Given f(x)=2^x and g(x)=f(x-3)+4, write the new function rule (equation) for function g and describe (using words*) the two transformations that occur between function f and function g.

Answers

Answer 1

Answer:

The first thing we do is find out what f(x-3) is[tex]f(x)=2^x\\f(x-3)=2^{x-3}[/tex] this is can be simplified using the rules of exponents[tex]f(x-3)=2^{x-3}\\f(x-3)=2^x\div2^3\\f(x-3)=\frac{2^{x}}{8}[/tex] Then we put that into g(x) [tex]g(x)=f(x-3)+4\\g(x)=\frac{2^{x}}{8}+4[/tex] The first transformation is at f(x), where it is divided by 8, and then inserted into g(x) which increases the new transformed f(x) by 4

Related Questions

15. Which of the following systems has no solution?
A. 3x – 2y = - 16x – 4y = 6
B. -x + y = 12x – 3y = 4
C. 4x + y = 7x + 4y = 4
D. 3x – 4y = 2 - 2x + 4y = 9

Answers

Answer:

A. has no solution

Step-by-step explanation:

The scale drawing of a building has a width of 3 inches and a height of 5 inches. If the width of the actual building is 36 feet, what is the height?

Answers

Answer:

The actual height is 720 feet.

Step-by-step explanation:

36 × 12 = 432

432 ÷ 3 = 144

144 × 5 = 720

Select the correct answer.
What is the equation of a line that passes through (7, 8) and has a slope of -3?
OA y=-3x+29
OB y=3x + 13
Ocy=((3)x - 299
D. 'y=(1/(3)x- 13

Answers

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3 , thus

y = - 3x + c ← is the partial equation

To find c substitute (7, 8) into the partial equation

8 = - 21 + c ⇒ c = 8 + 21 = 29

y = - 3x + 29 → A

Item 3 Amelie's bird cage is shaped like a rectangular prism. The cage has a height of 26 inches and a volume of 7,280 cubic inches. Amelie puts a piece of newspaper on the bottom of the cage. The newspaper fits the bottom of the cage perfectly. What is the area of the newspaper on the bottom of the cage?

Answers

Answer:

Step-by-step explanation:

The Volume of a rectangular prism is expressed as;

V = Base area * height of prism

Given

Volume of prism V = 7,280 cubic inches.

height of prism = 26in

Required

Base Area

Substitute the given parameter into the formula;

7280 = 26B

B = 7280/26

B = 280in²

Hence the area of the newspaper on the bottom of the cage is 280in²

The Morris family bought 3 crates of eggs last week. Each crate had 18 eggs. Since then, they have eaten 25 of the eggs. How many eggs are left?

Answers

Answer:

29

Step-by-step explanation:

3 x 8 = 54 - 25 = 29

which equation represents the same line as the table

Answers

Answer:

I think the second one I may be wrong tho

The answer should be A.)
*please mark brainliest If correct :-)

Which of the binomials below is a factor of this trinomial?
x^2+ 8x + 16
O A. X+ 8
O B. X+4.
O C. X-4
O D. X-8

Answers

A

Do you need a explanation or just a answer?
x+4

because

4•4 is 16
4+4=2

its a perfect square trinomial

Find the slope of the line through the points (10, 4) and (4, 15)
FIRST TO ANSWEEER GETS BRANLIEST PLZ HELP

Answers

I think it’s 24 I’m not sure

Answer:

I think it's 11/6 I think so

h(x)=4log2(x−6)+1

All real numbers greater than____

Answers

[tex]\huge\underline\mathfrak\blue{Answer:-}[/tex]

The demoin is all real numbers greater than 6

The domain of the function is "All real numbers greater than 6".

What are logarithmic functions?

Any exponential function may be represented in logarithmic form because logarithmic functions are the inverses of exponential functions.

The given equation is h(x) = 4log2(x-6) + 1.

The domain is the set of values that can be inserted into a function.

Note that the logarithmic of a negative number is not defined, therefore, the expression inside the log, x-6, must be greater than 0.

x - 6 > 0

x > 6

Hence, the domain of the function is "All real numbers greater than 6".

Learn more about the logarithmic functions:

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The complete question is:

What is the domain of the function h(x)=4log_5(x−6)+1 ? Enter your answer in the box.

All real numbers greater than______

Find the area of each figure.

Answers

Answer:

1).6cm squared

2). 36 cm squared

3).787.5

(im not sure 3 is correct)

Step-by-step explanation:

Angela baked cookies. She gave 1/3 of them to her sister, and she put 5/8 of the remaining cookies in the freezer. If she had 1 dozen cookies left, how many cookies did she bake?

Answers

Answer:

We find the fraction of a number by doing two steps: first, multiply the whole number by the numerator, and then divide the product we get by the denominator.

multiplying fraction by a number

Let's solve real-world problems about fractions of a number.

Word Problem Examples

cookies

Jane baked 24 chocolate chip cookies. She gave 1/3 of the cookies to her neighbor. How many cookies did she give to her neighbor?

What is the problem asking us to do?

That's right!

We need to figure out what 1/3 of 24 is.

1/3 of 24 is the same as this:

24 × 1/3 = ?

First, multiply 24 by the numerator:

24 × 1 = 24

Then, divide the product we got by the denominator:

24 ÷ 3 = 8

✅ Now we know that she gave 8 cookies to her neighbor.

Here are more questions about this problem:

Of the cookies that were left, Jane gave 3/4 to her parents, and she ate the rest. How many cookies did she give to her parents? How many cookies did she eat?

The problem tells us to figure out two things:

- the number of cookies that Jane gave to her parents,

- the number of cookies that Jane ate.

But first, we have to find out how many cookies were left, after Jane gave some away to her neighbor.

She started with 24 cookies and gave 8 cookies away.

Let's subtract:

24 - 8 = 16 cookies

So, Jane had 16 cookies left.

How many cookies did Jane's parents get if she gave them 3/4 of 16?

3/4 of 16 is the same as this:

16 × 3/4 = ?

First, multiply 16 by the numerator:

16 × 3 = 48

Then, divide the product we got by the denominator:

48 ÷ 4 = 12

✅ Jane gave 12 cookies to her parents.

Now, let's find out how many cookies Jane ate.

We know that Jane ate all the cookies that were left.

She had 16 cookies. Then, she gave 12 to her parents.

How many are left?

We need to subtract to figure this out:

16 - 12 = 4

✅ Jane ate 4 cookie

She baked 48 cookies in total as obtained by forming a numerical expression of the statement.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given that, Angela baked x cookies.

She gave 1/3 of them to her sister, and she put 5/8 of 5/8th of the remaining cookies in the freezer.

x - (1/3)x - (2/3)×(5/8)x = 12.

x - (1/3)x - (5/12)x = 12.

(2/3)x - (5/12)x = 12.

(8x - 5x)/12 = 12.

3x = 144.

x = 48

learn more about numerical expressions here :

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Stella is trying to make extra money on her summer vacation from school. She works
two different jobs, earning $10 per hour babysitting and $13 per hour clearing tables.
How much money would Stella earn in a week in which she worked 7 hours
babysitting and 9 hours clearing tables? How much money would Stella
week in which she worked b hours babysitting and c hours clearing tables?
earn in
a
7 hours babysitting and 9 hours clearing tables:
b hours babysitting and c hours clearing tables:
Submit Answer
attempt i outot

Answers

Answer:

$187

10b + 13c

Step-by-step explanation:

Payment for babysitting = $10 per hour

Payment for clearing tables = $13 per hour

How much money would Stella earn in a week in which she worked 7 hours babysitting and 9 hours clearing tables?

Total weekly payments = Payment for babysitting × number of hours + Payment for clearing tables × number of hours

= 10 × 7 + 13× 9

= 70 + 117

= $187

How much money would Stella

week in which she worked b hours babysitting and c hours clearing tables?

Total weekly payments = Payment for babysitting × number of hours + Payment for clearing tables × number of hours

= 10 × b + 13 × c

= 10b + 13c

Please helppppp!! Find the midpoint of the segment with the following end points (-2,7) and (2,3)

Answers

Answer:

[tex] \huge{ \boxed{ \bold{ \tt( \: 0 \: ,5 \: )}}}[/tex]

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

First, Let's explore about Midpoint :

Midpoint of the segment simply means middle point of a line segment. Formula of Midpoint :

[tex] \boxed{ \sf{(x _{ \: m \: } ,\: y_{m}) = ( \frac{x_{1} + x_{2}}{2} ,\: \frac{y_{1} + y_{2}}{2} )}}[/tex]

where ,

[tex]( \sf{x_{ \: m \: } ,\: y _{ \: m \: })}[/tex] = co-ordinates of the midpoint

[tex]( \sf{ x_{ \: 1 \: }, \: y_{ \: 1 \: }})[/tex] = co-ordinates of the first point

[tex] \sf{(x _{ \: 2 \: } ,\: y_{ \: 2 \: })}[/tex] = co-ordinates of the second point

The Midpoint Formula is used to find the exact center point between two defined points in a line segment.  The Midpoint formula is quite simple , so you should easily be able to remember it. It won't matter which point you pick to be the 'first" point you plug in. Just make sure that you're adding both an x to an x and a y to a y. Hence, keep in mind , in order to find the midpoint of a line segment, the first step is to add both ' x - co-ordinates' and divide it by 2 and then the second step is to add both ' y - co-ordinates ' and divide it by 2.

Now, Let's solve it!

Question :

Find the midpoint of the segment with the following end points ( - 2 , 7 ) and ( 2 , 3 ).

Step - by - step explanation :

Let P ( x , y ) divide the line joining the points A ( - 2 , 7 ) and B ( 2 , 3 ). Now, let :

A ( - 2 , 7 ) → ( x₁ , y₁ )B ( 2 , 3 ) → ( x₂ , y₂ )

Apply midpoint formula , then plug the values and lastly simplify it :

[tex] \sf{ midpoint \: = \: ( \frac{x _{ \: 1 \: } + x _{ \: 2 \: }}{2} ,  \: \frac{y_{ \: 1 \: } + y _{ \: 2\: }}{2} })[/tex]

➺ [tex] \sf{midpoint = ( \frac{ - 2 + 2}{2},  \: \frac{7 + 3}{2} )}[/tex]

➺ [tex] \sf{midpoint = ( \frac{0}{2} ,  \: \frac{10}{2} )}[/tex]

➺ [tex] \boxed{ \sf{ midpoint = ( \: 0 \: , 5})}[/tex]

Hence , The midpoint of the segment with the end points A ( - 2 , 7 ) and B ( 2 , 3 ) is ( 0 , 5 ) .

Hope I helped!

Have a wonderful time ッ

~TheAnimeGirl ♡

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Use rigid motions to explain whether the triangles in the figure are congruent. Be sure to describe specific rigid motions in your explanation.​

Answers

Answer:

6tg67g76g76g76

Step-by-step explanation:

Answer:

There are 2 steps:

1. 90° counterclockwise rotation about the origin

2. Translation downward 2 units

Step-by-step explanation:

1. 90° counterclockwise rotation about the origin = (x, y) to (-y, x),

D moves from (-2, 4) to (-4, -2)

W moves from (-1, 2) to (-2, -1)

P moves from (3, 3) to (-3, 3)

2. Translation downward 2 units = (x, y) to (x, y-2),

D moves from (-4, -2) to (-4, -4) = M

W moves from (-2, -1) to (-2, -3) = J

P moves from (-3, 3) to (-3, 1) = S

least to greatest :)

Answers

Answer:

2^1 + 3^1, 2^3 - 2^1 and 3^2.

Step-by-step explanation:

3^2 = 9.

2^3 - 2^1 = 8 - 2 = 6.

2^1 + 3^1 = 4.

what is the answer real quick

Answers

Answer:

19

Step-by-step explanation:

2d + 3      d = 8

2(8) + 3

16 + 3

19

is 350% of 34 less than​ 100, greater than 100 but less than​ 150, or greater than​ 150?

Answers

Answer:

greater then a hundred but less then 150

Step-by-step explanation:

I multilayered by 3.5

−4p − (1 − 6 p)
Please explain. I will give brainliest. I honestly don't understand how to do this.

Answers

Answer:

2p − 1

Step-by-step explanation:

I think, sry is its wrong. Do you have possible answrs?

-4p - (1 - 6p) = -4p - 1 + 6p = -4p + 6p - 1 = 2p - 1

(1) One side of a Rhombus measures 13 cm what is its perimeter
(2) The diagonals of a rhombus measues 6 cm and 8 cm,what is the perimeter of this rhombus
(3) MULTIPLE CHOICE: A Rhombus is labeled ABCD ,which line segment could be a diagonal: a) AB b) BC c) AC d) CD
(4) A square is both a rhombus and a rectangle TRUE or FALSE
(5) A Rhombus is labeled ABCD if the slope of AD is 2/3 what is the slope of BC
(6) A Rhombus is labeled ABCD if the slope of AC is 1/2 what is the slope of BD

Answers

Answer:

I want to get point

Step-by-step explanation:

can you help

Determine the length of the diagonal side of the roof truss. The height of the roof truss is 6.3m and the full span of the roof truss is 16.4m.

Answers

Answer:

7.96

Step-by-step explanation:

A combination of 3 erasers and 5 pencils cost $7.55. A combination of 6 erasers and 12 pencils cost $17.40. How much is each pencil?

Answers

Answer:

9.85

Step-by-step explanation:

I subtract 17.40 and 7.55 to get 9.85 they just wanted to know how much the pencil cost not erasers.

The cost of each pencil is $1.15.

What is a system of equation?

A system of equations is used when there are two variables, and you are given two pieces of information about how those variables are related.

Given that, A combination of 3 erasers and 5 pencils cost $7.55. A combination of 6 erasers and 12 pencils cost $17.40.

Let e represents eraser and p represents a pencil.

Establishing the equations,

3e+5p = 7.55

6e+12p = 17.40

Solving by elimination, we get,

p = 1.15

Hence, The cost of each pencil is $1.15.

For more references on system of linear equation, click;

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Plssss helpppp!!! I’ll give brainliest

Answers

need a question dog can’t do nun

Which of the following numbers is not a factor of 2004?
/4
/6
/8
/12

Answers

8 is not a factor or 2004

Answer:

8

Step-by-step explanation:

Please Help Me With A Paper For Math Class!!!

Answers

Answer:

a. 38

b.95

c.57

Step-by-step explanation:

What is the domain and range of the graph?

Answers

Answer:

Domain: [-1, 5]

Range: [-1, 2]

Step-by-step explanation:

SOMEONE PLZ HELP I HAVE TO TURN THIS IS BY 12:00
Mark ran a race at a local park. The distance was 5 Km. Mark learned from his awesome math teacher that 1 Km = 0.62 miles. Based on this, how many miles can he tell his parents that he ran at the race?

Answers

So what you do is make a fraction with the conversation between miles and km with km on the bottom to cancel out the units and multiply the fraction by the amount of km

5km (.62miles/1km) = 3.1 miles

-3(10)+5x=26
Answer this please ​

Answers

Answer:

10%2B3x=26-5x Start with the given equation. 3x=26-5x-10 Subtract 10 from both sides. 3x%2B5x=26-10 Add 5x to both sides. 8x=26-10

Step-by-step explanation:

32. At a fast food joint, five cheeseburgers and two large shakes cost $23. At
the same fast food joint, three cheeseburgers and three large shakes cost
$21. What is the costs of a cheeseburger, and what is the cost of a large
shake? Show all work in the space provided.
yoression

Answers

Answer:

multiple choice?

Step-by-step explanation:

Answer:

Cheesburger costs $3. Shake costs $4.

Step-by-step explanation:

c is cheesburger and s is large shake.

5c+2s=23

3c+3s=21

15c+6s=69

-6c-6s=-42

9c=27

c=3

Estimate the square root to the nearest integer.

Answers

Answer:
3
Explanation:
3^2 is equal to 9, and 4^2 is equal to 16, so sqrt(10) must be in between 9 and 16. Since 10 is closer to 9 than to 16, sqrt(10) is closer to 3 than 4, which means that to the nearest integer sqrt(10)=3

(8.5×108) + (2.3×107)

Answers

Answer:

1164.1

Step-by-step explanation:

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