Answers
Answer:
B
Step-by-step explanation:
This was originally a third degree polynomial:
[tex]2x^3+4x^2-4x+6[/tex], to be exact.
When you divide by -3, you are basically trying to determine if x + 3 is a zero of that third degree polynomial. The quotient is always one degree lesser than the polynomial you started with, and if there is no remainder, then x + 3 is a zero of the polynomial and you could go on to factor the second degree polynoial completely to get all 3 solutions. To perform the synthetic division, you always first bring down the number in the first position, in our case a 2. Then multiply that 2 by -3 to get -6.
-3| 2 4 -4 6
-6
2 -2
So far this is what we have done. Now we multiply the -3 by the -2 and put that up under the -4 and add:
-3| 2 4 -4 6
-6 6
2 -2 2
Now we multiply the -3 by the 2 to get -6 and put that up under the 6 and add:
-3| 2 4 -4 6
-6 6 -6
2 -2 2 0
That last row gives us the depressed polynomial, which as stated earlier here, is one degree less than what you started with:
[tex]2x^2-2x+2[/tex]
Answer: OPTION B
Step-by-step explanation:
You need to follow these steps:
- Carry the number 2 down and multiply it by the the number -3.
- Place the product obtained above the horizontal line, below the number 4 and add them.
- Put the sum below the horizontal line.
- Multiply this sum by the number -3.
- Place the product obtained above the horizontal line, below the number -4 and add them.
- Put the sum below the horizontal line.
- Multiply this sum by the number -3.
- Place the product obtained above the horizontal line, below the number 6 and add them.
Then:
[tex]-3\ |\ 2\ \ \ \ \ 4\ \ -4\ \ \ \ \ \ 6\\\.\ \ \ \ \ |\ \ \ \ -6\ \ \ \ \ 6\ \ \ -6[/tex]
[tex]-----------------[/tex]
[tex].\ \ \ \ \ \ 2\ \ \ -2\ \ \ \ 2\ \ \ \ \ 0[/tex]
Therefore, the quotient in polynomial form is:
[tex]2x^2-2x+2[/tex]
Related Questions
A scientist is studying the decay of a certain substance after being exposed to two different treatments. Under treatment A, the substance continuously decays at a rate of 4% daily. Under treatment B, another sample of the same substance continuously decays at a rate of 6.2% daily.A second scientist comes to record the amount remaining each day and only knows that there was initially less than 300 grams of the substance undergoing treatment A and at most 400 grams of the substance undergoing treatment B.What system of inequalities can be used to determine t, the number of days after which the remaining amount of each sample,y, in grams, is the same?
Answers
Answer:
0 < y < 300·0.96^t0 < y ≤ 400·0.938^tStep-by-step explanation:
When a quantity changes exponentially by a fraction r in some time period t, the quantity is multiplied by 1+r in each period. That is the quantity (y) as a function of t can be described by ...
y = y0·(1+r)^t
where y0 is the initial quantity (at t=0).
Here, the problem statement gives us two quantities and their respective rates of change.
Treatment A
y0 < 300, r = -0.04, so the remaining amount is described by ...
y < 300·0.96^t
__
Treatment B
y0 ≤ 400, r = -0.062, so the remaining amount is described by ...
y ≤ 400·0.938^t
__
When we graph these, we realize these inequalities allow the quantity of each substance to be less than zero. Mathematically, those quantities will approach zero, but not equal zero, so we can put 0 as a lower bound on the value of y in each case:
0 < y < 300·0.96^t0 < y ≤ 400·0.938^t_____
Comment on these inequalities
We suspect your answer choices will not be concerned with the lower bound on y.
Answer:
y (arrow left) 300e-0.04t
y (arrow left underlined) 400e-0.062t
Step-by-step explanation:
roblem: Report Error A partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the order of the numbers in the sum. For example, the number 4 can be written as a sum of one or more positive integers (where we don't care about the order of the numbers in the sum) in exactly five ways: \[4,\; 3 + 1,\; 2 + 2,\; 2 + 1 + 1,\; 1 + 1 + 1 + 1.\] So 4 has five partitions. What is the number of partitions of the number 7?
Answers
Answer:
There are 15 partitions of 7.
Step-by-step explanation:
We are given that a partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the numbers in the sum .
We have to find the partition of 7
We are given an example
Partition of 4
4=4
4=3+1
4=2+2
4=1+2+1
4=1+1+1+1
There are five partition of 4
In similar way we are finding partition of 7
7=7
7=6+1
7=5+2
7=5+1+1
7=3+3+1
7=3+4
7=4+2+1
7=3+2+2
7=4+1+1+1
7=3+1+1+1+1
7=2+2+2+1
7=3+2+1+1
7=2+2+1+1+1
7=2+1+1+1+1+1
7=1+1+1+1+1+1+1
Hence, there are 15 partitions of 7.
A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 70 pounds. The truck is transporting 70 large boxes and 55 small boxes. If the truck is carrying a total of 4450 pounds in boxes, how much does each type of box weigh?
Answers
Answer:
one large box is 40 pounds
one small box is 30 pounds
Step-by-step explanation:
let large be l and small be s ,
l + s = 70 ------- equation1
70l + 55s. = 4450 ------- equation 2
equation 1 multiply by 55,
55l + 55s = 3850 ------ equation 3
equation 3 - equation 2 ,
(70l + 55s) - (55l +55s) = 4450 - 3850
70l + 55s - 55l - 55s = 4450 - 3850
15l = 600
l = 40
sub l = 40 into equation 1
40 + s = 70
s = 70 - 40
s = 30
Probability of multiple Events
A.
B.
C.
D.
Answers
Given that [tex]P(Q)=\dfrac{3}{5},P(R)=\dfrac{1}{3}[/tex]
Also,
[tex]P(Q\wedge R)=P(Q)\cdot P(R)=\dfrac{3}{5}\cdot\dfrac{1}{3}=\dfrac{1}{5}[/tex]
We can conclude that,
[tex]P(Q\vee R)=P(Q)+P(R)=\dfrac{3}{5}+\dfrac{1}{3}=\boxed{\dfrac{14}{15}}[/tex]
The answer is B.
Hope this helps.
r3t40
A person who initially weighs 250 pounds loses 2 pounds per week. Let t represent the number of weeks and let W represent the person's weight, in pounds: W = − 2 t + 250
a. What is the person's weight after twelve weeks?
b. After how many weeks will the person weigh 234 pounds?
Answers
Answer:
a. 226 pounds
b. 8 weeks
Step-by-step explanation:
To solve this problem, simply plug in the numbers for the variables it told you they correspond to. 12 is the number of weeks, and t represents the number of weeks, so we can plug 12 in for t.
[tex]W=-2(12)+250[/tex]
Simplify and you'll have your answer.
[tex]W=-24+250\\W=226[/tex]
For part B, 234 is the amount of pounds, and W represents the weight in pounds, so we can plug 234 in for W.
[tex]234=-2t+250\\-16=-2t\\8=t[/tex]
E-mail fraud (phishing) is becoming an increasing problem for users of the internet. suppose that 70% of all internet users experience e-mail fraud. if 50 internet users were randomly selected, what is the probability that no more than 25 were victims of e-mail fraud?
Answers
The probability that no more than [tex]25[/tex] were victims of e-mail fraud is [tex]\fbox{0.00169}[/tex].
Further explanation:
Given:
The probability of a user experience e-mail fraud [tex]p[/tex] is [tex]0.7[/tex].
The number of individuals [tex]n[/tex] are [tex]50[/tex].
Calculation:
The [tex]\bar{X}[/tex] follow the Binomial distribution can be expressed as,
[tex]\bar{X}\sim \text{Binomial}(n,p)[/tex]
Use the normal approximation for [tex]\bar{X}[/tex] as
[tex]\bar{X}\sim \text{Normal}(np,np(1-p))[/tex]
The mean [tex]\mu[/tex] is [tex]\fbox{np}[/tex]
The standard deviation [tex]\sigma[/tex] is [tex]\fbox{\begin{minispace}\\ \sqrt{np(1-p)}\end{minispace}}[/tex]
The value of [tex]\mu[/tex] can be calculated as,
[tex]\mu=np\\ \mu= 50 \times0.7\\ \mu=35[/tex]
The value of [tex]\sigma[/tex] can be calculated as,
[tex]\sigma=\sqrt{50\times0.7\times(1-0.7)} \\\sigma=\sqrt{50\times0.7\times0.3}\\\sigma=\sqrt{10.5}[/tex]
By Normal approximation \bar{X} also follow Normal distribution as,
[tex]\bar{X}\sim \text{Normal}(\mu,\sigma^{2} )[/tex]
Substitute 35 for [tex]\mu[/tex] and 10.5 for [tex]\sigma^{2}[/tex]
[tex]\bar{X}\sim\text {Normal}(35,10.5)[/tex]
The probability that not more than [tex]25[/tex] were victims of e-mail fraud can be calculated as,
[tex]\text{Probability}=P(\bar{X}<25)}\\\text{Probability}=P(\frac{{\bar{X}-\mu}}{\sigma}<\frac{{(25+0.5)-35}}{\sqrt{10.5} })\\\text{Probability}=P(Z}<\frac{{25.5-35}}{\sqrt{10.5} })\\\text{Probability}=P(Z}<-2.93})\\[/tex]
The Normal distribution is symmetric.
[tex]P(Z>-2.93})=1-P(Z<2.93)\\P(Z>-2.93})=1-0.99831\\P(Z>-2.93})=0.00169[/tex]
Hence, the probability that no more than [tex]25[/tex] were victims of e-mail fraud is [tex]\fbox{0.00169}[/tex].
Learn More:
1. Learn more about angles https://brainly.com/question/1953744
2. Learn more about domain https://brainly.com/question/3852778
Answer Details:
Grade: College Statistics
Subject: Mathematics
Chapter: Probability and Statistics
Keywords:
Probability, Statistics, E-mail fraud, internet, Binomial distribution, Normal distribution, Normal approximation, Central Limit Theorem, Z-table, Mean, Standard deviation, Symmetric.
u and v are position vectors with terminal points at (-1, 5) and (2, 7), respectively. Find the terminal point of -2u + v.
(0, -3)
(4, -3)
(4, 17)
(9, -8)
Answers
Answer:
(4, -3)
Step-by-step explanation:
-2u +v = -2(-1, 5) +(2, 7) = (-2(-1)+2, -2(5)+7)
= (4, -3)
Use your TVM Solver to determine the future balance in a mutual fund account (a type of investment account) if you make weekly payments of $50 into an account that pays 2.0% interest compounded monthly. You open the account with $500 and pay into the account for 15 years.
Answers
Answer:
$46,141.71
Step-by-step explanation:
This looks about right, based on weekly deposits for the duration. However, I cannot vouch for it entirely, as the number of weekly deposits in 15 years will actually be 782.
_____
Computing this by hand doing the initial balance separately from the weekly deposits, I get a total of $46,252.10 using 782 weekly deposits. For that purpose, I tried to figure an equivalent weekly interest rate given monthly compounding and the fact there are 52 5/28 weeks in a year on average.
I suspect the only way to get this to the cent would be to build a spreadsheet with payment dates and interest computation/payment dates. Some months, there would be 5 deposits between interest computations; some years there would be 53 deposits.
The store has y shirts. It's almost alarm for $16 each, and the last dozen were sold on sale for $14 each. If it's all the shirts for $616, find the number of shirts sold.
Answers
The answer is 40 shirts.
Explanation
Equation: y= ((616-(14*12))/16)+12
First, multiply the 12*14 because we know that 12 shirts were $14. You'll get $168. Next, subtract that from 616, the total number of dollars, to get the 12 shirts out of the way. Your answer will be $448. Then, divide by 16 because that's the remaining money that was spent on the $16 shirts. You'll get 28 shirts. However, we can't forget about the dozen $14 shirts, so add 12 to your answer and you get 40 shirts.
A cubic inch of PVC material weight 0.063 pounds per cubic inch. What's the weight of a 36 inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches?
Answers
Answer:
0.196 lbs
Step-by-step explanation:
The area of the cross section is the difference of the areas of circles with the different diameters. The volume of the pipe material is the product of its cross section area and its length:
V = π(D² -d²)L/4 = π(0.82² -0.75²)36/4 ≈ 3.107 . . . in³
Then the weight of the material is this volume multiplied by the density.
W = V·δ = (3.107 in³)(0.063 lb/in³) ≈ 0.196 lb
Finding the weight of the PVC pipe involves calculating the volumes of the outer and inner cylinders then finding the difference, which is multiplied by the weight per cubic inch of PVC.
Explanation:The weight of a 36 inch piece of PVC pipe can be calculated using the formula for the volume of a cylinder and the given weight per cubic inch of PVC material. Firstly, calculate the volume of the outer cylinder, which we know the diameter and length (or height). The formula for the volume of a cylinder is πr²h, where r is the radius and h is the height. We need to halve the diameter to get the radius, which gives us 0.82/2 = 0.41 inches.
Secondly, we calculate the volume of the inner cylinder in the same way, except we use the inner diameter, which is 0.75 inches, halved gives us a radius of 0.375 inches. The volume of material used is then the volume of the outer cylinder minus the volume of the inner cylinder. Lastly, multiply the volume of material by the weight per cubic inch to get the total weight.
Learn more about Weight of PVC Pipe here:https://brainly.com/question/31632701
#SPJ12
What is the product?
(X^4)(3x^2-2)(4x^2+5x)
Answers
Answer:
[tex]12x^8+15x^7-8x^6-10x^5[/tex]
Step-by-step explanation:
Start by using the FOIL method on your second and third terms.
[tex](3x^2-2)(4x^2+5x)\\12x^4+15x^3-8x^2-10x[/tex]
Next, multiply the first term ([tex]x^4[/tex]) against your result.
[tex]x^4(12x^4+15x^3-8x^2-10x)\\12x^8+15x^7-8x^6-10x^5[/tex]
For this case we must find the product of the following expression:[tex](x ^ 4) (3x ^ 2-2) (4x ^ 2 5x) =[/tex]
We must bear in mind that to multiply powers of the same base, the same base is placed and the exponents are added:
Multiplying the terms of the first two parentheses, applying distributive property we have:
[tex](x ^ 4 * 3x ^ 2-x ^ 4 * 2) (4x ^ 2 5x) =\\(3x ^ 6-2x ^ 4) (4x ^ 2 5x) =\\3x ^ 6 * 4x ^ 2 3x ^ 6 * 5x-2x ^ 4 * 4x ^ 2-2x ^ 4 * 5x =\\12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5[/tex]
Answer:
The product is: [tex]12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5[/tex]
Each of 435 bags contains at least one of the following three items: raisins, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?
Answers
Answer:
320 bags
Step-by-step explanation:
IntroductionLet's first assign some literals, to simplify the problem. The goal is to set everything up, in order to only use one symbol.
[tex]p [/tex]: number of bags with only peanuts.
[tex] a [/tex]: number of bags with only almonds.
[tex] r [/tex]: number of bags with only raisins.
[tex] x [/tex]: number of bags with only raisins and peanuts.
Now, the problem establish 3 useful equations. We can find equations equivalences for the next sentences.
"The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts" is equivalent to [tex] r = 10p[/tex].
"The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts" is equivalent to [tex] a= 20x[/tex].
"The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds" is equivalent to [tex] p = \frac{1}{5} a [/tex].
Now, let's set every variable in function of [tex] x[/tex]We already know that [tex] a = 20x[/tex]. And because of that, we also know that
[tex]p = \frac{1}{5}a = \frac{1}{5}(20x) = 4x[/tex]
and to conclude this stage of the problem, we also know that [tex]r = 10p =10(4x) = 40x[/tex]
¡Let's draw it!As there are only 3 items, it is possible to use a Venn diagram. As we can see in the diagram, the entire quantity of bags is going to be
[tex]210 + 4x + x + 40x = 210 + 45x[/tex]
But, we also know that there are 435 bags, then we only have to solve the equation:
[tex]210 + 45x = 435[/tex]
[tex]45x = 435 - 210[/tex]
[tex]45x = 225[/tex]
[tex]x = 225/45 [/tex]
[tex]x = 5 [/tex]
ConcludeSubstituting [tex]x = 5[/tex] we get
[tex]a = 20 x = 20(5) = 100[/tex]
[tex]p = 4 x = 4(5) = 20[/tex]
[tex]r = 40 x = 40(5) = 200[/tex]
Finally [tex] ans = 100 + 20 + 200 = 320 [/tex]
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.
(a) Estimate the value of the population proportion. (Round your answer to 3 decimal places.)
Estimated population proportion
(b)
Develop a 95 percent confidence interval for the population proportion. (Round your answers to 3 decimal places.)
Answers
Answer:
a) The population proportion is 0.625
b) The confidence interval is (0.578 , 0.672)
Step-by-step explanation:
* Lets explain how to solve the problem
- The Fox TV network is considering replacing one of its prime-time
crime investigation shows with a new family-oriented comedy show
- There are 400 viewers
∴ The sample size is 400
- 250 of them indicated they would watch the new show and
suggested it replace the crime investigation show
∴ The number of success is 250
∵ The population proportion P' = number of success/sample size
∴ P' = 250/400 = 0.625
a) The population proportion is 0.625
* Lets solve part b
- Develop a 95 percent confidence interval for the population
proportion
∵ The confidence interval (CI) = [tex]P'(+/-)z*(\sqrt{\frac{P'(1-P')}{n}}[/tex],
where P' is the sample proportion, n is the sample size, and z*
is the value from the standard normal distribution for the desired
confidence level
∵ 95% z is 1.96
∴ z* = 1.96
∵ P' = 0.625
∵ n = 400
∵ [tex]\sqrt{\frac{P'(1-P')}{n}}=\sqrt{\frac{0.625(1-0.625)}{400}}=0.0242[/tex]
∴ CI = 0.625 ± (1.96)(0.0242)
∴ CI = (0.625 - 0.047 , 0.625 + 0.047)
∴ CI = (0.578 , 0.672)
b) The confidence interval is (0.578 , 0.672)
The perimeter of the rectangle is 28 units.
what is the value of w?
Answers
Answer:
5
Step-by-step explanation:
Since this is a rectangle, opposite sides are congruent.
That is, the perimeter in terms of w is:
(2w-1)+(2w-1)+(w)+(w)
or
2(2w-1)+2(w)
We can simplify this.
Distribute:
4w-2+2w
Combine like terms:
6w-2
We are given that the perimeter, 6w-2, is 28.
So we can write an equation for this:
6w-2=28
Add 2 on both sides:
6w =30
Divide both sides by 6:
w =30/6
Simplify:
w =5
w is 5
Check if w=5, then 2w-1=2(5)-1=10-1=9.
Does 5+5+9+9 equal 28? Yep it does 10+18=28.
Answer:
w=5
Step-by-step explanation:
To find the perimeter of the rectangle
P = 2(l+w)
where w is the width and l is the length
Our dimensions are w and 2w-1 and the perimeter is 28
Substituting into the equation
28 = 2(2w-1 +w)
Combining like terms
28 = 2(3w-1)
Divide each side by 2
28/2 = 2(3w-1)/2
14 = 3w-1
Add 1 to each side
14+1 = 3w-1+1
15 = 3w
Divide each side by 3
15/3 =3w/3
5 =w
Which question is statistical?
What is the address of the museum?
What time does the museum open tomorrow?
How many tours will the museum give this week?
How many visitors came to the museum each month last year?
Answers
Answer:
The correct option is D) How many visitors came to the museum each month last year?
Step-by-step explanation:
First, understand that what is the statistical question.
Statistical questions are those question which involves the collection of data. Which can be represented with the help of a chart or tables.
Now consider the provided options:
Options A, B and C are not a statistical question, because these questions do not require or involve the collection of data.
But the option D involves the collection of data because to find the number of visitors came to the museum each month, we need to collect the data.
Therefore the correct option is D.
Answer:
D.) How many visitors came to the museum each month last year?
i am taking the test rn :)
Bonnie is adding a ribbon border to the edge of her kite. Two sides of the kite measure 13.2 inches, while the other two sides measure 20.7 inches. How much ribbon does Bonnie need?
Answers
Answer:
Bonnie needs [tex]67.8\ in[/tex] of ribbon
Step-by-step explanation:
we know that
A Kite is a quadrilateral that has two pairs of equal sides
so
To find out how much ribbon Bonnie needs calculate the perimeter of the kite
[tex]P=2(L1+L2)[/tex]
where
L1 is the length of one side
L2 is the length of the other side
[tex]P=2(13.2+20.7)=67.8\ in[/tex]
An automotive store guaranteed its best tire for 50000 miles. A less expensive tire was guaranteed for only 20000 miles. The better tire had what percent greater performance than the less expensive one?
Answers
Answer:
150%
Step-by-step explanation:
Best Tire : 50,000 miles
Better Tire : 20,000 miles
Difference : 50,000 - 20,000 = 30,000
The difference expressed as a percentage of the less expensive tire
= (30,000 / 20,000) x 100%
=150%
How do you do this question?
Answers
Answer:
positive
Step-by-step explanation:
Find the sign of (2-2x+y) for any point (x,y) in quadrant 2.
In quadrant 2, the x's are negative and the y's are positive.
So choose a negative value for x and a positive value for y and evaluate:
2-2x+y
Let's try (-4,5):
2-2(-4)+5
2+8+5
15 (positive)
Let's try(-1/2 , 10):
2-2(-1/2)+10
2+1+10
3+10
13 (positive)
Let's try in general Let (x,y)=(-a,b) where a and b are positive:
2-2(-a)+b
2+2a+b
Since a and b are positive, then 2+2a+b is positive because you are adding three different positive numbers.
Find the greatest common factor of 28 and 42.
2
4
7
14
Answers
The greatest common factor (or GCF) is, as the name says, the greatest factor a set of numbers have in common. We can find this by listing out all the possible factors (multiples) of each number:
For 28:
1, 2, 4, 7, 14, 28
For 42
1, 2, 3, 6, 7, 21, 42
(note you don't need to list out all the factors, I just did it for visual purposes)
As you can see, 28 and 42 have 3 factors in common, with 7 being the greatest.
Therefore, the answer would be C: the GCF is 7.
Hope this helps! :)
Answer:
it is 14... have a blessed and amazing day
Step-by-step explanation:
I need help . This problem is confusing me.
Answers
Answer:
The answer is 3093.
3093 (if that series you posted actually does stop at 1875; there were no dots after, right?)
Step-by-step explanation:
We have a finite series.
We know the first term is 48.
We know the last term is 1875.
What are the terms in between?
Since the terms of the series form a geometric sequence, all you have to do to get from one term to another is multiply by the common ratio.
The common ratio be found by choosing a term and dividing that term by it's previous term.
So 120/48=5/2 or 2.5.
The first term of the sequence is 48.
The second term of the sequence is 48(2.5)=120.
The third term of the sequence is 48(2.5)(2.5)=300.
The fourth term of the sequence is 48(2.5)(2.5)(2.5)=750.
The fifth term of the sequence is 48(2.5)(2.5)(2.5)(2.5)=1875.
So we are done because 1875 was the last term.
This just becomes a simple addition problem of:
48+120+300+750+1875
168 + 1050 +1875
1218 +1875
3093
Need some help with this problem please!!
Answers
Answer:
sin(2x) = 120/169
Step-by-step explanation:
A suitable calculator can figure this for you. (See below)
__
You can make use of some trig identities:
sin(2x) = 2sin(x)cos(x)sec(x)² = tan(x)² +1cos(x) = 1/sec(x)tan(x) = sin(x)/cos(x)Then your function value can be written as ...
sin(2x) = 2sin(x)cos(x) = 2(sin(x)/cos(x))cos(x)² = 2tan(x)/sec(x)²
= 2tan(x)/(tan(x)² +1)
Filling in the given value for tan(x), this is ...
sin(2x) = 2(12/5)/((12/5)² +1) = (24/5)/(144/25 +1) = (120/25)/((144+25)/25)
sin(2x) = 120/169
Howdy! Do you know if they make any plugins to protect against hackers? I'm kinda paranoid about losing everything I've worked hard on. Any recommendations? Ekdfeakeaged
Answers
Answer:use a VPN and also write down your passwords, never keep them saved on your computer in case of a leak/breach of privacy and information
Step-by-step explanation:
Other than that all you got a do is download a VPN and also write your passwords and then proceed to be careful by not sharing any private/key info to identify who you are
What is the y-intercept of the line 10x - 5y = 407
Answers
Answer:
The y-intercept is (0,-407/5).
Step-by-step explanation:
The y-intercept can be found by setting x to 0 and solving for y.
10x-5y=407
10(0)-5y=407
0-5y=407
-5y=407
Divide both sides by -5:
y=(407/-5)
y=-407/5
The y-intercept is (0,-407/5).
A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?
Answers
Answer:
The tip of the man shadow moves at the rate of [tex]\frac{20}{3} ft.sec[/tex]
Step-by-step explanation:
Let's draw a figure that describes the given situation.
Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.
Here it forms two similar triangles.
Let's find the distance "y" using proportion.
From the figure, we can form a proportion.
[tex]\frac{y - x}{y} = \frac{6}{15}[/tex]
Cross multiplying, we get
15(y -x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
y = [tex]\frac{15x}{9\\} y = \frac{5x}{3}[/tex]
We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).
[tex]\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt}[/tex] ----(1)
We are given [tex]\frac{dx}{dt} = 4 ft/sec[/tex]. Plug in the equation (1), we get
[tex]\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec[/tex]
Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.
To find the speed at which the tip of the man's shadow is moving, we need to solve a proportional relationship between the length of the shadow and the distance of the man from the pole. Using similar triangles and setting up a ratio, we can find the length of the shadow and then find its rate of change with respect to time. The tip of the shadow is not moving when the man is 45 ft from the pole.
Explanation:To solve this problem, we need to use similar triangles. Let's call the length of the shadow x. The height of the pole is 15 ft and the height of the man is 6 ft. So, we can set up the following ratio:
15 / x = 6 / (x + 45)
To find x, we can cross-multiply:
(15)(x + 45) = 6x
Now, we can simplify and solve for x:
15x + 675 = 6x
9x = 675
x = 75 ft
To find the rate of change of the shadow's tip, we can take the derivative of x with respect to time:
dx/dt = 0
So, the tip of the shadow is not moving when the man is 45 ft from the pole.
Learn more about Rate of Change here:https://brainly.com/question/29181502
#SPJ12
Leonard wants to buy a car within a budget of $33,000. The base price of the cars at a dealership ranges from $24,000 to $48,000. The car accessories are one-tenth the base price of a car. The total cost of buying a car depends on the base price of the car. The domain that represents the base price of a car that Leonard can afford from this dealership is [ , ]. Before buying the car, Leonard decides to buy car insurance worth $2,200. After this payment, the domain for the function that represents the base price of a car that Leonard can afford is [ , ].
Answers
Final answer:
The domain for the base price of a car that Leonard can initially afford is [24,000, 30,000]. After buying car insurance worth $2,200, the domain changes to [24,000, 28,000], reflecting the reduced budget available for the car purchase.
Explanation:
Initially, Leonard can afford a car with a base price up to his budget of $33,000. Since car accessories cost one-tenth of the base price, we calculate the maximum base price he can afford as follows: Let x be the base price of the car. The total cost of the car, including accessories, would be x + (1/10)x = (1 + 1/10)x = (11/10)x. So, to stay within budget, (11/10)x ≤ $33,000. Solving for x gives us x ≤ $33,000 / (11/10) = $30,000.
Therefore, the domain representing the base price Leonard can afford is [24,000, 30,000].
After buying car insurance for $2,200, Leonard's budget for the car decreases. The new budget for the car including accessories is $33,000 - $2,200 = $30,800. Solving (11/10)x ≤ $30,800, we get x ≤ $30,800 / (11/10) = $28,000.
Now, the domain for the base price that Leonard can afford after the insurance payment is [24,000, 28,000].
The polynomial below is a perfect square trinomial of the form A2 - 2AB + B2.
Answers
Answer: Option B.
Step-by-step explanation:
Given the polynomial:
[tex]16x^2-36x+9[/tex]
Observe that [tex]16x^2[/tex] and [tex]9[/tex] are perfect squares. Then, you can rewrite the polynomial in this form:
[tex](4x)^2-36x+(3)^2[/tex]
You can identify that:
[tex]A=4\\B=3[/tex]
Then, we can check if [tex]2AB=36[/tex]
[tex]2(4x)(3)=36x\\\\24x\neq 36x\\\\2AB\neq36x[/tex]
Since [tex]2AB\neq36x[/tex], the polynomial [tex]16x^2-36x+9[/tex] IS NOT a perfect square trinomial of the form [tex]A^2 - 2AB + B^2[/tex]
Answer: B
Step-by-step explanation:
Please help me. This is real confusing.
Answers
Answer:
1st problem: b) [tex]A=2500(1.01)^{12t}[/tex]
2nd problem: c) [tex]A=2500e^{.12t}[/tex]
Step-by-step explanation:
1st problem:
The formula/equation you want to use is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
t=number of years
A=amount he will owe in t years
P=principal (initial amount)
r=rate
n=number of times the interest is compounded per year t.
We are given:
P=2500
r=12%=.12
n=12 (since there are 12 months in a year and the interest is being compounded per month)
[tex]A=2500(1+\frac{.12}{12})^{12t}[/tex]
Time to clean up the inside of the ( ).
[tex]A=2500(1+.01)^{12t}[/tex]
[tex]A=2500(1.01)^{12t}[/tex]
----------------------------------------------------
2nd Problem:
Compounded continuously problems use base as e.
[tex]A=Pe^{rt}[/tex]
P is still the principal
r is still the rate
t is still the number of years
A is still the amount.
You are given:
P=2500
r=12%=.12
Let's plug that information in:
[tex]A=2500e^{.12t}[/tex].
1. One inch equals 2.54 centimeters. How many centimeters tall is a 76-inch man?
Answers
Answer:
193.04
Step-by-step explanation:
If one inch equals 2.54 centimeters, a 76-inch tall man is 193.04 centimeters.
1 inch = 2.54 centimeters
76 inches
2.54 x 76 = 193.04
Answer:
193.04 cm
Step-by-step explanation:
So let's line up our corresponding information.
1 inch=2.54 cm
76 in =x cm
This is already setup for you to write a proportion:
[tex]\frac{1}{76}=\frac{2.54}{x}[/tex]
Cross multiply:
[tex]1(x)=76(2.54)[/tex]
Multiply:
[tex]x=193.04[/tex]
Which of the following is the function representing the graph below? graph begins in the third quadrant near the line y equals negative 3 and increases slowly while crossing the ordered pair 0, negative 2. When the graph enters the first quadrant, it begins to increase quickly throughout the graph.
f(x) = 4x
f(x) = 4x − 3
f(x) = 4x + 3
f(x) = 4(x + 3)
Answers
Answer:
f(x) = 4^x -3
Step-by-step explanation:
All of the listed functions are linear functions with a constant slope of 4. None of them goes through the point (0, -2).
__
So, we assume that there is a missing exponentiation operator, and that these are supposed to be exponential functions. If the horizontal asymptote is -3, then there is only one answer choice that makes any sense:
f(x) = 4^x -3
_____
The minimum value of 4^z for any z will be near zero. In order to make it be near -3, 3 must be subtracted from the exponential term.
In the figure below, if arc RS measures 100 degrees, what is the measure of angle Q?
Answers
Answer:
50 degrees
Step-by-step explanation:
The measure of an inscribed angle of a circle is half the degree measure of the intercepted arc.
m<Q = (1/2)m(arc)RS
m<Q = (1/2)(100 degrees)
m<Q = 50 degrees
Answer:
∠Q = 50°
Step-by-step explanation:
An inscribed angle whose vertex lies on a circle and whose sides are two chords of the circle is one half the measure of its intercepted arc.
arc RS is the intercepted arc, hence
∠Q = 0.5 × 100° = 50°