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The resulting expressions for [tex](f\,\circ\,g)(x)[/tex] and [tex](g\,\circ\,f)(x)[/tex] are [tex]5- 2\cdot x^{2}[/tex] and [tex]-4\cdot x^{2} + 12\cdot x -5[/tex], respectively.

A composition is a operation two functions in which the independent variable of the first function is substituted by the entire second function. In other words, we have the following expressions:

[tex](f\,\circ\,g) (x) = f(g(x))[/tex] (1)

[tex](g\,\circ \,f)(x) = g(f(x))[/tex] (2)

If we know that [tex]f(x) = 2\cdot x - 3[/tex] and [tex]g(x) = 4 - x^{2}[/tex], then we have the following compositions:

[tex](f\,\circ\, g) (x) = 2(4-x^{2})-3[/tex]

[tex](f\,\circ\,g)(x) = 5-2\cdot x^{2}[/tex]

[tex](g \circ f) (x) = 4 - (2\cdot x-3)^{2}[/tex]

[tex](g\,\circ f) (x) = -4\cdot x^{2} +12\cdot x -5[/tex]

The resulting expressions for [tex](f\,\circ\,g)(x)[/tex] and [tex](g\,\circ\,f)(x)[/tex] are [tex]5- 2\cdot x^{2}[/tex] and [tex]-4\cdot x^{2} + 12\cdot x -5[/tex], respectively.

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Answer:

y=2x

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

When solving for x, you want to get the variable by itself on one side of the equation. The first step is to subtract 10 from both sides. 43-10=33. So, it should look like:

3x = 33

Divide both sides of the equation by 3 to get x alone. 33/3 equals 11. So x =11. Hope this helped and lmk if you have more questions!!

Step-by-step explanation:

- 3 ( x + 2 ) + 9 + 7x = 4x + 5 - 2

- 3x - 6 + 9 + 7x = 4x + 5 - 2

- 3x + 7x + 9 - 6 = 4x + 5 - 2

4x + 3 = 4x + 3

Answer:

Eighty six thousand, five hundred and three

Step-by-step explanation:

Answer:

Expanded Notation Form:

86,503 =

80,000

+ 6,000

+ 500

+ 0

+ 3

Expanded Factors Form:

86,503 =

8 × 10,000

+ 6 × 1,000

+ 5 × 100

+ 0 × 10

+ 3 × 1

Expanded Exponential Form:

86,503 =

8 × 104

+ 6 × 103

+ 5 × 102

+ 0 × 101

+ 3 × 100

Word Form:

86,503 =

eighty-six thousand five hundred three

Step-by-step explanation:

:)

Answer:

I don't think it is

Step-by-step explanation:

I checked with desmos graphing calculator and the line produced is a parabola. I believe the y^2 made it into a parabola

No,  5x+y^2=25 is not a linear equation.

For the given equation;

5x+y^2=25

the highest power of the equation is 2.

Thus, the given equation is a quadratic equation or 2 degree equation.

Therefore, the given equation is not a linear equation.

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Answer:

Step-by-step explanation:

Answer:

2,9457

Step-by-step explanation:

100+7% = 1.07

(1.07)^50 = 29.45702506

y = 1000(29.46)

y = 29,460

Answer:

8 ounces

Step-by-step explanation:

16oz/lb

16*5= 80oz of cornstarch in bucket

4oz * 18students = 72oz

80-72= 8 oz remaining

The amount of cornstarch left is 8 ounce.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Each student get = 4 ounce of cornstarch

Total number of student = 18 students

And, Total amount of cornstarch = 5 pound

Here,

Since, Amount of total cornstarch to student = Each student get × Total number of student

⇒ Amount of total cornstarch to student = 4 × 18

⇒ Amount of total cornstarch to student = 72 ounce

Since, 1 pound = 16 ounces

So, We get;

⇒ Total amount of cornstarch = 5 × 16

⇒ Total amount of cornstarch = 80 ounces

Thus, Amount of cornstarch left = 80 - 72

⇒ Amount of cornstarch left = 8 ounces

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Answer:

0.

¯¯¯¯¯¯¯¯¯¯¯¯

571428

…

…

angles per times

Step-by-step explanation:

Answer:

40° and 140°

Step-by-step explanation:

let one angle be x then the other is 3.5x

A linear pair sum to 180° , then

x + 3.5x = 180

4.5x = 180 ( divide both sides by 4.5 )

x = 40 and 3.5x = 3.5 × 40 = 140

The angles are 40° and 140°

This question doesn't make sense.Are you sure you wrote it correctly?

The smallest integer 160 needs to be multiplied by to give a square number is 15.

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

The smallest integer 160 needs to be multiplied by to give a square number;

60 x 15= 900

Hence,

The square root of 900= 30

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Answer:

Step-by-step explanation:

Since Angle E is same for both triangles, as vertical angles, the sum of the other two interior angles should be same.

Then we have:

Answer:  

≈

17

%

Explanation:

A sum of 7 can be achieved the following ways.

5 and 2

2 and 5

4 and 3

3 and 4

6 and 1

1 and 6

There are

6/2

=

3/6

possible outcomes and 6 ways to obtain the sum of 7 so

6 3/6

≈

17

%

Answer:

Option B: Only (-2, 9)

Step-by-step explanation:

Given the linear equation, y = -2x + 5:

We'll plug in the given options to see which of the ordered pairs will satisfy the equation:

Substitute option  A: (2, -9) into the equation:

y = -2x + 5

-9 = -2(2) + 5

-9 = -4 + 5

-9 = 1 (False statement). Therefore, (2, -9) is not a solution.

Substitute option B: (-2, 9) into the equation:

y = -2x + 5

9 = -2(-2) + 5

9 = 4 + 5

9 = 9 (True statement). Therefore, the ordered pair, (-2, 9) is a solution.

The other two options are irrelevant at this point since we've proven that option B is the correct answer.

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Answer:

I think x = -8. Hope this helps!! :)

Answer:

Yes

Step-by-step explanation:

First off, let's use an example with the same equivalence:

[tex]\frac{12}{36} =\frac{16}{48}[/tex]

If you divide the denominator by the numerator you have to get 3, otherwise, it's not equivalent.

The constant of proportionality between the denominator and the numerator, if we use x and y, is:

[tex]y=3x[/tex]

So, just like the example and explanation I used, 3 divided 1 is 3 and 6 divided by 2 is 3.

Answer:

Yes, the 2 cups of mango and 6 cups of strawberries are equivalent.

Step-by-step explanation:

The question is based on ratios. Ratios are basically the quantitative relation between two amounts showing the number of times one value contains or is contained within the other. In this instance, you're altering the quantity by 2. So the 1 cup of mangoes becomes 2 cups of mangoes and the 3 cups of strawberries becomes 6 cups.

Another example of this could be:

In the store, for every 1 man there are 4 women. So if you change the amount of men in the store from 1 to 2, the quantity of women would go from 4 to 8.

Answer:

a. False

b. true

c. false

d. true

Step-by-step explanation:

Answer:

154 pounds

Step-by-step explanation:

If h=68, then w=5.5(68)-220=374-220=154

Answer:

8990

Step-by-step explanation:

The 9 underlined is in the tens place.

8990.97 ⇒ 8990

Since you can't round up, you replace everything after the underlined 9 with 0's.

8990.00 = 8990

Answer:

10 percent is the answer

Answer:

217.2

Step-by-step explanation:

You divide the two numbers. The tenths place is the number after the decimal. The answer without rounding is 217.19(other numbers). 9 raises 1 up to 2 so that's why the answer is 217.2.

Answer: 16

Step-by-step explanation: i took the quiz

Answer:

B.) You think about how your choice of narrator will affect the story before you begin writing, should be the most correct choice given. I hope this helps.