.050 22.429 8.456 20.589
Unpoisoned rats 11.074 9.686 12.064 9.351 8.182 6.642
Let μ 1 be the mean nerve sensitivity for rats poisoned with DDT.
Let μ 2 be the mean nerve sensitivity for rats not poisoned with DDT. The P ‑value for this test was between 0.01 and 0.05. Which statement is a reasonable conclusion?
Answers
Answer:
The p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to don't reject the claim that the group with DDT have a mean greater than the group for rats not poisoned.
Step-by-step explanation:
1) Data given and notation
P:[12.207 ,16.869, 25.050, 22.429, 8.456, 20.589]
UP:[11.074, 9.686 ,12.064, 9.351, 8.182, 6.642]
[tex]\bar X_{P}=17.6[/tex] represent the mean for the sample poisoned
[tex]\bar X_{UP}=9.50[/tex] represent the mean for the sample unpoisoned
[tex]s_{P}=6.34[/tex] represent the sample standard deviation for the sample poisoned
[tex]s_{UP}=1.95[/tex] represent the sample standard deviation for the sample unpoisoned
[tex]n_{P}=6[/tex] sample size for the group poisoned
[tex]n_{UP}=6[/tex] sample size for the group unpoisoned
t would represent the statistic (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the mean for rats exposed to DDT is greater than that for rats not poisoned , the system of hypothesis would be:
Null hypothesis:[tex]\mu_{P} \leq \mu_{UP}[/tex]
Alternative hypothesis:[tex]\mu_{P} > \mu_{UP}[/tex]
If we analyze the size for the samples both are less than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{P}-\bar X_{UP}}{\sqrt{\frac{s^2_{P}}{n_{P}}+\frac{s^2_{UP}}{n_{UP}}}}[/tex] (1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
3) Calculate the statistic
We can replace in formula (1) the results obtained like this:
[tex]t=\frac{17.6-9.5}{\sqrt{\frac{(6.34)^2}{6}+\frac{(1.95)^2}{6}}}}=2.99[/tex]
4) Statistical decision
For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{P}+n_{UP}-2=6+6-2=10[/tex]
Since is a unilateral test the p value would be:
[tex]p_v =P(t_{(10)}>2.99)=0.0067[/tex]
So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to don't reject the claim that the group with DDT have a mean greater than the group for rats not poisoned.
Question 1(Multiple Choice Worth 1 points) (01.04 LC) Solve for x: −3x + 3 < 6 x > −1 x < −1 x < −3 x > −3
Answers
To solve -3x + 3 < 6 and find the value of x, subtract 3 from both sides and divide by -3. The solution is x > -1.
Explanation:To solve the inequality -3x + 3 < 6, we want to isolate the variable x. First, subtract 3 from both sides to get -3x < 3. Then, divide both sides by -3 (remember to flip the inequality sign when dividing by a negative) to obtain x > -1. Therefore, the solution is x > -1.
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Tommy mows lawns and cleans pools during the summer he earns $20 per line and nine dollars per pool he needs $1500 to buy a car from his friend Tommy plans to mow 41 months this summer how many pools messy clean to earn at least $1500
Answers
Tommy must clean at least 76 pools, in addition to mowing 41 lawns, to earn the $1500 he needs to buy a car.
Explanation:Tommy has a summer job mowing lawns at $20 per lawn and cleaning pools at $9 per pool to save up for a car. To determine how many pools he needs to clean to reach his goal of $1500, we need to calculate his earnings from mowing lawns first and then see how much more he needs to earn from pool cleaning.
First, we calculate Tommy's lawn mowing earnings:
41 lawns × $20 per lawn = $820
After mowing lawns, Tommy will need an additional $1500 - $820 to buy the car. This difference is $680.
Next, to find out how many pools Tommy needs to clean, we divide the remaining amount by the amount he earns per pool:
$680 ÷ $9 per pool ≈ 75.56
Since Tommy can't clean a fraction of a pool, he will need to clean at least 76 pools to make enough money to buy the car. Therefore, the answer is 76 pools.
Please help answer this two question correctly and please show work please don't answer if you don't don't know the answer .
Answers
Answer:
Question 1 = $59.85.
Question 2 = 0.45
Step-by-step explanation:
Doug did cleaning for 1 ¾ hours.
Doug did paperwork for 2 1/3 hours.
Doug did serving for 1 5/8 hours.
Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.
=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.
In one hour Doug earns $10.50.
Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.
Hence, the total which Doug earned is $59.85.
Second question answer
5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5
Answer:
Answer:
Question 1 = $59.85.
Question 2 = 0.45
Step-by-step explanation:
Doug did cleaning for 1 ¾ hours.
Doug did paperwork for 2 1/3 hours.
Doug did serving for 1 5/8 hours.
Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.
=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.
In one hour Doug earns $10.50.
Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.
Hence, the total which Doug earned is $59.85.
Second question answer
5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5
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Question 1 = $59.85.
Question 2 = 0.45
Step-by-step explanation:
Doug did cleaning for 1 ¾ hours.
Doug did paperwork for 2 1/3 hours.
Doug did serving for 1 5/8 hours.
Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.
=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.
In one hour Doug earns $10.50.
Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.
Hence, the total which Doug earned is $59.85.
Second question answer
5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5
Click to let others know, how helpful is it
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Step-by-step explanation:
MARKING BRAINLIESTTT!!! PLUS 30PTS EARNED!! HELP ASAPP PLZZZ!!!!
1. Write an inequality for the range of the third side of a triangle if two sides measure 4 and 13.
2. If LM = 12 and NL = 7 of ∆LMN, write an inequalty to describe the lenght of MN.
3. Use the Hinge Theorem to compare the measures of AD and BD.
Answers
Answer:
1. 9 < s < 17
2. 5 < MN < 19
3. AD > BD
Step-by-step explanation:
1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:
the sum of the shortest two sides is greater than the length of the longest sidethe length of any side lies between the sum and the difference of the other two sidesHere, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...
9 < s < 17
(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)
__
2. Same as (1) using different numbers.
12 -7 < MN < 12 +7
5 < MN < 19
__
3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:
AD > BD
Which expression is equal to 2x/x−2−x+5/x+3 ?
A. x^2+11x−6/(x−2)(x+3)
B. x^2+9x+6/(x−2)(x+3)
C. 3x^2+11x+6/(x−2)(x+3)
D. x^2+3x+10/(x−2)(x+3) I think is the correct answer.
Please help, thanks!
Answers
Answer:
D is correct
Step-by-step explanation:
2x/(x-2) - (x+5)/(x+3)
2x(x+3)/(x-2)(x+3) - (x+5)(x-2)/(x+3)(x-2)
2x^2+6x/(x-2)(x+3)-(x^2+3x-10)(x+3)(x-2)
(x^2+3x+10)/(x+3)(x-2)
Answer:
x^2+3x+10/(x-2)(x+3)
Step-by-step explanation:
Just took the test
Bowling cost $2 to rent shoes,plus $5 per game. Mini golf cost $5 to rent a club, plus $4 per game. How many games would be the same total cost for bowling and mini golf? And what is that cost
Answers
Answer:
Step-by-step explanation:
Assuming the same number of bowling and mini golf games are played, let x represent the total number of games played, either bowling or mini golf. let y represent the total cost of bowling. Let z represent the total cost of golfing
Bowling cost $2 to rent a club plus $5 per game. It means that the cost, y for x bowling games will be
y = 2 + 5x
Mini golf cost $5 to rent a club, plus $4 per game. It means that the cost, y for x mini golf games will be
z = 5 + 4x
For the total cost to be the same, we will equate both equations(y = zl
2 + 5x = 5 + 4x
5x - 4x = 5 - 2
x = 3
There would be 3 games before total cost would be the same
The length of a violin string varies inversely with the frequency of its vibrations. A violin string 14 inches long vibrates at a frequency of 450 cycles per second. Find the frequency of a 12 inch violin string.
Answers
Answer: 525 cycles per second.
Step-by-step explanation:
The equation for inverse variation between x and y is given by :-
[tex]x_1y_1=x_2y_2[/tex] (1)
Given : The length of a violin string varies inversely with the frequency of its vibrations.
A violin string 14 inches long vibrates at a frequency of 450 cycles per second.
Let x = length of a violin
y= frequency of its vibrations
To find: The frequency of a 12 inch violin string.
Put [tex]x_1=14,\ x_2=12\\y_1=450,\ y_2=y[/tex] in equation (1) , we get
[tex](14)(450)=(12)(y)[/tex]
Divide both sides by 12 , we get
[tex]y=\dfrac{(14)(450)}{12}=525[/tex]
Hence, the frequency of a 12 inch violin string = 525 cycles per second.
The frequency of a 12 inch violin string is approximately 388.57 cycles per second.
Explanation:The length of a violin string varies inversely with the frequency of its vibrations. This means that as the length of the string decreases, the frequency of the vibrations increases, and vice versa. To find the frequency of a 12 inch violin string, we can set up the following proportion:
14 inches / 450 cycles per second = 12 inches / x cycles per second
To solve for x, we can cross multiply:
14 inches * x cycles per second = 12 inches * 450 cycles per second
x = (12 inches * 450 cycles per second) / 14 inches
Simplifying:
x = 388.57 cycles per second
Therefore, the frequency of a 12 inch violin string is approximately 388.57 cycles per second.
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Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
Answers
Answer:
t=4 seconds to reach the cannon floor
Step-by-step explanation:
ax^2+bx+c=0
0=-16t^2+255
-255=-16t^2
t^2=15.9375
t= 3.99
round it up...
t=4 seconds to reach the cannon floor
hope this helps!!! :)
please help I already did the hint part but I’m not sure how to get the width or I don’t even know
Answers
Answer:
1 foot
Step-by-step explanation:
Set equal:
4w² + 70w = 74
Move to one side:
4w² + 70w − 74 = 0
Simplify:
2w² + 35w − 37 = 0
Factor. Using the AC method, ac = 2×-37 = -74. Factors of -74 that add up to 35 are 37 and -2. Dividing by a, the factors reduce to 37/2 and -1/1.
(w − 1) (2w + 37) = 0
Set each factor to 0 and solve:
w − 1 = 0
w = 1
2w + 37 = 0
w = -18.5
Since w must be positive, w = 1. The width of the wood border is 1 foot.
Answer:
1 footsie
Step-by-step explanation:
the first thing ur gonna wanna do is set them equal:
4w^2 + 70w = 74
now in order to solve it you are goonna put it all onto one side:
4w^2+ 70w − 74 = 0
Now, you are gonna simplify this:
2w² + 35w − 37 = 0
(w − 1) (2w + 37) = 0
Set each factor to 0 and solve:
w − 1 = 0
w = 1
2w + 37 = 0
w = -18.5
Since w must be positive, w = 1. so the width must be 1 foot
A rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters. A dart is randomly thrown at the board. A triangle is inside of a rectangle. The height of the triangle is the same as the height of the rectangle. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle?
Answers
Answer:
25%.
Step-by-step explanation:
Let E be the event that the dart lands inside the triangle.
We have been given that a rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters.
We know that probability of an event represents the chance that an event will happen.
[tex]\text{Probability}=\frac{\text{Favorable no. of events}}{\text{Total number of possible outcomes}}[/tex]
[tex]\text{Probability that dart lands inside the triangle}=\frac{\text{Area of triangle}}{\text{Area of rectangle}}[/tex]
[tex]\text{Probability that dart lands inside the triangle}=\frac{162}{648}[/tex]
[tex]\text{Probability that dart lands inside the triangle}=0.25[/tex]
Convert into percentage:
[tex]0.25\times 100\%=25\%[/tex]
Therefore, the probability that dart lands inside the triangle is 25%.
Answer:
25%
Step-by-step explanation:
Every week, cross country team members run more than 15 miles. Write an inequality that represents this situation. Let m represent the number of miles ran each week by cross country team members.
Answers
Answer:
m > 15
Step-by-step explanation:
Let m represent the number of miles ran each week by cross country team members
therefore, every week, m > 15.
At Polynomials Pizza, a large cheese pizza costs $6.50. Each additional topping for the pizza costs $1.45. The total for a large pizza that Brandon ordered was $13.75. PART A Define the variable t = PART B Write the equation. PART C How many toppings did Brandon have on his pizza? Enter answer
Answers
Answer:x
=
5
toppings
Step-by-step explanation:Total cost of cheese pizza:
$
10.75
Any additional topping adds:
+
$
1.25
So a cheese pizza with
1
additional topping is:
$
10.75
+
$
1.25
=
$
12.00
A cheese pizza with
2
additional toppings is:
$
10.75
+
$
1.25
+
$
1.25
=
$
10.75
+
2
×
$
1.25
=
$
13.25
A cheese pizza with
3
additional toppings is:
$
10.75
+
$
1.25
+
$
1.25
+
$
1.25
$
10.75
+
3
×
$
1.25
=
$
14.50
If you pay attention to the pattern you can see that, for any number of toppings, say
x
toppings, the price is going to be:
$
10.25
+
x
×
$
1.25
We are told the final cost is
$
17.00
. That is
$
10.25
+
x
×
$
1.25
=
$
17.00
Subtract
$
10.25
from both sides
$
10.25
−
$
10.25
+
x
×
$
1.25
=
$
17.00
−
$
10.25
x
×
$
1.25
=
$
6.25
Divide both sides by
$
1.25
x
×
$
1.25
$
1.25
=
$
6.25
$
1.25
x
=
5
B) 6.50+1.45t=13.75
C) brandon had five toppings
13.75-6.50= 7.25
7.25/1.45= 5
The Olsens rented a car for a $35.99 a day plus an additional fee per mile.The rental company charged them $90.99. If they traveled 550 miles total,what was the additional fee per mile that they were charged?
Answers
Answer:
$0.1 is the additional fee per mile.
Step-by-step explanation:
Given:
Fixed charge = $35.99
Total Bill charged = $90.99
Number of miles traveled = 550 miles
Let additional fee per mile be x.
Now total bill Charge = Fixed charge + additional fee per mile × Number of miles traveled
The expression can be represented as;
[tex]\$35.99 + 550x = \$90.99\\550x = \$90.99-\$35.99\\550x= 55\\x= \frac{55}{550}=\$0.1[/tex]
Hence, the additional fee per mile is $0.1.
The area of a square is decreasing at a rate of 43 square inches per second. At the time when the side length of the square is 7, what is the rate of change of the perimeter of the square? Round your answer to three decimal places (if necessary).
Answers
Answer: -12.286 in/sec
Step-by-step explanation:
Differentiate A=s^2 to get d(A)/d(t) = 2s * d(s)/d(t).
Plug in -43 for d(A)/d(t) since it is the rate of change for area. Plug in 7 for s since it is the value of the side length. -43 = 2(7) * d(s)/d(T).
d(s)/d(T) equals -3.0714286
Differentiate P=4s to get d(P)/d(t) = 4 * d(s)/d(t)
Plug in -3.0714286 to d(P)/d(t) = 4 * d(s)/d(t).
d(P)/d(s)= -12.286 in/sec
Final answer:
To find the rate of change of the perimeter when the square's side length is 7 inches and its area decreases at a rate of 43 square inches/sec, we calculate ds/dt and then use it to find dP/dt. The perimeter is decreasing at a rate of approximately -12.284 inches/sec.
Explanation:
The question involves finding the rate at which the perimeter of a square changes given that the area of the square is decreasing at a rate of 43 square inches per second. To solve this problem, let's denote the side length of the square as s and the area as A, so A = s². The perimeter of the square, P, is given by P = 4s.
Given that the area is decreasing at a rate of -43 square inches per second, we represent this rate of change as dA/dt = -43 inches^2/sec. We also know that at the instant when s = 7 inches, we want to find dP/dt, the rate at which the perimeter is changing.
First, we find the rate of change of the side length, ds/dt, given by differentiating A = s² with respect to time (t), giving 2s(ds/dt) = dA/dt. Substituting the given values, we get 2*7(ds/dt) = -43, solving for ds/dt gives us -43/14 = -3.071 inches/sec.
Finally, since the perimeter's rate of change, dP/dt, is 4(ds/dt), we substitute the value we found for ds/dt, resulting in dP/dt = 4*(-3.071), which equals -12.284 inches/sec. Hence, the perimeter of the square is decreasing at a rate of approximately -12.284 inches per second.
These marbles are placed in a bag and two of them are randomly drawn. What is the probability of drawing two pink marbles if the first one is placed back in the bag before the second draw? Give your answer as a ratio, reduced to simplest terms. [?] Hint: Multiply the probability of the 1st Event by the probability of the 2nd Event to get your answer. Enter Corporation. All Rights Reserved.
Answers
The probability of drawing two pink marbles from a bag with replacement can be calculated using the multiplication rule of independent events as P(pink and pink) = P(pink) x P(pink), where P(pink) is the probability of drawing a pink marble.
Explanation:The subject of this problem is probability in Mathematics, particularly with replacement. The scenario involves drawing two pink marbles from a bag with replacement. This means that after the first marble is drawn, it is put back into the bag before the second one is drawn.
The probability of drawing a pink marble on the first draw is calculated by dividing the number of pink marbles by the total number of marbles. Similarly, the probability of drawing a pink marble on the second draw, with replacement, stays the same because the total number of marbles in the bag is the same as in the first draw.
To calculate the final probability, you use the multiplication rule of independent events (events where the outcome of the first event does not affect the outcome of the second event). According to this rule, the probability of both events happening is the product of the probabilities of each event. Hence, if P(pink) represents the probability of drawing a pink marble, the probability of drawing two pink marbles (with replacement) is P(pink and pink) = P(pink) x P(pink).
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A phone store employee earns a salary of $450 per week plus 10% comission on her weekly sales. A) What function rule models the employee's weekly earnings? B)If the employee earned $570 in a week, what was the amount of her sales for that week?
Answers
Answer:
A) [tex]E(w)=450+0.10w[/tex]
B) $1200
Step-by-step explanation:
Let w represent employee's weekly sales and [tex]E(w)[/tex] be total weekly earnings.
We have been given that a phone store employee earns a salary of $450 per week plus 10% commission on her weekly sales.
A) The total weekly earnings of employee would be weekly salary plus 10% of weekly sales.
10% of weekly sales, w, would be [tex]\frac{10}{100}*w=0.10w[/tex]
[tex]E(w)=450+0.10w[/tex]
Therefore, the function [tex]E(w)=450+0.10w[/tex] models the employee's weekly earnings.
B) To find the weekly sales in the week, when employee earned $570, we will substitute [tex]E(w)=570[/tex] in our formula and solve for w as:
[tex]570=450+0.10w[/tex]
[tex]570-450=450-450+0.10w[/tex]
[tex]120=0.10w[/tex]
[tex]0.10w=120[/tex]
[tex]\frac{0.10w}{0.10}=\frac{120}{0.10}[/tex]
[tex]x=1200[/tex]
Therefore, the amount of employee's weekly sales was $1200.
A food manufacturer uses an extruder (a machine that makes bite size cookies)that yields revenue for the firm at a rate of $200 per hour when in operation. However, the extruder breaks down an average of two times every day it operates. If Y denotes the number of breakdowns per day, the daily revenue generated by the machine is
R=1600−50Y².
Find the expected daily revenue for the extruder.
Answers
Answer:
$1300
Step-by-step explanation:
The extruder yields a revenue of $200per hour
Y denotes the number of breakdown per day.
The daily revenue generated is given as
R = 1600 - 50Y^2
We have an average of 2 breakdown per day
Lamda = 2
Represent lamda as β
E(Y) = β
E(Y(Y-1)) = β^2
E(Y^2) = E[Y(Y-1)] + E(Y)
= β^2 + β
E(R) = E(1600 - 50Y^2)
= 1600 - 50E(Y^2)
= 1600 - 50(β^2 +β)
Recall that β = lamda = 2
= 1600 - 50(2^2 + 2)
= 1600 - 50(4+2)
= 1600 - 50(6)
= 1600 - 300
= 1300
$1300
The expected daily revenue of the extruder is $1300
Samantha had $620 in her savings. She wanted to have at least $200 in her account after her five days in San Diego. Write an inequality to show how much she can spend each day. PLZ HELP
Answers
Answer:
Step-by-step explanation:
Samantha had $620 in her savings. She wanted to have at least $200 in her account after her five days in San Diego. This means that the amount that she can spend in 5 days would be her savings minus the least amount that she wants to have left. It becomes 620 - 200 = $420
If she decides to spend her spendable amount of $420 equally per day, it means that each day, she will spend 420/5 = $84
The inequality representing the amount that she can spend for each day will be
Let y = the amount that she can pend each day. Then, it will be
y lesser than or equal to 84
the number of newly reported cases of HIV in the united states from 2000 to 2010can be modeled by the following formule f(t)=41(0.9842)t where t is the number of years after 2000 calculate the estimated number of new HIV cases reported in 2004
Answers
Answer:
38
Step-by-step explanation:
The year 2004 is 4 years after the year 2000, so the corresponding value of t is 4. Using that value in the formula, we get ...
f(4) = 41(0.9842^4) ≈ 38.47 ≈ 38
The estimated number of new HIV cases reported in 2004 is 38.