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charle [14.2K]
2 years ago
13

Find the area in square centimeters of the composite shape shown below. Enter only a number as your answer.

Mathematics
1 answer:
Fed [463]2 years ago
8 0

Answer:

136 cm^2

Step-by-step explanation:

you can divide the shape into two shapes:

first : draw a line ⊥ to BC from point E to point F

rectangle : DCEF : Area = L*W=7*13=91 cm^2

the other shape AEBF is a trapezoid:

Area of AEBF= [(a+b)/2] h where a and b are the base and h is the height

height =18-13=5

a=7, b=11

A=[(7+11)/2]*5=45 cm^2

add the two areas : 45+91=136 cm^2

hope it works, many ways to find the area

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The one-to-one functions g and h are defined as follows
Debora [2.8K]

Answer:

g^-^1(x)=-8

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Step-by-step explanation:

When given the following functions,

g=[(-2,-7),(4,6),(6,-8),(7,4)]

h(x)=3x+4

One is asked to find the following,

1. Question 1

g^-^1(4)

When finding the inverse of a function that is composed of defined points, one substitutes the input given into the function, then finds the output. After doing so, one must substitute the output into the function, and find its output. Thus, finding the inverse of the given input;

g^-^1(4)

g(4)=6\\g(6)=-8\\g^-^1(4)=-8

2. Question 2

h^-^1(x)

Finding the inverse of a continuous function is essentially finding the opposite of the function. An easy trick to do so is to treat the evaluator (h(x)) like another variable. Solve the equation for (x) in terms of (h(x)). Then rewrite the equation in inverse function notation,

h(x)=3x+4\\\\h(x)-4=3x\\\\\frac{h(x)-4}{3}=x\\\\\frac{x-4}{3}=h^-^1(x)

h^-^1(x)=\frac{x-4}{3}

3. Question 3

(h^-^1 \ o\ h)(-3)

This question essentially asks one to find the composition of the function. In essence, substitute function (h) into function (h^-^1) and simplify. Then substitute (-3) into the result.

h^-^1\ o\ h

\frac{(3x+4)-4}{3}\\\\=\frac{3x+4-4}{3}\\\\=\frac{3x}{3}\\\\=x

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