Answer: About 8.5 cubic yards
Step-by-step explanation:
Given : The length of the garden = 16 ft.
The width of the garden = 34 ft.
The depth of the thick layer of topsoil on the garden = 5 inch
=[tex]\dfrac{5}{12}\text{ ft.}[/tex] [Since 1 foot = 12 inches]
The volume of a rectangular prism :-
[tex]V=l*w*h[/tex], where l is length , w is width and h is height.
The number of cubic feet of topsoil required will be
[tex]V=16\times34\times\dfrac{5}{12}=\dfrac{680}{3}\text{cubic feet}[/tex]
Since 1 yard = 3 feet
[tex]1\text{ foot}=\dfrac{1}{3}\text{ yard}[/tex]
[tex]V=\dfrac{680}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}=8.3950617284\approx8.50\text{cubic yards}[/tex]
Sakura speaks 150 words per minute on average in Hungarian, and 190 words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent 555 minutes in total giving both instructions, and spoke 270 more words in Polish than in Hungarian. How long did Sakura speak in Hungarian, and how long did she speak in Polish?
Answer:3 minute
Step-by-step explanation:
Sakura speaks hungarian =150 words per minute
Sakura speaks polish =190 words per minute
and it is given she speaks 270 more words in polish than in hungarian
She speaks for a total of 5 minutes
let she speaks hungarian for t mins
therefore [tex]150\times t+270=190\left ( 5-t\right )[/tex]
t=2 mins
therefore sakura speaks hungarian for 2 mins and polish for 3 mins
Sakura speaks hungarian for 2 mins and polish for 3 mins
Solve: e^2x + 5 = 4
help pls
Answer:
The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex] ⇒ 3rd answer
Step-by-step explanation:
* Lets explain how to solve this problem
- The function f(x) = e^x is called the (natural) exponential function
- The natural logarithm (㏑), or logarithm to base e, is the inverse
function to the natural exponential function
∵ [tex]e^{2x+5}=4[/tex] is an exponential function
∴ We can solve it by using the inverse of e (㏑)
- Remember:
# [tex]ln(e)=1[/tex]
# [tex]ln(e^{m})=m(ln(e))=m[/tex]
- Insert ln in both sides
∴ [tex]ln(e^{2x+5})=ln(4)[/tex]
∵ [tex]ln(e^{2x+5})=(2x+5)ln(e)=2x+5[/tex]
∴ 2x + 5 = ㏑(4)
- Subtract 5 from both sides
∴ 2x = ㏑(4) - 5
- Divide both sides by 2 to find x
∴ [tex]x=\frac{ln(4)-5}{2}[/tex]
* The solution of the equation is [tex]x=\frac{(ln4)-5}{2}[/tex]
Answer:
Answer is C on edge
Step-by-step explanation:
x= (ln 4)- 5/2
Select the correct answer.
Which table shows a proportional relationship between x and y?
Answer: The answer would be choice C because there is a constant rate of change of 3 :)
Step-by-step explanation:
Answer:
C.Step-by-step explanation:
If x and y are proportional then the ratio y/x is constant.
[tex]A.\\\\\dfrac{4}{2}=2,\ \dfrac{6}{3}=2,\ \dfrac{9}{4}\neq2\\\\B.\\\\\dfrac{4}{3},\ \dfrac{16}{9}\neq\dfrac{4}{3}\\\\C.\\\\\dfrac{12}{4}=3,\ \dfrac{15}{5}=3,\ \dfrac{18}{6}=3\ \qquad\bold{CORRECT}\\\\D.\\\\\dfrac{4}{1}=4,\ \dfrac{8}{2}=4,\ \dfrac{15}{3}=5\neq4[/tex]
The two rectangles are similar. Which is the correct proportion for corresponding sides? (12)
Answer:
The answer is
D.
GD/MJ = DE/JK
Answer:
GD/MJ = DE/JK
Step-by-step explanation:
This answer is correct because GD and MJ are similar sides and DE and JK are similar sides as well
What must the total momentum of the system be after the train cars collide?
Answer:
The total momentum of the system remains the same.Momentum before collision is equal to momentum after collision
Step-by-step explanation:
Momentum is defined as the product of mass and velocity of the bodies.According to the law of conservation of momentum, a collision that occurs in an isolated system, the momentum before collision equals that after collision.After collision, the bodies can move in the same direction thus their momentum is combined.
Answer:
The total momentum must remain the same.According to the law of conservation of momentum, in a system where particles collide, the momentum loss on one particles is gained by the other one. This is what create an reaction during the collision, for example, if two bodies collide, one will decrease its speed while the other will increase its speed, that's why the momentum is conserved.
So, basically, after the train cars collide, the momentum must be conserved, remaining the same.
PLEASE HELP ASAP!!
At a frozen yogurt store, customers can purchase gelatin spheres as a yogurt topping. Each sphere contains 100.48/3 cubic millimeters of gelatin. Which statements about the measurements of the sphere are true? Check all that apply. (Use 3.14 for π. Recall that the formula for the volume for a sphere is V= 4/3πr³ .)
The radius of a sphere is 8 millimeters.
The radius of a sphere is 2 millimeters.
The circumference of the great circle of a sphere is 9.42 square millimeters.
The surface area of a sphere is 50.24 square millimeters.
The circumference of the great circle of a sphere is 12.56 square millimeters.
The surface area of a sphere is 25.12 square millimeters.
Answer:
The radius of a sphere is 2 millimeters
The surface area of a sphere is 50.24 square millimeters.
The circumference of the great circle of a sphere is 12.56 millimeters.
Step-by-step explanation:
Verify each statement
case A) The radius of a sphere is 8 millimeters
The statement is false
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=100.48/3\ mm^{3}[/tex]
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]100.48/3=\frac{4}{3}(3.14)r^{3}[/tex]
[tex]r^{3}=(100.48)/(4*3.14)[/tex]
[tex]r=2\ mm[/tex]
case B) The radius of a sphere is 2 millimeters
The statement is True
(see the case A)
case C) The circumference of the great circle of a sphere is 9.42 square millimeters
The statement is false
The units of the circumference is millimeters not square millimeters
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]C=2(3.14)(2)[/tex]
[tex]C=12.56\ mm[/tex]
case D) The surface area of a sphere is 50.24 square millimeters.
The statement is True
Because
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]SA=4(3.14)(2)^{2}[/tex]
[tex]SA=50.24\ mm^{2}[/tex]
case E) The circumference of the great circle of a sphere is 12.56 millimeters.
The statement is true
see the case C
case F) The surface area of a sphere is 25.12 square millimeters
The statement is false
because the surface area of the sphere is [tex]SA=50.24\ mm^{2}[/tex]
see the case D
Answer:
B, D,E
Step-by-step explanation:
In a given week, it is estimated that the probability of at least one student becoming sick is 17/23. Students become sick independently from one week to the next. Find the probability that there are at least 3 weeks of no sick students before the 2nd week of at least one sick student.
Answer:
0.614
Step-by-step explanation:
Let the time be given by = t
and P(S ) = probability that a person is sick
P(s) = probability that a person is not sick
P(s) = [tex](\frac{17}{23})^{23}* (1-\frac{17}{23})\\[/tex]
Then the probability for that there are at least 3 weeks of no sick students before the 2nd week of at least one sick student is given by:
[tex](\frac{17}{23})(\frac{17}{23})(\frac{17}{23})(\frac{17}{23}) + \frac{6}{23} + 3(\frac{17}{23})^{3}\\ = 0.614[/tex]
Find the hypotenuse of the triangle. Round your result to two decimal places. Can anybody help me with this??
Answer:
x = 16.49
Step-by-step explanation:
By Pythagorean Formula
8.34² + 14.22² = x²
x² = 69.556 + 202.208
x² = 271.764.
x = √271.764
x = 16.4852
x = 16.49 (rounded to 2 dec. pl)
The following chart represents the record high temperatures recorded in Phoenix for April - November. Select the answer below that best describes the mean and median of the data set ( round answers to the nearest tenth)
A. The mean is 114.5F and the median is 111.9F.
B. The mean is 121F and the median is 118.5F.
C. The mean is 111.9F and the median is 114.5F.
D. The mean is 118.5F and the median is 121F
Answer:
C. The mean is 111.9F and the median is 114.5F.
Step-by-step explanation:
The mean is 111.9 given that (105 + 113 + 122 + 121 + 116 + 118 + 107 + 93)/8 = 111.875 which can be rounded to 111.9 F.
Organizing the values we have:
[93, 105, 107, 113, 116, 118, 121, 122]
We find that the median is going to be between 113 and 116. Therefore:
(113 + 116) / 2 = 114,5
Therefore, the correct answer is option C.
The answer would be "C"
mean = 111.9F
median = 114.5F
For the mean, we would add up all the numbers in the data. In this case, we would add...
105 + 113 + 122 + 121 + 116 + 118 + 107 + 93 = 895
Next, we would divide the sum by the number of bars we have in the graph. There are 8 bars in the graph with 8 different temperatures so we would divide 895 by 8 and we will get a quotient of 111.875. 111.875 rounded to the nearest tenths place is 111.9F
For the median, we would first place all the numbers in order from least to greatest.
least to greatest- 93,105,107,113,116,118,121,122
next, we need to find the two middle numbers because there is no middle number in an even set of data.
The two middle numbers in the data set are 113 and 116. The halfway point between 113 and 116 is 114.5 so our median would be 114.5
HELP!!!!
Select the correct answer.
What is the volume of this cone in terms of ?
Answer:
168.75π cm^3 is your answer.
Volume of a cone is 1/3 πr^2h.
Here, radius is given 7.5cm and height is given 9cm. So by using the formula we get the above answer.
For this case we have that by definition, the volume of a cone is given by:
[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]
Where:
h: It's the height
r: It is the cone radius
According to the data we have:
[tex]h = 9cm\\r = 7.5cm[/tex]
Substituting:
[tex]V = \frac {\pi * (7.5) ^ 2 * 9} {3}\\V = \frac {\pi * 56.25 * 9} {3}\\V = 168.75\pi[/tex]
Thus, the volume of the cone is [tex]168.75 \pi \ cm ^ 3[/tex]
Answer:
Option C
A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance.
Answer:
the music is both dubstep and trance
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Fred and Gina are playing tennis. The first player to win 2 sets wins their match. Fred has a 3/5 chance to win each set while Gina has a 2/5 chance. What is the probability that the match is decided in only two sets?
From the information below the games is over in 3 sets. For Gina to win the match there are 3 possibilities.
1) Gina wins the first 2 sets with probability
2)Gina wins the first set. Looses the next set. Wins the third set.
3)Gina looses the first set. Wins the next 2 sets.
The required probability that Gina wins is the sum of the above 3 probabilities . That is the probability that Gina wins the match is
Answer:[tex] P=\frac{9+4}{25}=\frac{13}{25}[/tex]
Step-by-step explanation:
Given
Fred has a chance of 3/5 to win
and Gina has a chance of 2/5 to win
Probability(P) that the match is decided in only two sets is when
Either Fred or Gina win both matches continuously
P=P(Fred win both match)+P(Gina win both match)
[tex]P=\frac{3\times 3}{5\times 5}+\frac{2\times 2}{5\times 5}[/tex]
[tex] P=\frac{9+4}{25}=\frac{13}{25}[/tex]
Sue graphed the formula for converting temperatures from Fahrenheit to Celsius. If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius
Answer:
Second Option (10° Celsius)
Step-by-step explanation:
There is a formula to convert the temperature which is in degree Celsius into degree Fahrenheit and vice versa. The formula to convert the temperature in degree Fahrenheit into degree Celsius is:
C° = (F° - 32) * 5/9.
It is given that the temperature is 50° Fahrenheit. Therefore, F° = 50°. Substituting F° = 50° in the formula gives:
C° = (50° - 32) * 5/9.
Further simplification results in:
C° = 18 * 5/9. Therefore, C° = 10°.
So the correct answer is 10° Celsius!!!
Find the distance between the points given
(0, -6) and (9, 6)
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-0]^2+[6-(-6)]^2}\implies d=\sqrt{(9-0)^2+(6+6)^2} \\\\\\ d=\sqrt{9^2+12^2}\implies d=\sqrt{225}\implies d=15[/tex]
⊙M≅⊙N and AB=31.8. Identify PQ, rounded to the nearest tenth.
Answer:
[tex]PQ=9.6\ units[/tex]
Step-by-step explanation:
In this problem
If AB=31.8 units
then
ZY=31.8 units
ZP=PY=31.8/2=15.9 units
In the right triangle MZP
we have
[tex]ZP=15.9\ units[/tex]
[tex]MZ=18\ units[/tex] ----> the radius of the circle
Applying Pythagoras Theorem Find MP
[tex]MP^{2}=MZ^{2}-ZP^{2}[/tex]
substitute
[tex]MP^{2}=18^{2}-15.9^{2}[/tex]
[tex]MP^{2}=71.19[/tex]
[tex]MP=8.4\ units[/tex]
Find the value of PQ
we know that
[tex]MQ=MP+PQ\\ PQ=MQ-MP[/tex]
we have
[tex]MQ=18\ units[/tex]
[tex]MP=8.4\ units[/tex]
substitute
[tex]PQ=18-8.4=9.6\ units[/tex]
The distribution of heights of women for a certain country is approximately Normal, with a mean of 63.6 inches and a standard deviation of 2.8 inches. How tall are the shortest 15% of all women in this country?
Answer: 66.50 inches
Step-by-step explanation:
Given : The distribution of heights of women for a certain country is approximately Normal with ,
[tex]\mu=\text{63.6 inches }\\\\\sigma=\text{2.8 inches}[/tex]
To find the height of the shortest 15% of all women, first we need to find the z-score corresponding to the p-value 0.15 from the standard normal distribution table, we get 1.0364.
Let x be the random variable that represents the height of the randomly selected woman.
Then[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]1.0364=\dfrac{x-63.6}{2.8}\\\\\Rightarrow\ x=2.8\times1.0364+63.6\\\\\Rightarrow\ x=66.50192\approx66.50[/tex]
Hence, the height of the shortest 15% of all women in this country =66.50 inches.
The graph of f(x) = 2x is shown on the grid.
The graph of g(x) = (1/2)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?
Answer:
see below
Step-by-step explanation:
Oddly enough, it is the one that with f(x) reflected over the y-axis. All points on the graph are mirrored across that axis (x is changed to -x, y is left alone).
When a graph gets reflected over y-axis it means that a horizontal reflection reflects a graph horizontally over the y-axis.
The graph of [tex]f(x) = 2^x[/tex] is shown on the grid.
The graph of [tex]g(x) = (\dfrac{1}{2})^x[/tex] is the graph of f(x) reflected over the y-axis.
For x= 0 , [tex]g(x) = (\dfrac{1}{2})^0=1[/tex]
For x= 1 , [tex]g(x) = (\dfrac{1}{2})^1=\dfrac{1}{2}=0.5[/tex]
For x= 2 , [tex]g(x) = (\dfrac{1}{2})^2=\dfrac{1}{4}=0.25[/tex]
i.e. graph of g(x) passes through (-1,2) , (0,1) , (1,0.5) , (2,0.25)
From all the given graph , the correct graph is shown below .
It is showing the exact mirror-image of the given graph across y-axis and it is passing through the(-1,2) , (0,1) , (1,0.5) , (2,0.25) .
whats the absolute vaule of -1 1/3
Answer:
1 1/3
Step-by-step explanation:
Absolute values are how far away it is from 0, so it is always positive. It is always the positive number of itself, so absolute values of negative numbers are the opposite, and the absolute value of positive numbers and just the same numbers.
Answer:
Step-by-step explanation:
/ -1 1/3/ = -(-11/3) = 11/3
The formula to find the period of orbit of a satellite around a planet is T2=(4π2GM)r^3 where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant. If you are given all the values except r, how do you rewrite the formula to solve for r?
Answer:
[tex]r=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}}[/tex]
Step-by-step explanation:
Divide by the coefficient of the r factor, then take the cube root.
[tex]T^2=\dfrac{4\pi^2}{GM}r^3 \qquad\text{given formula}\\\\\dfrac{T^2GM}{4\pi^2}=r^3 \qquad\text{divide by the coefficient of the r factor}\\\\r=\sqrt[3]{\dfrac{T^2GM}{4\pi^2}} \qquad\text{cube root}[/tex]
Answer:
The formula to solve r is [tex]r=\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}[/tex].
Step-by-step explanation:
Consider the provided formula:
[tex]T^{2}=\frac{4\pi^{2}r^{3}}{GM}[/tex]
Where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant.
Multiply both side by GM.
[tex]T^{2}GM=4\pi^{2}r^{3}[/tex]
Further solve the above equation.
[tex]\frac{T^{2}GM}{4\pi^{2}}=r^{3}[/tex]
[tex]\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}=r[/tex]
Hence, the formula to solve r is [tex]r=\sqrt[3]{\frac{GMT^{2}}{4\pi^{2}}}[/tex].
Which expression is equivalent to (10x)–3?
The given expression evaluates to 1/(1000x^3).
Option (C) is correct.
What are exponents?The exponent of a number of says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.
As per the given data:
The given expression is (10x)^(–3)?
We can write the expression as:
= [tex]\frac{1}{(10x)^3}[/tex]
= [tex]\frac{1}{10^3x^3}[/tex]
= [tex]\frac{1}{1000x^3}[/tex]
= 1/(1000x^3)
Hence, the given expression evaluates to 1/(1000x^3).
To learn more about Exponents, click:
brainly.com/question/30066987
#SPJ7
(The given question is incomplete, the complete question is given below)
Which expression is equivalent to (10x)^-3?
a. 10/x^3
b. 1000/x^3
c. 1/(1000x^3)
d. 1/10x^3
Ana, Mateo, and Elena are arguing about who has to give the dog a bath. How
can they make a fair decision?
Select all the correct answers
A. Roll a number cube. If the number rolled is 2 or 4, Ana bathes the
dog. If the number is odd, Elena bathes the dog. If it lands on any
other number, Mateo bathes the dog.
B. Put each person's name on a separate piece of paper in a bag
Randomly draw a name. The person whose name is chosen
bathes the dog
c. Flip a coin twice. If both tosses are heads, Ana bathes the dog. If
one is heads and one is tails, Mateo bathes the dog. If both are
tails, Elena bathes the dog
D. Roll a number cube. If the number rolled is 1 or 2, Ana bathes the
dog, If the number is 3 or 4, Mateo bathes the dog If the number
Answer:
B and D.
Step-by-step explanation:
B This is a fair method. There is an equal chance for all 3 people because picking one of the three is random.
D. I can't see all of it but it looks like it will be ' if the number is 5 or 6 Elena will bathe the dog. This is fair because the probabilities are all 1/3.
Method D is a fair method because the probability of each is equal.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
Ana, Mateo, and Elena are arguing about who has to give the dog a bath.
Then a fair decision will be
A. Roll a number cube. If the number rolled is 2 or 4, Ana bathes the dog. If the number is odd, Elena bathes the dog. If it lands on any other number, Mateo bathes the dog.
This is not a fair method because the probability of each is not equal.
B. Put each person's name on a separate piece of paper in a bag Randomly draw a name. The person whose name is chosen bathes the dog.
This is not a fair method because the number of pieces of paper is not given.
C. Flip a coin twice. If both tosses are heads, Ana bathes the dog. If one is headed and one is tail, Mateo bathes the dog. If both are tails, Elena bathes the dog.
This is not a fair method because the probability of each is not equal.
D. Roll a number cube. If the number rolled is 1 or 2, Ana bathes the dog. If the number is 3 or 4, Mateo bathes the dog. If the number rolled is 5 or 6, Elena bathes the dog.
This is a fair method because the probability of each is equal.
Then the correct option is D.
More about the decision-making link is given below.
https://brainly.com/question/3369578
#SPJ2
Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely. Compute the probability of the event E={2, 4}.
Answer:
0.2
Step-by-step explanation:
we have given sample space = {1,2,3,4,5,6,7,8,9,10}
favorable outcomes E={2,4}
we know that probability is defined as the ratio of favorable otcomes to the sample space
probability [tex]P=\frac{favorable\ outcomes}{ sample\ space }[/tex]
we have favorable outcomes E={2,4} that is favorable outcomes=2
and sample sapce = {1,2,3,4,5,6,7,8,9,10}
so the probability [tex]p=\frac{2}{10}=0.2[/tex]
The probability of event E={2,4} from the sample space S={1,2,3,4,5,6,7,8,9,10} is 1/5 or 20%, calculated by dividing the number of favorable outcomes (2) by the total number of outcomes (10).
Explanation:The student asked to compute the probability of event E={2,4} from a sample space S={1,2,3,4,5,6,7,8,9,10}. Since the outcomes are equally likely, we use the formula for theoretical probability, which is the number of favorable outcomes divided by the total number of possible outcomes in the sample space.
To find P(E), first count the number of outcomes in event E, which includes just 2 and 4. There are two favorable outcomes. The total number of outcomes in the sample space S is 10. Therefore, P(E) equals 2/10 or 1/5 when simplified. This means the probability of event E occurring is 0.20 or 20%.
On December 31, 2016, Osborn Company purchased 30% of Shea Company’s common stock for $220,000. During 2017, Shea Company had a net income of $75,000 and paid cash dividends of $30,000. What would the balance of Osborn’s Equity Investment (Shea) account be at the end of 2017 if they use the equity method?A. $242,500 B. $211,000 C. $220,000 D. $233,500
Answer:
the balance of Osborn’s Equity Investment (Shea) account be at the end of 2017 is $233,500
Step-by-step explanation:
Given data
Acquistion price = $220000
purchased = 30%
net income = $75,000
cash dividends = $30,000
to find out
the balance of Osborn’s Equity Investment (Shea) account be at the end of 2017
solution
we will find out balance of investment i.e. given by formula
balance of investment = Acquistion price + share of income - share of dividend .................1
so here
share of income = 30% of net income
share of income =30% × 75,000 = $22500 ..............2
and
share of dividend = 30% of cash dividends
share of dividend = 30% × 30000 = $9000 ...............3
put equation 2 and 3 in equation 1 and we get
balance of investment = Acquistion price + share of income - share of dividend
balance of investment = 220000 + 22500 - 9000
balance of investment = $233,500
Find the equation for the horizontal line and the vertical line passing through ( − 10 , 7 )
Answer:
Step-by-step explanation:
Horizontal lines have the form " y = " where vertical lines have the form " x = ".
Horizontal lines run parallel to the y = 0 line, the x-axis, so horizontal lines are found in the y coordinate of the point. Therefore, the horizontal line at that point is y = 7.
The vertical lines run parallel to the y-axis, which is the line x = 0. The vertical lines are found then in the x coordinate of the point. Therefore, the vertical line at that point is x = -10
What polynomial has roots of −6, −4, and 1?
x3 − 9x2 − 22x + 24
x3 − x2 − 26x − 24
x3 + x2 − 26x + 24
x3 + 9x2 + 14x − 24
Answer:
x^3+9x^2+14x-24 has roots of -6,-4 and 1
Option D is correct
Step-by-step explanation:
If the polynomial has roots of -6 -4 and 1
then x=-6, x=-4, x=1
Which can be written as:
(x+6)(x+4)(x-1)
Multiplying we get,
(x+6)(x(x-1)+4(x-1))
(x+6)(x^2-x+4x-4)
(x+6)(x^2+3x-4)
x(x^2+3x-4)+6(x^2+3x-4)
x^3+3x^2-4x+6x^2+18x-24
x^3+3x^2+6x^2-4x+18x-24
x^3+9x^2+14x-24
So, x^3+9x^2+14x-24 has roots of -6,-4 and 1
Option D is correct
The figures are similar. Find the area.
The area of △ABC is 15 square cm. The height of △ABC is 5 cm and the height of △DEF is 13 cm. Find the area of △DEF. Round to the nearest square cm if necessary.
Answer:
The area of triangle DEF is [tex]101\ cm^{2}[/tex]
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its heights is proportional and this ratio is called the scale factor and the ratio of its areas is equal to the scale factor squared
step 1
Find the scale factor
Let
z ----> the scale factor
[tex]z=\frac{13}{5}[/tex] ----> ratio of its heights
step 2
Find the area of triangle DEF
Let
z ----> the scale factor
x ----> the area of triangle DEF
y ----> the area of triangle ABC
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{13}{5}[/tex]
[tex]y=15\ cm^{2}[/tex]
substitute and solve for x
[tex](\frac{13}{5})^{2}=\frac{x}{15}[/tex]
[tex]x=(\frac{169}{25})(15)[/tex]
[tex]x=101\ cm^{2}[/tex]
Sanjeet paid $32.85 for a file and 3 identical pens.Leon paid $83.50 for 2 such files and 8 such pens.Find the cost of 1 pen.How do you do it?Help pls.
Answer:
Step-by-step explanation:
Let f and p represent the costs of a file and a pen, respectively. The two purchases are ...
f +3p = 32.85
2f +8p = 83.50
Subtracting twice the first equation from the second gives an equation for the cost of pens:
(2f +8p) -2(f +3p) = (83.50) -2(32.85)
2p = 17.80 . . . . simplify
p = 8.90 . . . . . . divide by 2
The cost of one pen is $8.90.
_____
Comment on "how do you do it?"
You are given two purchases related to the costs of two items. Write equations that describe the purchases. (The total cost is sum of the costs of each of the items, which will be the product of the number of items and the cost of each. You have been shopping, so you know this.)
Once you have a "system of equations", there are many ways they can be solved. You are usually instructed on "elimination" and "substitution" as methods of solution. Above, we used "elimination" to eliminate the "f" variable and give an equation only in "p".
I know that these answers are correct, but I don't understand how to get it using the De Moivere Theorem. Can someone please explain in detail? Thank you so much!
Step-by-step explanation:
10.
First, convert 1+i from Cartesian to polar.
r = √(1² + 1²)
r = √2
θ = atan(1/1), θ in first quadrant
θ = 45°
Therefore:
(1+i)²⁰ = (√2 (cos 45° + i sin 45°))²⁰
(1+i)²⁰ = 1024 (cos 45° + i sin 45°)²⁰
Now applying the De Moivre theorem:
1024 (cos (20×45°) + i sin (20×45°))
1024 (cos (900°) + i sin (900°))
1024 (-1 + 0)
-1024
11.
Repeat the same steps from Question 10. First, convert to polar:
r = √(1² + (-1)²)
r = √2
θ = atan(-1/1), θ in fourth quadrant
θ = 315°
Therefore:
(1−i)¹⁰ = (√2 (cos 315° + i sin 315°))¹⁰
(1−i)¹⁰ = 32 (cos 315° + i sin 315°)¹⁰
Now applying the De Moivre theorem:
32 (cos (10×315°) + i sin (10×315°))
32 (cos (3150°) + i sin (3150°))
32 (0 − i)
-32i
WANT FREE 15 POINTS + BRAINLIEST? ANSWER THIS CORRECTLY AND I GOT YOU
Which statements are true based on the diagram?
Check all that apply.
A. Points A, B, and D are on both planes.
B. Point H is not on plane R.
C. Plane P contains point F.
D. Points C, D, and A are noncollinear.
E. The line containing points F and G is on plane R.
F. The line containing points F and H is on plane R.
Answer:
A. Points A, B, and D are on both planes. B. Point H is not on plane R. D. Points C, D, and A are noncollinear. E. The line containing points F and G is on plane R.Step-by-step explanation:
A. Points A, B, and D are on both planes.
-- true. These points are on the line of intersection of the planes, so are in both planes.
B. Point H is not on plane R.
-- true. Point H is not shown as being on either of the identified planes.
C. Plane P contains point F.
-- false. Point F is shown as being in plane R, not P.
D. Points C, D, and A are noncollinear.
-- true. Point C is not on the line containing points A and D.
E. The line containing points F and G is on plane R.
-- true. F and G are both in plane R, so the line containing them will also be in that plane.
F. The line containing points F and H is on plane R.
-- false. Point H is not in plane R, so will not be on any line in plane R.
The answer to this is a, b, d, e