if the function f(x) has a domain of -2≤x≤8 and a range of -4≤y≤6 and the function g(x) is defined by the formula g(x)= 5f(2x) then what are the domain and range of g. explain your thought process

Answers

Answer 1

Answer:

Domain: -1 ≤ x ≤ 4

Range: -20 ≤ 5f(2x) ≤ 30

Step-by-step explanation:

Inputs of f are between -2 and 8

Input is now 2x, so

-2 ≤ 2x ≤ 8

-1 ≤ x ≤ 4

(Horizontal stretch, factor 1/2)

Range of f is -4 ≤ y ≤ 6

So,

-20 ≤ 5y ≤ 30

(Vertical stretch, factor 5)

Answer 2

The domain of g(x) is [-1, 4].

The  range of g(x) is [-20, 30].

What is a function?

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Domain of f(x) = [-2, 8]

Range of f(x) = [-4, 6]

g(x) = 5 f(2x)

Since -2 ≤ x ≤ 8 and -2 ≤ 2x ≤ 8 = -1 ≤ x ≤ 4.

The domain of g(x) = [-1, 4]

Now,

The range of g(x) = [-20, 30]

Since -4 ≤ y ≤ 6,

5 x (-4) ≤ 5y ≤ 5 x 6

-20 ≤ 5y ≤ 30

Thus,

The domain and range of g(x) are

[-1, 4] and  [-20, 30].

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Related Questions

3) A TREE CASTS A SHADOW THAT IS 43 FEET LONG. MARCO. WHO IS 6 FEET TALL. CASTS A SHADOW 10
FEET LONG. HOW TALL IS THE TREE?

Answers

Answer:

Step-by-step explanation:

25.8

6 out of 10 is 60% so 60% percent of 43 is 25.8

The height of the tree is 25.8 feet which is casting a shadow of 43 feet long.

What are ratio and proportion?

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, A tree casts a shadow that is 43 feet long, and boy cast shadow of 10 feet who is 6 feet tall.

Assuming the height of the tree to be x.

43 : 10 : : x : 6.

43/10 = x/6.

10x = 258.

x = 25.8 feet.

So, the height of the tree is 25.8 feet.

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50 POINTS!!!!!!!!!!!!!
Solve 4x+2 = 12 for x using the change of base formula log base b of y equals log y over log b.

Answers

Answer:

2.5

Step-by-step explanation:

What is the solution to the system of equations below?
y=3x-4 and Y =-2x-9

A(-2, -5)
B(-2,-3)
C(2,-3)
D(2,-13)

Answers

C(2,-3)

That is your answer

Thank you for choosing brainly

My answer might be wrong

1. y = 5x + 1
4x + y = 10

Answers

Answer:

4x + 5x + 1 = 10

9x + 1 = 10

9x = 9

x = 1

y = 5(1)+1= 5+1= 6

(1,6)

Answer:

(1,6)

Step-by-step explanation:

Which expression are solution to the equation 2.4y=13.75

Answers

Final answer:

The solution to the equation 2.4y=13.75 is found by isolating the variable y, which gives us y = 5.729167.

Explanation:

The question asks for the solution to the equation 2.4y =13.75. To solve this equation, we simply need to isolate the variable y. This can be done by dividing both sides of the equation by 2.4.

So, now the equation becomes y =13.75 ÷ 2.4.

After performing the division, you get y = 5.729167. Thus, y=5.729167 is the solution to the equation 2.4y=13.75.

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YOU PROBABLY CAN'T ANSWER THIS :/
Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?

explain your answer step by step

Answers

Rate of change of the function: 60

Step-by-step explanation:

The exponential function in this problem is

[tex]f(x)=2^{x+3}[/tex]

The rate of change of a function between a certain interval [tex]x_1 \leq x \leq x_2[/tex] is given by

[tex]r=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

where

[tex]f(x_1)[/tex] is the value of the function calculated in [tex]x_1[/tex]

[tex]f(x_2)[/tex] is the value of the function calculated in [tex]x_2[/tex]

In this problem, the interval is

[tex]1\leq x \leq 5[/tex]

So we have:

[tex]f(x_1)=f(1)=2^{1+3}=2^4=16[/tex]

and

[tex]f(x_2)=f(5)=2^{5+3}=256[/tex]

Therefore, the rate of change is:

[tex]r=\frac{256-16}{5-1}=60[/tex]

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Three times the sum of a number and 12 is 45 plz help!

Answers

This can be written as 3(n+12)=45, where n is the unknown number

3(n+12)=45 <- Starting Equation

3n+36=45 <- Distributive Property

3n=9 <- Cancel 36 on both sides

n=3 <- Divide both sides by 3

So n=3

Hope this helped!

Answer:

3

Step-by-step explanation:

Can anyone help with my math problems because I need help and you need to be quick. I will mark brainliest.

Answers

What are the math problems?

What is 2 x 3-5 and how do you get that answer

Answers

2 x 3-5

= 6-5

= 1

1 is the answer

Jarred wants to see the difference between the heaviest and lightest objects in his office.

Lamp : 9,451 g

Desk : 62 kg

Chair : 17 kg

Computer : 8,716 g


The difference between the heaviest and lightest object in jarreds office is ______ grams.​

Answers

Answer:

53.284 kg

Step-by-step explanation:

62 kg - 8.716kg = 53.284 kg

Hope it helps you in your learning process.

Answer:

53,284 grams

Step-by-step explanation:

Kilograms resemble a thousand grams. Therefore:

Desk = 62000

Chair = 17000

So then the heaviest object is the desk and the lightest is the computer.

So:

62000grams -8716grams = 53284grams

I really don't get it can you give me the answer then explain why it is that one please ​

Answers

Answer:

[tex]\frac{100}{9}[/tex] is the answer.

Step-by-step explanation:

Well the first thing we would do is simplify all the exponents first inside the parenthesis. So 2^-3 is equal to 1/8. To solve negative exponents you would just divide the number instead of multiply, so 2 divided by 2 divided by 2 is equal to ⅛ or .125

Next would be to do the 2^-9. This would equal 1/512

Now would be to simplify 5^0. Anything to the power of 0 is always one. So now we simplify all the products meaning 7*5*2 and 7*3.  

Now we would simplify both fractions.

The picture are pretty much self explanatory. If you have any questions feel free to ask in the comments - Mark

Also when you have the chance please mark me brainliest.

Answer:

e (i said this so the other dude could be mark brainlist)

Step-by-step explanation:

Which set of integers is not a pythagorean triple and are not the side lengths of a right triangle

Answers

Answer:

the side lengths

Step-by-step explanation:

Answer:

the answer is C) 69.you have to add 69 to -26 which gives you 96. in other word C) is the answer

Step-by-step explanation:

If 5 worksites take 31.5 hours to prepare, how long will it take to prepare 13 worksites

(Answer to be in hours pls)​

Answers

Answer:

81.9 hours.

Step-by-step explanation:

5 work sites take   31.5 hours to prepare, so

1   work sites take   31.5 / 5 hours to prepare, and

13  work sites take .  (31.5  * 13) / 5  hours to prepare

=  409.5 / 5

=  81.9 hours.

31.5%5=6.3
6.3*13= 81.0

Two cars start from towns 805 miles apart and travel toward each other. They meet after 7 hours. Find the speed of each car if one travels 15 mph faster than the other.

Answers

Answer:

One car was going 50 mph and the other was going 65 mph.

Step-by-step explanation:




What is the surface area of this triangular prism rounded to the nearest tenth?
A) 18.5 m2
B) 36.9 m2
C) 43.6 m2
D) 87.2 m2

Answers

Answer:

c

Step-by-step explanation:

i got it right

Answer:

C.

Step-by-step explanation:

I'm too lazy to do it here for an explanation.

I did it in my notebook and I got it right.

A gain of 5 yard



write an integer to represent each situation​

Answers

Answer:+5 or just 5

Step-by-step explanation:

What is the area of the following circle?

the diameter is 10.

Answers

Answer: The area of the circle with a diameter of 10 cm is 78.5 cm2.

Answer: 78.5 units²

Step-by-step explanation: To find the area of a circle, start with the formula for the area of a circle.

Area = πr²

Notice that here, we're given the diameter instead of the radius. It's important to understand that the radius is equal to half of the diameter so the radius of this circle will be equal to half of 10 or 5.

So plugging into the formula, we have (π)(5)².

A common mistake is to plug 10 into the formula but remember that we must plug in the radius and not the diameter.

Multiplying, (5)² is equal to 5 x 5 or 25 so we have 25π.

So the area of the circle is 25π.

Now, remember that π is approximately equal to 22/7 or 3.14 so we can estimate the area of the circle by plugging in 3.14 for π.

So we have (25)(3.14) which is equal to 78.5 units².

Since there were no labels, I just add units to the end.

So the area of the circle is approximately equal to 78.5 units².

Solve the equation 11x + 7 = 73?

Answers

Answer:

6

Step-by-step explanation:

answer: x=6 || 11x=66

At a basketball practice you made 59 out of 80 shots. What percentage did you score

Answers

Answer:

You have scored 73.75 percentage

Step-by-step explanation:

Given:

Total number of shots =  80

Total number shot made =  59

To find:

The percentage of the score = ?

Solution:

The percentage of the score = [tex]\frac{\text{number of shots made}}{\text {total number of shots}} \times 100[/tex]

Now on substituting the values

The percentage of the score =[tex]\frac{59}{80} \times 100[/tex]

The percentage of the score =[tex]0.7375 \times 100[/tex]

The percentage of the score = 73.75 %

How many extraneous solutions does the equation below have?
StartFraction 9 Over n squared + 1 EndFraction = StartFraction n + 3 Over 4 EndFraction
0
1
2
3

Answers

Answer:

We can say that the given equation has no extraneous solutions.

The correct option is A.) 0

Step-by-step explanation:

the given equation is [tex]\frac{9}{n^{2} +1} = \frac{n+3}{4}[/tex]

this equals to [tex]36 = (n^{2} +1)(n+3) = n^{3} + 3n^{2} + n + 3[/tex]

therefore [tex]n^{3} +3n^{2} +n+3 = 36 \hspace{0.3cm}\Rightarrow \hspace{0.3cm}n^{3} +3n^{2} +n-33=0[/tex]

Solving the equation through Newton-Raphson method we get n  [tex]\approx[/tex]  2.3845.

We can say that the given equation has no extraneous solutions.

Answer:

A. 0

Step-by-step explanation:

How many extraneous solutions does the equation below have?

StartFraction 9 Over n squared + 1 EndFraction = StartFraction n + 3 Over 4 EndFraction

0

1

2

3

Find constant proprotionality

Answers

Answer:

Cool

Step-by-step explanation:

Answer:

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Step-by-step explanation:

Cecilia plots the points (–2, 2), (–2, –2), (3, 2) and (3, –2) in the coordinate plane. She connects the points to form a polygon. Explain how she could find the distance around the figure.

Answers

Answer:

The polygon that is formed is a rectangle. Because all sides are horizontal or vertical line segments, she can count to find the distance. She should find the distance of each side and add them together. The total distance around the rectangle is 18 units.

Step-by-step explanation:

The calculation of the distance between the points is simplified, given

that the points are on the same perpendicular or horizontal line.

Correct response:

The distance around the figure is the sum of the lengths of the sides.

Details on how to find the distance around the figure

The given points can be presented as follows;

A(-2, 2), D(-2, -2), B(3, 2), and C(3, -2)

By observation, given that there are two pairs of points that have the

same x-coordinates, and two pair of points have the same y-coordinates,

we have;

The shape of the figure is a rectangle.

The distance between two points is given by the difference between the variables that are not the same as follows;

Distance between point (-2, 2), and (-2, -2), AD = 2 - (-2) = 4

Distance between points (3, 2), and (3, -2), BC = 2 - (-2) = 4

Distance between points (-2, -2), and (3, -2), CD  = 3 - (-2) = 5

Distance between points (-2, 2), and (3, 2), AD = 3 - (-2) = 5

The distance around the figure is; AD + BC + CD + AD = 4 + 4 + 5 + 5 = 18

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6.4 divided by 136.32

Answers

0.0469483568 is your answer.
Final answer:

To divide 6.4 by 136.32, you can use long division. The answer is approximately 0.0469.

Explanation:

To divide 6.4 by 136.32, you can use long division. Set up the problem with 6.4 as the dividend and 136.32 as the divisor. Start dividing by the highest place value of the divisor, which in this case is the hundreds place. The result is 0, since 136.32 does not go into 6.4 hundreds of times. Bring down the next digit, which is 4, and divide 43.2 (the current partial dividend) by 136.32. Repeat this process until you have the desired level of accuracy in your quotient.

The answer to 6.4 divided by 136.32 is approximately 0.0469 (rounded to four decimal places).

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3=3/4(b-8)
Please help me thank you!

Answers

So you need to isolate/get "b" by itself in the equation:

[tex]3=\frac{3}{4}(b-8)[/tex]       Distribute/multiply 3/4 into (b - 8)

[tex]3=(\frac{3}{4}(b))+(\frac{3}{4}(-8))[/tex]

[tex]3=(\frac{3}{4} b)+(-6)[/tex]           Don't know which goes into the parentheses....think the one above makes more sense...maybe....sorry

[tex]3=\frac{3}{4} b-6[/tex]           Add 6 on both sides

[tex]9=\frac{3}{4} b[/tex]        Multiply the reciprocal of 3/4 to get rid of the fraction and get b by itself, which would be 4/3  [basically flipping the fraction or switching the numerator and the denominator]

[tex]\frac{36}{3} =b[/tex]            Simplify the fraction

12 = b

You earned a 75% on a test. You answered 24 questions correctly.How many questions were on the test?

Answers

Answer: 32questions

Step-by-step explanation:let the total number of test = x

Therefore: 24/x * 100 = 75

x = 24*100 / 75

= 32questions

1.25 tons convert to pounds

Answers

Answer:

2,500 pounds

Step-by-step explanation:

one ton = 2000 pounds

1.25*2000= 2,500

Find the difference 18,354 4,672

Answers

Answer:

18,354 - 4,672= 13,682

Step-by-step explanation:

I'm not sure what you meant but above is the answer of what I think you were asking.

The difference between 22,456 and 5,893 is 16,563.

Subtracting 5,893 from 22,456 involves determining the quantity that, when added to 5,893, yields 22,456.

To find the difference, we can follow these steps:

Subtract the numbers:

22,456 - 5,893 = 16,563

Therefore, the difference between 22,456 and 5,893 is 16,563.

Complete question:

Find the difference between 22,456 and 5,893.

convert the rate 175 miles per 5 gallons to feet per quart.​

Answers

Answer: 46200 feet per quart.

Step-by-step explanation:

We know that 1 gallon = 4 quarts

1 mile = 5280 feet

Therefore , 5 gallons = 5 x 4 quarts

= 20 quarts                 (i)

175 miles = 175 x  5280 feet

i.e. 175 miles  = 924000 feet                    (ii)

Now , 175 miles per 5 gallons = [tex]\dfrac{\text{ 175 miles }}{\text{5 gallons}}[/tex]

[tex]=\dfrac{ 924000 \text{ feet}}{\text{20 quarts}}[/tex]    [From (i)and (ii)]

[tex]\dfrac{46200\text{ feet }}{1\text{ quart}}\\\\=46200\text{ feet per quart}[/tex]

Hence, 175 miles per 5 gallons = 46200 feet per quart.

Answer:

175 miles per 5 gallons = 46200 feet per quart.

Suppose a basketball player typically makes one-third of his foul shots. Which simulation could be used to generate frequencies and determine the probability that the player will make his next two foul shots?

Answers

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Roll two fair dice, when a 1 or 2 is rolled for both dice simultaneously it is recorded as both foul shots being made. This process is repeated for 50 trials.

The probability of a 1 or 2 from a roll of a die is

2

6

or

1

3

which equals the probability of the player making a single foul shot. Therefore, the compound event of two foul shots being made is equal to a 1 or 2 being rolled on both dice simultaneously, (

1

3

)(

1

3

) =

1

9

.

Simplify the expression. 7y+3x+3-2y+6

What is the coefficient of y

What is the constant

Answers

The coefficient is 5
And the constant is 9

Answer:

Step-by-step explanation: combine like terms 7y minus 2y is 5y then combine 3 plus 6 which is 9 then u get 3x+5y+9

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