The graph of y=x^3 is transformed as shown in the graph below. Which equation represents the transformed function?
y = x cubed minus 4
y = (x minus 4) cubed
y = (negative x minus 4) cubed
y = (negative x) cubed minus 4
Answers
Answer:
y = (-x)^3 - 4
Step-by-step explanation:
Ok, for the function:
y = x^3
When x = 0, we have:
y = 0^3 = 0
So the original graph passes through the point (0, 0)
If we look at the given graph, we can see that the y-intercept (the value of y when x = 0) is:
y = -4
So, this is the graph of y = x^3 moved down 4 units.
You can also see that the graph goes downward as x increases (and up as x decreases) while for the function:
y = x^3
as x increases, we should see that y also increases.
Then we have a reflection across the x-axis.
Ok, now let's describe a vertical shift.
For a general function f(x), a vertical shift of N units is written as:
g(x) = f(x) + N
if N is positive, the shift is upwards
if N is negative, the shift is downwards.
And for a function f(x), a reflection across the x-axis is written as:
g(x) = - f(x)
Here we first apply the reflection across the x-axis, so we get:
g(x) = -f(x)
now we apply the shift 4 units downwards
g(x) = - f(x) - 4
replacing f(x) by our function, x^3
we get:
g(x) = -x^3 - 4
And because of the odd power, we can write:
-x^3 = (-x)^3
Then the function is:
g(x) = (-x)^3 - 4
The correct option is the last one.
y = (-x)^3 - 4
Related Questions
Create a new project called 02.03 Math Class Methods. Create a class called PyTheorem in the newly-created folder. Use the appropriate Math class methods to calculate the hypotenuse of two right triangles. The value of each side (sides a and b) should be randomly generated using Math.random(). The range should from 5 (inclusive) to 23 (exclusive). Print the value of each side of both triangles as well as the value of the hypotenuse for both triangles.
Answers
Answer:
The program in Java is as follows:
import java.util.*;
public class PyTheorem{
public static void main(String [] args){
Random rNum = new Random();
int a = rNum.nextInt(17) + 5;
int b = rNum.nextInt(17) + 5;
System.out.println("a: "+a);
System.out.println("b: "+b);
double hyp = Math.sqrt(Math.pow(a,2)+Math.pow(b,2));
System.out.print("Hypotenuse: "+hyp);
}}
Step-by-step explanation:
This generates random number for a
int a = rNum.nextInt(17) + 5;
This generates random number for b
int b = rNum.nextInt(17) + 5;
Print a
System.out.println("a: "+a);
Print b
System.out.println("b: "+b);
Calculate the hypotenuse
double hyp = Math.sqrt(Math.pow(a,2)+Math.pow(b,2));
Print the calculated hypotenuse
System.out.print("Hypotenuse: "+hyp);
WILL GIVE MOST BRAINIEST
Which of the following functions best describes this graph?
A. y (x + 4) (x + 5)
Answers
Answer:
D. y =
Step-by-step explanation:
The solutions to this graph (meaning when y equals 0 or when the graph crosses the x-axis) are 4 and 5.
The only answer choice that has the solutions 4 and 5 when you factor it out is D.
Here's the proof:
[tex]x^{2} -9x + 20[/tex]
Factors of 20: - 5 & -4
Sums that add up to -9: -5 + (-4)
[tex]x^{2} -4x-5x+20[/tex]
(factor the first two terms and the last two terms separately)
[tex](x^{2}-4x)(-5x+20)[/tex]
[tex]x(x-4) -5(x-4)[/tex]
(x - 5) (x - 4)
Hope it helps (●'◡'●)
Solve y = -7(-13)
I'm giving 30 points!
Answers
y = -7(-13)
=> y = -7 × (-13)
= y = 91
please help me out with this.
Answers
Answer:
B. -infinity < x < infinity
Step-by-step explanation:
Since it's linear and kind of horizontal, it stretches to infinity on both sides (indicated by arrows on both sides of the line.
Plss helpp
I need to pass
Answers
9514 1404 393
Answer:
P' = (3, -5)
Step-by-step explanation:
Rotation 180° about the origin is the same as reflection across the origin. The transformation is given by ...
(x, y) ⇒ (-x, -y) . . . . . . the signs of the coordinates are both changed
P(-3, 5) ⇒ P'(3, -5)
Type the correct answer in each box. Use numerals instead of words.
Multiply the expressions.
If a = 1, find the values of b, c, and d that make the given expression equivalent to the expression below.
Answers
Answer:
a=1, b=9, c=-2, d=4
Step-by-step explanation:
A computer monitor is listed as being 22 inches. This distance is the diagonal distance across the screen. If the screen measures 12 inches in height, what is the actual width of the screen to the nearest inch?
22 inches
18.43 inches
25.05 inches
32.5 inches
Answers
Answer
The width of the screen is 18.43.
Explanation
Use the Pythagorean Theorem (a^2+b^2=c^2) to find the height.
In a right triangle, a and b are legs. In this instance, a and b would be the height and width of the computer monitor. Let's say the height is a and the width is b (you're trying to find b). The hypotenuse of a right triangle is c. For the computer monitor, c is the diagonal.
So put in everything you know to find b; 12^2+b^2=22^2.
12^2 is 144 and 22^2 is 484. Now you have 144+b^2=484. When you simplify, you get b^2=340. When you simplify again, you find that b is about 18.43.
Jose bought 750 bags of peanuts for 375.00. He intends to sell each bag for 0.15 more the he paid. How much should he charge for each bag
Answers
375.00 divided by 750 = 0.50 cents
0.50 + 0.15 = 0.65 cents
Jose should charge 0.65 cents for each bag.
Answer:
Charge for each bag = 0.65
Step-by-step explanation:
Let the cost of 1 bag be = x
Bags Cost
750 375.00
1 x
[tex]\frac{750}{1} = \frac{375}{x}\\\\x \times 750 = 375 \times 1\\\\x = \frac{375}{750} = 0.50[/tex]
Therefore, the amount Jose paid for each bag = 0.50
He is going to sell each bag for 0.15 more than he paid,
that is , 0.50 + 0.15 = 0.65
When the Bucks play Chiefs at football, the probability that the Chiefs, on present form, will win is 0.56. In a competition, these teams are to play two more pgames. If Swallows beats Bucks in at least4one of these games, they will win the competition, otherwise Bucks will win the trophy. NB: Round off to 2 decimal places. a. The probability that Swallows will win the trophy is [a] probability that Rucks will win the trophy is
Answers
Answer:
The probability that Swallows will win the trophy is 0.8064
The probability that Rucks will win the trophy is 0.1936
Step-by-step explanation:
For each game, there are only two possible outcomes. Either the Swallows win, or they do not. The probability of them winning a game is independent of any other game, which means that the binomial probability distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Probability the Swallows wins is 0.56
This means that [tex]p = 0.56[/tex]
2 games:
This means that [tex]n = 2[/tex]
The probability that Swallows will win the trophy is
Probability they win at least one game, so:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.56)^{0}.(0.44)^{2} = 0.1936[/tex]
Then
[tex]P(X \geq 1) = 1 - 0.1936 = 0.8064[/tex]
0.8064 = 80.64% probability the Swallows win the trophy and 0.1936 probability that the Rucks win the trophy.
Is [0,2) is compact in R?
Answers
Answer:
no it is not compact in R
Suppose 49% of American singers are Grammy award winners. If a random sample of size 502 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%
Answers
Answer:
0.0726 = 7.26% probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose 49% of American singers are Grammy award winners.
This means that [tex]p = 0.49[/tex]
Sample of size 502
This means that [tex]n = 502[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.49[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.49*0.51}{502}} = 0.0223[/tex]
What is the probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%?
Proportion below 49% - 4% = 45% or above 49% + 4% = 53%. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.
Probability the proportion is below 45%
p-value of Z when X = 0.45. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.45 - 0.49}{0.0223}[/tex]
[tex]Z = -1.79[/tex]
[tex]Z = -1.79[/tex] has a p-value of 0.0363.
2*0.0363 = 0.0726
0.0726 = 7.26% probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%
In the diagram, DG ∥ EF.
On a coordinate plane, quadrilateral D E F G is shown. Point D is at (negative 2, 2), point G is at (1, 2), point F is at (3, negative 3), and point E is at (negative 4, negative 3).
What additional information would prove that DEFG is an isosceles trapezoid?
DE ≅ GF
DE ≅ DG
EF ≅ DG
EF ≅ GF
Answers
Answer:
[tex]DE \cong GF[/tex]
Step-by-step explanation:
Given
See attachment for quadrilateral
Required
What proves DEFG as isosceles trapezoid
The non-parallel sides of an isosceles trapezoid are similar and equal.
From the attached quadrilateral, the non-parallel sides are: DE and GF
Hence, for DEFG to be an isosceles trapezoid;
[tex]DE \cong GF[/tex]
Answer:DE ≅ GF
Step-by-step explanation:
cause i said so
Look at the numbers in the bon
5
9
-11
6
-21
9
-6
-10
20
1
Find four numbers whose sum is 5
Answers
A cylinder has a radius of 2.5 inches (in.) and a height of 11 in., as shown.
2.5 in.
11 in.
What is the surface area, in square inches, of the cylinder?
Answers
Answer:
212.06
Step-by-step explanation:
can't really explain since the formula is fricking long but trust me that's uts 212.06 in²
Find the volume of the figure. Express answers in terms of , then round to the nearest
whole number
Please help :)
Answers
Answer:
26244π in³
Step-by-step explanation:
Applying,
Voluem of a sphere
V = 4/3(πr³).......... Equation 1
Where r = radius of the sphere, π = pie
From the diagram,
Given: r = 54/2 = 27 in
Substitute these value in equation 1
V = 4/3(27³)(π)
V = 26244π in³
Hence the volume of the figure expressed in terms of π is 26244π in³
Kayo earns a weekly salary of $372 at All Sports, Next month, she will be promoted from assistant buyer to head buyer. In her new position, she will be paid $831.33
semimonthly. How much more per year will Kayo earn as a head buyer than as assistant buyer?
Answers
Answer:
ok so if she gets paid 372 we just multiply this by 4 since there's 4 weeks in a month then we multiply by 4 so
372*4*12=17856
now we just multiply 831.33 by 2 since she is paid semimonthly and we multiply by 12
831.33*2*12=19951.92
now we just subtract
19951.92-17856=2095.92
so she gets paid 2095.92 more dollars per year
Hope This Helps!!!
What’s this answer help please
Answers
B is the answer for this question hope it helps
y is inversely proportional to x when y=9, x=24
Answers
Answer:
216
Step-by-step explanation:
y=k÷x
k=xy
k=9×24
k=216
Water lilies are often used to decorate ponds, as shown in the photo. But they are also famous for their unusual growth pattern!
Answers
Answer:
what is the question
pls mark me as brainlist
Thank you for the points
I'm not sure if this will be easy for some of you I really need help
Answers
8t-(5-2t) = 5(2t-1)
distribute the negative on the left side, distribute on the right
8t-5+2t = 10t-5
combine like terms
10t-5 = 10t-5
t=0 or (-infinity, infinity)
Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x = 0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
I error l ≤
Answers
Answer:
upper bound for the error, | Error | ≤ 0.0032
Step-by-step explanation:
Given the data in the question;
[tex]e^{0.4[/tex] < e < 3
Using Taylor's Error bound formula
| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]
where m = [tex]| f^{N+1 }(x) |[/tex]
so we have
| Error | ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]
| Error | ≤ ( 0.125 ) 0.0256
| Error | ≤ 0.0032
Therefore, upper bound for the error, | Error | ≤ 0.0032
The list of ingredients for chocolate brownies given at right will make 16 brownies. Use the list to decide how much of each ingredient is needed to make 6 brownies.
Answers
Given: Given that for 16 brownies we need
Butter- [tex]\frac{2}{3}[/tex] cups
unsweetened chocolate-5 ounces
sugar-1-1/2 cup
vanilla-2 teaspoons
eggs-2
flour- 1 cup
To find: The amount of ingredients to make 6 brownies.
Solution: The amount we need to make 6 brownies is,
Butter
[tex](\frac{2}{3}.16)/6\\=0.25125 cups[/tex]
unsweetened chocolate
[tex]\frac{5.6}{16}\\=\frac{30}{16}[/tex]ounces
sugar-0.5625 cup
vanilla-[tex]\frac{12}{16}[/tex]teaspoons
eggs-[tex]\frac{12}{16}[/tex]
flour- [tex]\frac{6}{16}[/tex] cup
Step 1: For each circle (A-G) in the table below, use the given information to determine the missing
information. Include supporting work showing and explaining how you found the missing information.
Circle
Center
Radius
Equation
A
(x - 9)2 + (y - 12)2 = 64
B
(-1,-17)
5
С
(-9,13)
9n
D
x2 + (0 - 1)2 = 36
E
x2 + y2 – 26x = -160
F
*2 + y2 + 22x +12y = -93
G
x2 + y2 – 10x+12y = -52
Answers
Answer:
I don't really understand the question
Step-by-step explanation:
c
Find the value of X in each case:
Answers
Answer:
hi, see mate the third angle is not in the photo, please upload another one
Can you help me figure out this question I’ve been stuck on this for 20 minutes
Answers
Step-by-step explanation:
[tex]\dfrac{2x^2+x-6}{x+x-6} = \dfrac{(2x-3)(x+2)}{2(x-3)}[/tex]
How long will it take the same crew to clear the entire plot of 2 1/2 acres?
Answers
Answer:
It will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
Step-by-step explanation:
Given that a crew clears brush from 1/3 acre of land in 2 days, to determine how long will it take the same crew to clear the entire plot of 2 1/2 acres, the following calculation must be performed:
1/3 = 0.333
1/2 = 0.5
0.333 = 2
2.5 = X
2.5 x 2 / 0.333 = X
15 = X
Therefore, it will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
A bank records deposits as positive numbers and withdrawals as negative numbers.
Mike withdrew \$60$60dollar sign, 60 from his bank account 333 times.
What is the change in Mike's account balance after all 333 withdrawals?
\$$dollar sign
Answers
Answer:
i think that $19980 is the answer
Step-by-step explanation:
i hope it will help u
Question 8
Points 3
Identify the functions whose lines are parallel.
0 3x + 2y = 45 and 8x + 4y = 135
x + y = 25 and 2x + y = 15
O 2x + 2y = 50 and 4x + 2y = 90
O 2x + 2y = 4 and 4x + 4y = 16
Answers
Answer:
2x + 2y = 4 and 4x + 4y = 16
Step-by-step explanation:
For two lines to be parallel, they must have the same slope.
To determine the correct answer to the question, we shall determine the slope of each equation in the given options to see which have the same slope. This can be obtained as follow:
1st option:
3x + 2y = 45 and 8x + 4y = 135
We shall rearrange the above equations to look like y = mx + c
NOTE: m is the slope.
3x + 2y = 45
rearrange
2y = –3x + 45
Divide both side by 2
y = –3x/2 + 45/2
Slope (m) = –3/2
8x + 4y = 135
Rearrange
4y = –8x + 135
Divide both side by 4
y = –8x/4 + 135/4
Slope (m) = –8/4 = –2
The two equation has different slopes. Thus, they are not parallel.
2nd option:
x + y = 25 and 2x + y = 15
x + y = 25
Rearrange
y = –x + 25
Slope (m) = –1
2x + y = 15
Rearrange
y = –2x + 15
Slope (m) = –2
The two equations has different slopes. Thus, they are not parallel.
3rd option:
2x + 2y = 50 and 4x + 2y = 90
2x + 2y = 50
Rearrange
2y = –2x + 50
Divide both side by 2
y = –2x/2 + 50/2
Slope (m) = –2/2 = –1
4x + 2y = 90
Rearrange
2y = –4x + 90
Divide both side by 2
y = –4x/2 + 90/2
Slope (m) = –4/2 = –2
The two equations has different slopes. Thus, they are not parallel.
4th option:
2x + 2y = 4 and 4x + 4y = 16
2x + 2y = 4
Rearrange
2y = –2x + 4
Divide both side by 2
y = –2x/2 + 4/2
Slope (m) = –2/2 = –1
4x + 4y = 16
Rearrange
4y = –4x + 16
Divide both side by 4
y = –4x/4 + 16/4
Slope (m) = –4/4 = –1
The two equations have the same slopes. Thus, they are parallel.
A computer disk that once sold for $2.25 now sells for 25% less. How much does the computer.
Answers
Answer:
$ 1.6875 or $1.69 or $1.70
Joe works as a salesman at the baby retail store. He receives a 5% commission on the first $ 10 000,9% on the next $ 7000, and 13% on any additional sales. Calculate how much Joe must sell to make $ 2082.9 in commission
Answers
Answer:
Joe must sell $ 24,330 to make $ 2,082.9 in commission.
Step-by-step explanation:
Since Joe works as a salesman at the baby retail store, and he receives a 5% commission on the first $10,000, 9% on the next $7,000, and 13% on any additional sales, to calculate how much Joe must sell to make $2082.9 in commission the following calculation must be performed:
10,000 x 0.05 = 500
7,000 x 0.09 = 630
2,082.90 - 500 - 630 = X
952.90 = X
0.13X = 952.90
X = 952.90 / 0.13
X = 7.330
10,000 + 7,000 + 7,330 = X
24,330 = X
Therefore, Joe must sell $ 24,330 to make $ 2,082.9 in commission.
