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anygoal [31]
2 years ago
15

Use the function values for f and g shown in the table below to evaluate the following expression.

Mathematics
1 answer:
Vikentia [17]2 years ago
5 0

The function f(g(2)) is an illustration of a composite function

The value of f(g(2)) is 2

<h3>How to determine the value of the function f(g(2))?</h3>

Given:

The table of values for functions f(x) and g(x)

To calculate f(g(2)), we start by calculating g(2)

From the table;

g(2) = 6

So, we have:

f(g(2)) = f(6)

From the table;

f(6) = 2

So, we have:

f(g(2)) = 2

Hence, the value of f(g(2)) is 2

Read more about composite functions at:

brainly.com/question/10687170

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A circular pond 24 yd in
Schach [20]

Answer:

The walk will cost $8164.

Step-by-step explanation:

Given:

Diameter of the circular pond (D) = 24 yd

Width of the gravel path (x) = 2 yd

Cost per yard of the path = $50

Now, radius of the circular pond is half of the diameter and is given as:

Radius,R=\frac{D}{2}=\frac{24}{2}=12\ yd

Now, area of the pond is given as:

A_{pond}=\pi R^2=3.14\times (12)^2=3.14\times 144=452.16\ yd^2

Area of the complete path including the pond area is given as:

A_{outer}=\pi(R+x)^2=3.14\times(12+2)^2=3.14\times196=615.44\ yd^2

Now, area of the gravel path can be obtained by subtracting the pond area from the total outer area. This gives,

A_{path}=A_{outer}-A_{pond}\\\\A_{path}=615.44-452.16=163.28\ yd^2

Now, using unitary method,

Cost of 1 square yard of path = $50

∴ Cost of 163.28 square yard of path = 50 × 163.28 = $8164

Hence, the walk will cost $8164.

5 0
3 years ago
Read 2 more answers
STEP By Step Explaination needed
NeX [460]

Answer:

8/11

Step-by-step explanation:

5+3=8

6 0
2 years ago
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Draw graphs of the following lines: The line through the origin having a slope of 1/4
KengaRu [80]
I think its 1 on the graph correct me if im wrong
4 0
3 years ago
Calculate the volume of the cylinder.
Lera25 [3.4K]
Since the formula for the base of the cylinder is \pi r^{2}, multiplying that by 10 we get 90\pi. Hope this helps!
6 0
3 years ago
Consider the following division of polynomials.
Bond [772]

x^4=x^2\cdot x^2. Multiplying the denominator by x^2 gives

x^2(x^2+2x+8)=x^4+2x^3+8x^2

Subtracting this from the numerator gives a remainder of

(x^4+x^3+7x^2-6x+8)-(x^4+2x^3+8x^2)=-x^3-x^2-6x+8

-x^3=-x\cdot x^2. Multiplying the denominator by -x gives

-x(x^2+2x+8)=-x^3-2x^2-8x

and subtracting this from the previous remainder gives a new remainder of

(-x^3-x^2-6x+8)-(-x^3-2x^2-8x)=x^2+2x+8

This last remainder is exactly the same as the denominator, so x^2+2x+8 divides through it exactly and leaves us with 1.

What we showed here is that

\dfrac{x^4+x^3+7x^2-6x+8}{x^2+2x+8}=x^2-\dfrac{x^3+x^2+6x-8}{x^2+2x+8}

=x^2-x+\dfrac{x^2+2x+8}{x^2+2x+8}

=x^2-x+1

and this last expression is the quotient.

To verify this solution, we can simply multiply this by the original denominator:

(x^2+2x+8)(x^2-x+1)=x^2(x^2-x+1)+2x(x^2-x+1)+8(x^2-x+1)

=(x^4-x^3+x^2)+(2x^3-2x^2+2x)+(8x^2-8x+8)

=x^4+x^3+7x^2-6x+8

which matches the original numerator.

3 0
3 years ago
Read 2 more answers
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