The graph of F(x), shown below in pink, has the same shape as the graph of
G(x) = x3, shown in gray. Which of the following is the equation for F(x)?

The Graph Of F(x), Shown Below In Pink, Has The Same Shape As The Graph OfG(x) = X3, Shown In Gray. Which

Answers

Answer 1

Greetings from Brasil...

In this problem we have 2 translations: 4 units horizontal to the left and 3 units vertical to the bottom.

The translations are established as follows:

→ Horizontal

F(X + k) ⇒ k units to the left

F(X - k) ⇒ k units to the right

→ Vertical

F(X) + k ⇒ k units up

F(X) - k ⇒ k units down

In our problem, the function shifted 4 units horizontal to the left and 3 units vertical to the bottom.

F(X) = X³

4 units horizontal to the left: F(X + 4)

3 units vertical to the bottom: F(X + 4) - 3

So,

F(X) = X³

F(X + 4) - 3 = (X + 4)³ - 3
Answer 2

The transformed function is f ( x ) = ( x + 4 )³ - 3 and the graph is plotted

What happens when a function is transformed?

Every modification may be a part of a function's transformation.

Typically, they can be stretched (by multiplying outputs or inputs) or moved horizontally (by converting inputs) or vertically (by altering output).

If the horizontal axis is the input axis and the vertical is for outputs, if the initial function is y = f(x), then:

Vertical shift, often known as phase shift:

Y=f(x+c) with a left shift of c units (same output, but c units earlier)

Y=f(x-c) with a right shift of c units (same output, but c units late)

Vertical movement:

Y = f(x) + d units higher, up

Y = f(x) - d units lower, d

Stretching:

Stretching vertically by a factor of k: y = k f (x)

Stretching horizontally by a factor of k: y = f(x/k)

Given data ,

Let the function be represented as g ( x )

Now , the value of g ( x ) = x³

And , the transformed function has coordinates as A ( -4 , -3 )

So , when function is shifted 4 units to the left , we get

g' ( x ) = ( x + 4 )³

And , when the function is shifted vertically by 3 units down , we get

f ( x ) = ( x + 4 )³ - 3

Hence , the transformed function is f ( x ) = ( x + 4 )³ - 3

To learn more about transformation of functions click :

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The Graph Of F(x), Shown Below In Pink, Has The Same Shape As The Graph OfG(x) = X3, Shown In Gray. Which

Related Questions

Find the midpoint of the segment between the points (8,−10) and (−10,−8) A. (−1,−9) B. (0,−6) C. (0,0) D. (−1,2)

Answers

Answer:

Hey there!

We can use the midpoint formula to find that the midpoint is (-1, -9).

Let me know if this helps :)

The midpoint of the segment between the points (8,−10) and (−10,−8) will be (−1, −9). Then the correct option is A.

What is the midpoint of line segment AB?

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The midpoint of the segment between the points (8,−10) and (−10,−8)

x = (8 – 10) / 2

x = –1

y = (– 10 – 8) / 2

y = –9

Then the correct option is A.

More about the midpoint of line segment AB link is given below.

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HELP
PLSFind all the missing elements:

Answers

Answer:

a = 6.7 , c = 2.0

Step-by-step explanation:

For side a

To find the missing side a we use the sine rule

[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]

From the question

B = 58°

b = 6

A = 109°

Substituting the values into the above formula we have

[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex]

[tex] |a| \sin(58) = 6\sin(109) [/tex]

Divide both sides by sin 58°

[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]

a = 6.728791

a = 6.7 to the nearest tenth

For side c

To find side c we use the sine rule

That's

[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]

C = 13°

[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex]

[tex] |c| \sin(58) = 6 \sin(13) [/tex]

Divide both sides by sin 58°

[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]

c = 1.591544

c = 2.0 to the nearest tenth

Hope this helps you

Answer:

B=58 a=6.7 c=1.6

Step-by-step explanation:

It was right on Acellus

Sorry I cant give a better explanation but this unit is killing me.

ASAP Which dimensions cannot create a triangle? three angles measuring 10 degrees, 25 degrees, and 145 degrees three sides measuring 9 m, 15 m, and 9 m three angles measuring 40 degrees, 70 degrees, and 65 degrees three sides measuring 6 cm, 8 cm, and 10 cm

Answers

Answer:

Three angles measuring 40°, 70° and 65°

Step-by-step explanation:

Because they don't add up to 180°

Answer:

The correct answer is 10° 25° 145°

Step-by-step explanation:

It's because the two smallest angles added up must be greater than the largest angle to create a triangle. Your welcome.

Which of the following is true about congruent figures?
They're the same shape and the same size.
They're the same size, but not the same shape.
They're not the same shape or size.
They're the same shape, but not the same size.​

Answers

Answer:

A

Step-by-step explanation:

congruent means they have the same shape and size. hope this helps :)

The locksmith is 37.9 kilometers west of the bank and 77.9 kilometers west of the garbage dump. The garbage dump is 128.6 kilometers east of the pet store. The pet store is 35.0 kilometers north of the hardware store. Which is closer to the pet store, the hardware store or the locksmith?

Answers

The correct answer is Hardware store

Explanation:

In this case, you need to determine the distance between the pet store and the locksmith to know if the distance is longer than the one from the pet store and the hardware (35 kilometers). Now this distance can be calculated by subtracting the distance from the locksmith to the garbage dump from the total distance between the pet store and the garbage dump. This is because the locksmith is between the pet store and the garbage, which means the distance between the pet store and the locksmith is a portion of the total distance, which is the distance from the pet store and the garbage dump. The process is shown below:

128.6 kilometers (distance from the garbage dump to the pet store) - 77.9 kilometers (distance from the garbage dump to the locksmith) = 50.7 (distance from the locksmith to the pet store

50.7 kilometers is greater than 35 kilometers, which means the  hardware store is closer to the pet store

14. Twice the sum of a number and eight

Answers

Answer: 2(x + 8) is the expression.

Use distributive property to simplify,

2x+16

I didn't know which answer you wanted so....

Answer:

2(x + 8)

Step-by-step explanation:

Hello!

Twice the sum means we multiply by 2

2

the sum of a number and eight is x + 8

2 * x + 8

Since we have to twice the sum we put x + 8 in parenthesis to show to do that first

2(x + 8)

Hope this Helps!

What is the third quartile?

Answers

Answer:

17

Step-by-step explanation:

The third quartile is positioned at the right end of the box, thus

third quartile = 17

A city of Punjab has a 15 percent chance of wet weather on any given day. What is the probability that it will take a week for it three wet weather on
3 separate days? Also find its Standard Deviation

Answers

Answer:

a. 0.06166

b. 0.9447

Step-by-step explanation:

15 percent is the probability it will rain on any given day. P = 0.15

lets define x as the number of days it will rain in one week.

this solution will follow a binomial distribution.

p(X=x) = nCxP^x(1-p)^x

n = 7

x = 3

1-p = 0.85

p =0.15

inserting these values into the formula

p(X=3)=7C3(0.15)^3(0.85)^4

= 7!/4!3! × 0.003375 × 0.5220

= 35 × 0.003375 × 0.5220

= 0.06166

sd = √np(1-p)

= √7 × 0.15(0.85)

= 0.9447

which expression is equivalent to x^-5/3

Answers

Answer:

B

Step-by-step explanation:

Since the power is negative, you automatically know it has to be a or b, because the only way it would be negative is if it was brought from the denominator to the numerator.

The answer is B, because the numerator of the power, is what is inside the square root, while the denominator is what is outside the square root.

List the sides of ΔRST in ascending order (shortest to longest). m∠R=2x+11°, m∠S=3x+23°, and m∠T=x+42°

Answers

Answer:

ST, RS, RT

Step-by-step explanation:

Angles of a triangle add up to 180°.

2x + 11° + 3x + 23° + x + 42° = 180°

6x + 76° = 180°

x = 17⅓

m∠R = 2x+11° = 45⅔°

m∠S = 3x+23° = 75°

m∠T = x+42° = 59⅓°

The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.

ST, RS, RT

Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 2x2 from (−1, 2) to (2, 8)
(a) Find a function f such that F = ∇f. f(x, y) =
(b) Use part (a) to evaluate C ∇f · dr along the given curve C.

Answers

(a)

[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]

[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]

[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]

(b)

[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]

IM GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!

Show ALL work please! <3

Answers

Answer:

B

Step-by-step explanation:

What work is there to show? you basically isolate x. add 2 to both sides. and you get x is greater than or equal to 5. So the answer is B.

x-2[tex]\geq[/tex]3

 +2 +2

x[tex]\geq[/tex]5

For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.

Answers

Answer:

The  standard score  [tex]z = 0.6[/tex]

The  the percentile   [tex]P(z < 0.6 ) = 72.57\%[/tex]

Step-by-step explanation:

From the question we are told that

   A data value is  0.6 standard deviations above the mean.

The above statement can be mathematically represented as

     [tex]x = 0.6 \sigma + \mu[/tex]

Where [tex]\sigma[/tex] is the standard deviation and  [tex]\mu[/tex] is the mean

   Generally the standard score is mathematically represented as

            [tex]z = \frac{x - \mu}{\sigma}[/tex]

   =>      [tex]z = \frac{(0.6 \sigma + \mu) - \mu}{\sigma}[/tex]

   =>     [tex]z = 0.6[/tex]

Now the percentile is obtained from the z-table , the value is  

        [tex]P(z < 0.6 ) = 0.7257[/tex]

=>    [tex]P(z < 0.6 ) = 72.57\%[/tex]

Complete the recursive formula of the geometric sequence -0.3,0.9,-2.7,8.1

Answers

Answer:

[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] with a₁ = - 0.3

Step-by-step explanation:

The recursive formula for a geometric sequence is of the form

[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex]

where r is the common ratio

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{0.9}{-0.3}[/tex] = - 3 , thus

[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] with a₁ = - 0.3

12. 12 ounces is roughly the same as
O A. 340 grams.
B. 356 grams.
O C. 400 grams.
O D. 120 grams.
Mark for review (Will be highlighted on the movin

Answers

Answer:

A. 340 grams

Step-by-step explanation:

My brain

Evaluate the expression: (-2) + (-44) + (18 - 23).

A) -17
B) - 19
C) 3
D) 19​

Answers

Answer:

-51

Step-by-step explanation:

-46+(-5)

= -51

Answer:

the answer is -17

I hope this helps you

It cost Evan $17.70 to send 177 text messages. How many text messages did he send if he spent $19.10

Answers

Answer:

191

Step-by-step explanation:

17.70---- 177

19.10-----191

First just take 177/17.70= 10

all you have to do is multiply by 10

so

19.10= 191

The number of text messages he can send with $19.10 is 191 messages

solve using ratio

let

x = number of text messages he can send with $19.10

cost of messages : number of messages

$17.70 : 177 = $19.10 : x

17.70 / 177 = 19.10 / x

cross product

17.70 × x = 177 × 19.10

17.70x = 3380.7

divide both sides by 17.70

x = 3380.7 / 17.70

x = 191 messages.

Therefore, number of text messages he can send with $19.10 is 191 messages

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A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sampled for an experiment and randomly divided into two groups. One of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. The professor measures the menstrual cycle (in days) of each woman during the second month. The following data are obtained.

High stress 20 23 18 19 22
Relatively stress free 26 31 25 26 30

Required:
1. The obtained value of the appropriate statistic is _______

a. tobt = -4.73
b. tobt = -4.71
c. tobt = -3.05
d. tobt = -.047

2. The df for determining tcrit are ____.

a. 4
b. 9
c. 8
d. 3

3. Using a = 0.052 tail, tcrit = ____.

a. +- 2.162
b. +- 2.506
c. +- 2.462
d. +- 2.306

4. Using a = .052 tail, your conclusion is ____.

a. Accept H0; stress does not affect the menstrual cycle
b. Retain H0; we cannot conclude that stress affects the menstrual cycle
c. Retain H0; Stress affects the menstrual cycle
d. Reject H0; stress affects the menstrual cycle

Answers

Answer:

1. a. tobt = -4.73

2. b. 9

3. a. +- 2.162

4. d. Reject H0; stress affects the menstrual cycle.

Step-by-step explanation:

The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted.

If is an angle bisector of ∠QOR and ∠QOP = 71°, then find the angle measure of ∠QOR. Question 8 options: A) 71° B) 142° C) 35.5° D) 35°

Answers

Answer:  B. 142°.

Step-by-step explanation:

Given: OP is an angle bisector of ∠QOR and ∠QOP = 71°.

We know that an angle bisector divides an angle into two equal parts.

So, if OP is an angle bisector of ∠QOR and ∠QOP = 71°.

Then, the angle measure of ∠QOR = Twice of ∠QOP

⇒ Angle measure of ∠QOR = 2 (71°)

⇒ Angle measure of ∠QOR = 142°

Hence, correct option is B. 142°.

In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ

Answers

Answer:

2.7 in²

Step-by-step explanation:

Given that ∆BAC ~ is similar to ∆EDF, the ratio of the area of ∆BAC to the area of ∆EDF = the square of the ratio of their corresponding sides.

Thus, let x be the area of ∆EDF

[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]

[tex] \frac{6}{x} = \frac{9}{4} [/tex]

Cross multiply

[tex] x*9 = 4*6 [/tex]

[tex] 9x = 24 [/tex]

[tex] \frac{9x}{9} = \frac{24}{9} [/tex]

[tex] x = 2.67 [/tex]

Area of ∆EDF = 2.7 in²

(a^8)3/2 in simplest form ​

Answers

Answer:

[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]

Step-by-step explanation:

([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]

Remove the parenthesis by multiplying

[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]

This expression cannot be simplified further

[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]

Hope this helps :)

HELP :Write the expression as the
sine or cosine of an angle.

Answers

Answer:

sin(4π/21)

Step-by-step explanation:

Step 1: Rearrange expression

sin(π/3)cos(π/7) - cos(π/3)sin(π/7)

Step 2: Use sin(A ± B)

sin(π/3 - π/7)

Step 3: Evaluate

sin(4π/21)

And we have our answer!

Which set of numbers is arranged from least to greatest?

Answers

Answer:

The correct answer is option B

Evaluating function expressions

-1•f(-8)-4•g(4)=

Answers

Answer: -7

Step-by-step explanation:

To find f(-8) look at the f function. Find the y value when x = -8

To find g(4) look at the g function. Find the y value when x = 3

Plug these values into the equation

-1 f(-8) - 4 f(4)

-1 (-5) - 4 (3)

5 - 12 = -7

)Patrick buys some bananas for 35%. He sells all the bananas for $40.60. Calculate profit
percentage. Show your working.

Answers

Answer:

Profit Percentage= Bought price\ Sales price * 100

= 35/ 40 * 100

=87.5%

Step-by-step explanation:

AC is included between __________

Answers

Answer:

AC is included between <A and <C.

Step-by-step explanation:

i think, not sure tho

Find the perimeter of a rectangle that is 7 centimeters long and 7 centimeters wide

Answers

Answer:

28cm

Step-by-step explanation:

2L+2W=

14+14=28

(It’s a square)

If two events are mutually exclusive, can they occur concurrently? Explain. Yes. By definition, mutually exclusive events can occur together. No. By definition, mutually exclusive events cannot occur together. No. Two events will never occur concurrently. Yes. Any two events can occur concurrently.

Answers

Answer:

No. By definition, mutually exclusive events cannot occur together.

Step-by-step explanation:

If two events are mutually exclusive, can they not occur concurrently because by definition, mutually exclusive events cannot occur together or at the same time. This ultimately implies that the events or outcome of the sampling is disjointed.

Mathematically, if two events A and B are mutually exclusive;

[tex]P(AnB) = 0[/tex]

From the above expression, we can deduce that the probability of the two (2) events occurring or having an intersection is zero (0).

[tex]P(A or B) = P(A) + P(B)[/tex]

From the above expression, we can deduce that the probability of either of the two (2) events occuring is the sum of the probability of each occurrence.

For example, when a fair die is tossed once, the outcomes are mutually exclusive.

P(d) = 1, 2, 3, 4, 5 and 6.

Other examples include;

1. Tossing a coin once, you'll either get a head or a tail but not a head and a tail at the same time.

2. In cards, both a king and an ace or a king and a queen are mutually exclusive because you can't have both occurring at the same time.

I buy 6 CDs costing £6.99.
How much change do I get from
£50?

Answers

Answer:

subtract the 6.99 from 50 and you get your answer

Step-by-step explanation:

Answer:

8.06

Step-by-step explanation:

Take the cost of a cd and multiply by 6

6.99 *6

41.94

Subtract this from 50.00

50.00 - 41.94

8.06

You will get 8.06 back

A tennis team played a total of 25 games and won 20 of them. What percent of the games did the team win?

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

80%

▹ Step-by-Step Explanation

20/25 = 0.8 → 80%

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

20/25 x 100 = 80
Therefore the team won 80% of the games.
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