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2 years ago

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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2 years ago

The length of a rectangle is four times its width. If the perimeter of the rectangle is 20 feet, how many feet long is the recta

Gemiola [76]

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3 years ago

The one-to-one functions g and h are defined as follows

Debora [2.8K]

Answer:

$g^-^1(x)=-8$

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

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

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.

$h^-^1\ o\ h$

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

Now substitute (-3) in place of (x),

$=-3$

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2 years ago

Winston drove 70 mph. If he drives for 3.5 hours how many miles will Winston drive?

Fofino [41]

This problem can be solved using two equations:
The first represents the total trip, which is the miles driven in the morning added to those in the afternoon. Let's call the hours driven in the morning X and the hours driven in the afternoon Y. We get: X + Y = 248.
The second equation relates the miles driven in the morning compared to the afternoon. Since 70 fewer miles were driven in the morning than the afternoon, then X = Y - 70.
Now substitute the equation for morning hours (equation 2) into the total miles equation (equation 1). We get:
(Y - 70) + Y = 248
2Y - 70 = 248
2Y = 318
Y = 159
We know that Winston drove 159 miles in the afternoon.

To find the morning hours, just substitute 159 into the equation for morning hours (equation 2)
X = 159 - 70
X = 89
We now know that Winston drove 89 miles in the morning.

We can check our work by plugging both distances into the total distance equation: 89 + 159 = 248

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