Can someone please help me with proofs

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A composite function to find the area of the region at time t is written as-

A(r(t)) = π(0.25 + 2t + 4t²)

f(g(x)) or (f ∘ g)(x) represents the composition of functions f(x) & g(x), where g(x) acts first (x). It integrates a number of functions to produce another.

The output of one function inside the parenthesis is becoming the input of the other function in a function composition. i.e.,

Now, as per the given question;

To create a composite function, we pertain one function to another. In this scenario, we would like to find area in terms of time, so we apply the function A(r) to the function r. (t).

To accomplish this, we substitute r with r(t).

Since we know that r(t) = 0.5 + 2t, we can replace r to 0.5 + 2t:

A(r(t)) = π(0.5+2t)²

To make things easier, we'll simplify this same squared term:

A(r(t)) = π(0.5 + 2t)(0.5 + 2t)

A(r(t)) = π[(0.5×0.5) + (0.5×2t) + (2t×0.5) + (2t×2t)]

A(r(t)) = π(0.25 + t + t + 4t²)

A(r(t)) = π(0.25 + 2t + 4t²)

Therefore, the composite function to find the area of the region at time t is written as A(r(t)) = π(0.25 + 2t + 4t²).

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The complete question is-

A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A(r) = πr2, where r is the radius of the circle at time t. Explain how to write a composite function to find the area of the region at time t.

Answer:

0.04

Step-by-step explanation:

You have to divide 1 and 25 and your answer will be 0.04 :)

Roses will have six arrangements, while daisies will have ten.

Each bouquet will contain two flowers.

The highest common factor (HCF) between two or more numbers is two.

Amanda is arranging flowers in accordance with the question. She has 36 tulips, 20 daises, and 16 roses.

Every bouquet must have an equal amount of daisies, a reasonable quantity of roses, and an equal number of tulips.

The least common divisor, which is 2 instead of HCF, which would make it the least amount of arrangements, is the most arrangements she is capable of making.

based on the facts provided;

So,

20 daisies divided by 2 is 10 arrangements.

12 roses divided by 2 is 6 arrangements.

There will be 2 flowers in each kind of arrangements.

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Answer:

[tex]18\; {\rm in}[/tex].

Step-by-step explanation:

Let [tex](x\; {\rm in})[/tex] be the length of the base.

The question states that the length of each congruent side is [tex]8\; {\rm in}[/tex] less than twice the length of the base. Twice the length of the base would [tex](2\, x\; {\rm in})[/tex]. The length of each congruent side would be [tex](2\, x - 8)\; {\rm in}[/tex].

Sum up the length of each side to find the perimeter of this triangle:

[tex](2\, x - 8) + (2\, x - 8) + x = 5\, x - 16[/tex].

Substitute in the actual perimeter of this triangle:

[tex]5\, x - 16 = 74[/tex].

Solve for [tex]x[/tex]:

[tex]x = 18[/tex].

Therefore, the length of the base of this isosceles triangle would be [tex]18\; {\rm in}[/tex].

Answer:

c is correct option

Step-by-step explanation:

this is confirm answer

Answer:

The first one

Step-by-step explanation:

5^2= 25 and then you would need multiply 25 by 25 again so that gives you 625.

Answer:

thats me in among us

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

Answer:

{ }, {4}, {6}, {7}, {4, 6} {4, 7}, {6, 7}, {4, 6, 7}

Step-by-step explanation:

The empty set is a subset of every set.

Also, a set is a subset of itself.

S = {4, 6}

T = {6, 7}

S U T = {4, 6, 7}

Subsets of S U T: { }, {4}, {6}, {7}, {4, 6} {4, 7}, {6, 7}, {4, 6, 7}

The population has increased by 4.44 million

The current population of the city is 6.34 million residents

In 1914 of the city was 1.9 million residents

Therefore the population increase can be calculated by subtracting the population of residents in 1914 from the population after the year 1914, this means subtracting 1.9 million from 6.34 million

= 6.34 - 1.9

= 4.44

Hence the population increase is 4.44 million

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Answer:

The opposite of multiplication is division. The opposite of division is multiplication. The opposite of taking a square root is squaring

Step-by-step explanation:

Answer:

9/20

Step-by-step explanation:

first you have to make 1 1/4 an improper fraction so since the denominator is 4 you add 4 to the numerator which is 1 so your fraction would be 5/4.

Second you make the denominators the same so you have to multiply them together. but since your multiplying the denominators you have to multiply the numerator as well. so for 5/4 you would multiply both the numerator and denominator by 10 so your fraction will now be 50/40. now you  multiply 8/10 by 4 so your new fraction is now 32/40

Third you subtract. you only have to subtract the numerators so 50-32 is 18 so your answer is 18/40

Last you need to simplify the highest number you can divide both of them by is 2 so now you divide 18 by 2 which makes 9 then you divide 40 by 2 which is 20 so your answer is 9/20

Sorry i'm not the best at explaining things but i tried my best

Hope this helps you out and have a great day : )

Answer:

C. 12x

Each box has 12 envelopes.

The number of total envelopes will be the number of envelopes in a box multiplied by the number of boxes. The number of boxes is unknown, so it is replaced by the variable. This gives us 12x

Answer:

-9 7/15

Step-by-step explanation:

Ans

c=9

Step-by-step explanation:

2 x 9 = 18 +9 = 27

Answer:

C

Step-by-step explanation:

If you plug in the numbers into that equation you get

1 = -2(2) + 5

1 = -4 + 5

1 = 1

You can also do this again with x = 5 y = -5

-5 = -2(5) + 5

-5 = -10 + 5

-5 = -5

Answer:

a = 24

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define Equation

-a = -24

Step 2: Solve for a

Step 3: Check

Plug in a into the original equation to verify it's a solution.

Here we see that -24 does indeed equal -24.

∴ a = 24 is the solution to the equation.

This is not full question I think

Answer: A

Step-by-step explanation: because the slope is positive 1/3 on the line

Answer: it’s a

Step-by-step explanation:

9514 1404 393

Answer:

  5 minutes; 60 gallons

Step-by-step explanation:

The volume in tank A is initially 35 gallons. Its rate of change is 5 gallons per minute. The equation for volume can be written as ...

  y = 35 +5x . . . . . . where y is gallons, and x is minutes

The volume in tank B is initially 100 gallons. Its rate of change is -8 gallons per minute. The equation for volume can be written as ...

  y = 100 -8x

We want to find the values of x and y such that both are the same for both tanks.

  35 +5x = y = 100 -8x

  13x = 65 . . . . . . . . add 8x-65 to both sides of the equation

  x = 5

  y = 100 -8·5 = 60

Both tanks will hold 60 gallons after 5 minutes.

Answer:

the answer would be A i believe

Answer:

They are equal

Step-by-step explanation:

90/2=45

135/3=45

Answer:

When solving for x in the following equation: -6x + 18 = -6

step 1: -6x +18 - 18 = -6 - 18 (subtract 18 from both side)

step 2. -6x/-6 = -24 / -6 (divide both sides by -6 to isolate x by itself)

x = 4

Step-by-step explanation:

The value of x in the expression  - 6x + 18 = - 6, is 4.

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

Given an expression - 6x + 18 = - 6 solving for x is the same as finding the value of x.

∴ - 6x + 18 = - 6.

- 6x = - 6 - 18.

- 6x = - 24.

6x = 24.

x = 4.

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Answer:

Jj

Step-by-step explanation: