Which translation shifts the graph of f(x)=3x+3 onto g(x)=3x-3

Answers

Answer 1

Answer:

vertical translation of - 6

Step-by-step explanation:

given f(x) = 3x + 3

then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift of c units up ↑

• If c < 0 then a shift of c units down

shift from + 3 to - 3 is a vertical shift of 6 units down


Related Questions

What is the surface area of the figure? (Easy 20 points pls help)

Answers

408 ft

Can I have brainliest?

:)

In a class of 25 students, 15 of them have a cat , 16 of them have a dog and 3 of them have neither. Find the probability that a student chosen at random has a cat and a dog. Find the probability that a student chosen at random has a cat and a dog

Answers

ANSWER

[tex] \frac{9}{25} [/tex]

EXPLANATION

The given information is represented on the Venn diagram above, where x represents students who have both cat and dog.

The sum of all the regions should give us 25.

[tex](15 - x) + x + (16 - x) + 3 = 25[/tex]

Group similar terms to obtain;

[tex] - x + x - x = 25 - 15 - 16 - 3[/tex]

Simplify

[tex] - x = - 9[/tex]

[tex]x = 9[/tex]

The probability that a student chosen at random has a cat and a dog is

[tex] = \frac{9}{25} [/tex]

The probability that a student chosen at random has a cat and a dog is; P(cat and dog) = 9/25.

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

The information above are drawn in a Venn diagram in the attached image.

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

Therefore, the number of students who own a cat and a dog is 9.

The probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Read more;

https://brainly.com/question/1980403

WILL GIVE BRAINLIEST!! PLEASE HELP ASAP !!!
The ceiling of Katie’s living room is a square that is 12 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 10 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work.

Answers

Answer:

The minimum number of rolls she should buy is 9 rolls

Step-by-step explanation:

* Lets study the information in the problem

- Katie wants to put the crepe paper around the perimeter of the

 ceiling which shaped a square of side length 12 feet

- And also from each corner to the opposite corner

- She needs the length of the 4 sides of the square and the length

 of its 2 diagonals

* Lets find the length of the diagonal of the square

∵ The two adjacent sides of the square formed two legs of a right

   angle triangle and the diagonal joining the endpoints of the legs

  is the hypotenuse of the triangle

- Use Pythagoras theorem to find the length of the diagonal

∴ The length of the diagonal = √(s² + s²) √(2s²) = s√2

∵ The length of the side of the square = 12 feet

∴ The length of the diagonal = 12√2

* Now lets find the length of the crepe papers she needs

∵ She needs the length of the 4 sides of the square and the length

  of its 2 diagonals

∴ The length of crepe papers = 12 + 12 + 12 + 12 + 12√2 + 12√2 = 81.94 feet

∵ Each roll of the crepe papers contain 10 feet

- To find the number of rolls divide the length of the crepe papers by 10

∴ The number of rolls = 81.94 ÷ 10 = 8.194

* She must to buy 9 rolls to have enough crepe papers to decorate

 her ceiling

* V.I.N:

- If she decide to buy 8 rolls, some part of ceiling will not decorate

 because the 8 rolls have 80 feet only and she needs 81.94 feet

Functions f(x) and g(x) are shown below:

f(x) = x2
g(x) = x2 − 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)?


Left by 4 units

Right by 4 units

Left by 8 units

Right by 8 units

Answers

Answer:

B, Right by 4 units

Step-by-step explanation:

we want to factor g(x), and the factorization of that would be (x - 4)² as its a perfect square trinomial

when translating on a graph, we determine the translation. the translation of g(x) is a horizontal shift 4 units to the right, as we are subtracting 4. if it was adding 4, we would be shifting to the left 4 units

ANSWER

Right by 4 units

EXPLANATION

The given functions are

[tex]f(x) = {x}^{2} [/tex]

and

[tex]g(x) = {x}^{2} - 8x + 16[/tex]

To obtain how much f(x) is shifted to obtain g(x), we need to rewrite g(x) in vertex form.

Observe that,

[tex]g(x) = {x}^{2} - 8x + ( - 4) ^{2} [/tex]

is a perfect square trinomial.

The vertex form is

[tex]g(x) = {(x - 4)}^{2} [/tex]

When f(x) is shifted 4 units to the right, we obtain g(x).

The student body at a high school was surveyed about sports participation. The table below shows the data by grade level. What does the joint relative frequency 28/612 represent?

Answers

Im doing this question rn and I believe the answer should be C) the ratio of the student body that are in 12th grade and play two or more sports.

Step-by-step explanation: I chose this bc there are 28 12th graders that play 2 or more sports and the total student body is 612. So 28/612 makes most sense to me. Sorry this is so late but I just checked and it’s right!

Answer:

c

Step-by-step explanation:

Given the polynomial 21x 4 + 3y - 6x 2 + 34 What polynomial must be subtracted from it to obtain 29x 2 - 7 ? What polynomial must be added to it to obtain a first degree polynomial?

Answers

Answer:

1. 21x⁴+3y-35x² + 41

2. -21x⁴-3y+6x² + x

Step-by-step explanation:

When adding and subtracting polynomials , you can use the distributive property to add or subtract the coefficients of like terms.

1. The polynomial is 21x⁴ + 3y -6x² + 34

To obtain polynomial 29x² -7 , we must subtract some polynomial from it.

Let that polynomial be k.

So, 21x⁴ + 3y -6x² + 34 - k =  29x² -7

k = 21x⁴ + 3y - 6x² +34 - 29x² +7 = 21x⁴ + 3y - 35x² + 41

2. To obtain a first degree polynomial, let that polynomial be x +34

So, 21x⁴ + 3y - 6x² + 34 + K = x + 34

K = x + 34 - 21x⁴ -3y + 6x² - 34

  = -21x⁴ - 3y + 6x² + x

The radius of circle L is 16 cm.

What is the length of its diameter?

A. 8 cm

B. 16 cm

C. 32 cm

D. 64 cm

Answers

Answer:

Diameter = 2*Radius

So, 2*16cm = 32cm

The answer is 32. I hope this helps!

In a recent student government election, the ratio of students who voted for the winner to all the students who voted was 0.64. The number of students who voted was 125. How many votes did the winner get?

Answers

Answer:

80

Step-by-step explanation:

The total was 125

0.64 of them voted for the winner.

The number who voted for the winner = ratio * total

Votes for the winner = 0.64 * 125

Votes for the winner = 80

Can one of y'all smart people help

Answers

i think the answer is 8

Please help me thank you​

Answers

Answer:

Q1: -2

Q2: 13

Q3: 15

Q4: -12

Q5: 7

Q6: -4

Q7: 12p + 3

A hypothetical square grows so that the length of it's diagonals are increasing at a rate of 8 m/min. How fast is the area of the square increasing when the diagonals are 4m each?

Answers

Answer:

32[tex]m^{2}/min[/tex]

Step-by-step explanation:

We let the length of the square be l, the diagonal be z and the area be A.

Then by Pythagoras theorem;

[tex]l^{2}+l^{2}=z^{2}\\2l^{2}=z^{2}[/tex]

The are of a square of length l is given as;

[tex]A=l^{2}[/tex]

Combining these two equations yields;

[tex]z^{2}=2A[/tex]

[tex]A=\frac{z^{2} }{2}[/tex]

Next, we have been given;

[tex]\frac{dz}{dt}=8[/tex]

We are required to find;

[tex]\frac{dA}{dt}[/tex] when z = 4

By chain rule;

[tex]\frac{dA}{dt}=\frac{dA}{dz}*\frac{dz}{dt}[/tex]

Differentiating [tex]A=\frac{z^{2} }{2}[/tex] with respect to z yields;

[tex]\frac{dA}{dz}=z[/tex]

Therefore,

[tex]\frac{dA}{dt}=\frac{dA}{dz}*\frac{dz}{dt}[/tex] = 8z

When z is 4m the area of the square will be increasing at a rate of;

8m/min * 4m = 32[tex]m^{2}/min[/tex]

Final answer:

The area of the square is increasing at a rate of 32 m^2/min when the diagonals are each 4 meters long. This is calculated using the relationship between the diagonal and the side length of the square, and applying the concepts of calculus.

Explanation:

The subject of your question is related to Mathematics, specifically in the field of calculus, which deals with rates of change and accumulation. In this scenario, we're looking at how fast the area of a square is increasing given that its diagonals are increasing at a steady rate.

In a square, the diagonal and the side length 's' have a specific relationship, given by the Pythagorean theorem as diagonal = s * sqrt(2). As the diagonal is increasing at 8 m/min, ds/dt = 8/(sqrt(2)) m/min. Now, the area of a square (A) is given by A = s^2. By differentiating this respect to time 't', dA/dt = 2s*(ds/dt). Substituting the given length of the diagonal (4 m), we find s = diagonal/sqrt(2) = 2 sqrt(2) m. Now, substituting s and ds/dt into the equation for dA/dt, we find dA/dt = 2s*(ds/dt) = 2*2sqrt(2)*8/sqrt(2) = 32 m^2/min. So, the area of the square is increasing at the rate of 32 m^2/min when the diagonals are 4 meters each.

Learn more about Rate of Change here:

https://brainly.com/question/29181502

#SPJ3

Which net folds into the rectangular prism?

Answers

Answer:

the correct answer is the letter X

Step-by-step explanation:

because the shaded sides are between the two larger rectangles

I believe the answer your looking for is “X”

One kilogram of cheese costs £6.70How much would 400g cost?

Answers

Answer:

2680

Step-by-step explanation:

i just did 6.70 times 400g

Answer:

400 grams (or 0.4 kg) of this cheese would cost £2.68.

Step-by-step explanation:

Let's write and solve an equation of ratios:

 0.4 kg            x

------------- = -------------

  1.0 kg         £6.70

Cross multiplying to solve for x, we get:

0.4(6.70) = x, or

x = £2.68

400 grams (or 0.4 kg) of this cheese would cost £2.68.

a car drives 52 km at a speed of 13km/h. how long does the journey take

Answers

Answer:

The journey took 4 hours.

Step-by-step explanation:

The relationship between distance, speed, and time is expressed in the formula;

[tex]Speed=\frac{Distance}{Time}[/tex]

The car covered 52 km at a speed of 13km/h.

This means that; distance =52km and speed =13km/h

We substitute the given values into the formula to get;

[tex]13=\frac{52}{Time}[/tex]

[tex]Time=\frac{52}{13}[/tex]

This simplifies to:

[tex]Time=4hrs[/tex]

The journey took 4 hours.

The speed is the ratio of distance to time. Then the time taken by the journey is 4 hours.

What is speed?

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity.

We know that the speed formula

[tex]\rm Speed = \dfrac{Distance}{Time}[/tex]

Then the time is given as

[tex]\rm Time = \dfrac{Distance}{Speed}[/tex]

A car drives 52 km at a speed of 13km/h.

Then the time taken will be given as

[tex]\rm Time = \dfrac{52}{13} \\\\ Time = 4[/tex]

More about the speed link is given below.

https://brainly.com/question/7359669

Alyssa is saving up for a computer and knows she'll need to spend at least $750 to get the one she wants. She saves $80 each month. How long will she need to save before she can go computer shopping? Which of the following inequalities could you use to solve this problem? A. x < 750 B. x 750 C. 80x 750 D. 80x 750

Answers

Answer:

[tex]80x\geq 750[/tex]

She'll need to save at least 10 months to be able to go buy the computer.

Step-by-step explanation:

Let

x ----> the number of months

we know that

The inequality that represent this situation is equal to

[tex]80x\geq 750[/tex]

solve for x

[tex]x\geq 750/80[/tex]

[tex]x\geq 9.4\ months[/tex]

therefore

The minimum number of months is 10

PLS HELP MEEEEEE!!!!!!!!

Answers

Answer:

A

Step-by-step explanation:

the y intercerpt is what is given as (0,5) and the slope is given as -4, so using y=mx+b where m=slope and b=y int, we get y=-4+5

Answer:

A, y = -4x + 5

Step-by-step explanation:

the slope intercept form is y = mx + b with mx being the slope, and y being the y-intercept

we are given the y-intercept (0,5) and the slope -4, so we plug this into slope intercept form

y = -4x + 5

the answer is A

Find the number of real number solutions for the equation. x^2+0x-1=0

Answers

Answer:

+1

-1

Step-by-step explanation:

Given equation :

[tex]x^{2} +0x-1[/tex] = 0

[tex]x^{2} -1 = 0\\x^{2} =1\\x=\sqrt{1}[/tex]

x= ±1

x= 1 and x= -1

±1 lies in solution set of real numbers !

This shouldn't be too difficult i just don't know what i'm doing please help

Write the expression below as a function of cos only.

sin²x/1+cos x

Answers

Answer:

[tex]\frac{1-cos^2x}{1+cosx}[/tex]

Step-by-step explanation:

We are given the expression

[tex]\frac{sin^2x}{1+cosx}[/tex]

We can use the Pythagorean identity of [tex]sin^2x+cos^2x=1[/tex] when solved for [tex]sin^2x=1-cos^2x[/tex]

Now we can substitute in our identity for [tex]sin^2x[/tex]

[tex]\frac{1-cos^2x}{1+cosx}[/tex]

Twelve is what percent of 20? 17 6 60 80

Answers

12 to 20 is 60 percent

12 is 60% of 20

To find the percent you must divide to two numbers 12 and 20. You then get 0.6 which is 60 percent because 6 is in the tenths place which also determines how many zeros there are.

Find all solutions for a triangle with B=36degrees b=19 c=30

Answers

Answer:

m∠A = 76° , m∠C = 68° , a = 31.4

Step-by-step explanation:

* Lets revise how to solve a triangle

- In ΔABC

- a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A

# b is opposite to angle B

# c is opposite to angle C

- m∠B = 36°  

- b = 19  

- c = 30

* To solve the triangle we can use the sin Rule

- In any triangle the ratio between the length of each side  

to the measure of each opposite angle are equal

- a/sinA = b/sinB  = c/sinC

* Lets use it to find a and m∠C

∵ m∠B = 36° , b = 19 and c = 30

∵ 19/sin36° = 30/sinC ⇒ by using cross multiplication

∴ sinC = 30 × sin36° ÷ 19 = 0.928

∴ m∠C = sin^-1(0.928) = 68°

- Find measure of angle A

∵ The sum of the measures of the interior angles in a triangle is 180°

∵ m∠A = 180° - (68° + 36°) = 180° - 104° = 76°

∴ m∠A = 76°

- Now we can Find a

∵ a/sinA = b/sinB

∴ a/sin76° = 19/sin36° ⇒ by using cross multiplication

∴ a = 19 × sin(76°) ÷ sin(36°) = 31.4

* m∠A = 76° , m∠C = 68° , a = 31.4

Answer:

Triangle 1

A =75.86, B=36, C=68.14, b=19, c=30, a=31.34

Triangle 2

A=32.14, B=36, C=111.86, b=19, c=30, a=17.19

Step-by-step explanation:

We have two sides of triangle (b and c) and an angle (B)

To solve the triangle we use the sine theorem:

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

We substitute the values of b, B and c in the equation and solve for C

[tex]\frac{sin(36)}{19}=\frac{sin(C)}{30}\\\\sin(C) = 30*\frac{sin(36)}{19}\\\\sin(C) = 0.9281\\\\C=arcsin(0.9281)\\\\C=68.14\°\ \ or\ \ C=111.86[/tex]

The sum of the internal angles of a triangle is 180, then

[tex]68.14 + 36 + A=180\\\\A=180-68.14 - 36\\\\A=75.86\°[/tex]

or

[tex]111.86 + 36 + A=180\\\\A=180-111.86 - 36\\\\A=32.14\°[/tex]

No we find "a" for both cases.

[tex]\frac{sin(36)}{19}=\frac{sin(75.86\°)}{a}\\\\0.03094a=sin(75.86\°)\\\\a=\frac{sin(75.86\°)}{0.03094}\\\\a=31.34[/tex]

or

[tex]\frac{sin(36)}{19}=\frac{sin(32.14\°)}{a}\\\\0.03094a=sin(32.14\°)\\\\a=\frac{sin(32.14\°)}{0.03094}\\\\a=17.19[/tex]

6. Find the area of the parallelograr

Answers

Answer:

A = 42 cm²

Step-by-step explanation:

The formula of an area of a parallelogram:

[tex]A=ah[/tex]

a - base

h - height

We have

[tex]a=11\dfrac{2}{3}\ cm,\ h=3\dfrac{3}{5}\ cm[/tex]

Convert the mixed numbers to the improper fractions:

[tex]11\dfrac{2}{3}=\dfrac{(11)(3)+2}{3}=\dfrac{35}{3}\\\\3\dfrac{3}{5}=\dfrac{(3)(5)+3}{5}=\dfrac{18}{5}[/tex]

Substitute:

[tex]A=\left(11\dfrac{2}{3}\right)\left(3\dfrac{3}{5}\right)=\left(\dfrac{35\!\!\!\!\!\diagup^7}{3\!\!\!\!\diagup_1}\right)\left(\dfrac{18\!\!\!\!\diagup^6}{5\!\!\!\!\diagup_1}\right)=(7)(6)=42\ cm^2[/tex]

A bag contains 5 white marbles and 5 blue marbles. You randomly select one marble from the bag and put it back. Then, you randomly select another marble from the bag. Which calculation proves that randomly selecting a white marble the first time and a blue marble the second time are two independent events?

Answers

Answer:

Event A = white marble is selected

Event B = blue marble is selected

P(A) = 5/10 = 1/2

p(B) = 5/10 = 1/2

Probability that A and B are independent events is:

P(A∩B) = 1/2 × 1/2

Answer: 1/4

Answer:  C) P(A and B) = 1/2  1/2

if the driver looks 49 inches above the road bed, at what distances from the tower will the drivers eyes be at the same height as the cable?​

Answers

Replace h with 49 ( the given height) and solve for d ( distance).

49 = d^2 - 36d +324

Subtract 49 from both sides:

0 = d^2 - 36d + 275

Factor the polynomial, by finding two numbers when added together equal -36 and when multiplied equal 275.

(d-25)(d-11) = 0

Now solve for d by setting both equations to 0:

d-25 = 0

d = 25

d-11 = 0

d = 11

The two distances would be 11 yards and 25 yards.

Identify the vertex of the parabola

Answers

Answer: The vertex is 1

Step-by-step explanation:

The vertex is the line that passes through the center of the parabola

Please help and thank you

Answers

Answer:

The answer is D

Step-by-step explanation:

Answer: B. .06%

Step-by-step explanation: In the first column, 0.04% owned a bird and fish. .02% owned a bird, but not a fish. So:

0.04% + 0.02% = 0.06%

Help with these problems

Answers

Answer:

1- D   2-A

number one: you multiply all the numbers together...

number two: you add the numbers together and i got A because if you add it all up, it is 42.593 and that is greater than 42.537.

hope dis helps! :p

Can You Please Help Me.
Write an inequality that matches the number line model.​

Answers

13. x≤-3

14. x<1 1/2

:) :) :)

find the area of each triangle. Round your answers to the nearest tenth​

Answers

Answer:

5. 25.4     6. 53.5        7. 107.9

Step-by-step explanation:

since you do not know the height you do the side time the base times the gamma or the angle degrees

Encuentra la densidad de la tierra considerado su volumen como una forma esferica regular toma en cuenta que el radio de la tierra es 6,38×10 ala 6 y su masa es de 5,98 × 10 ala 24 kg

Answers

Answer:

So sorry can you type in english to understand

Step-by-step explanation:

What function equation is represented by the graph?

A f(x)=−2/3x+2

B f(x)=3x−2

C f(x)=2/3x−2

D f(x)=−2x+3

Answers

Answer:

C.2/3x−2

Step-by-step explanation:

The answer is definitely C

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