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finlep [7]
3 years ago
14

A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4feet. Find the height of the tree.

Mathematics
1 answer:
Nitella [24]3 years ago
7 0

Answer:

30 ft

Step-by-step explanation:

This is a problem of similar triangles.

         | \

         |    \

         |      \

     h  |        \

         |          \

         |         5|\

         |           | 4\

          <----24---->

      tree     man

The height of the man is 5 ft.

The shadow of the tree is 24 ft.

The shadow of the man is 4 ft.

We have similar triangles, so the lengths of their sides are proportional.

h/24 = 5/4

Cross multiply.

4h = 24 * 5

Divide both sides by 4.

h = 6 * 5

h = 30

Answer: 30 ft

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1. What is the value of the y variable in the solution to the following system of equations?
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we have

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7x-5y=-11 ------> equation B

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Multiply by 3 the equation B

3*(7x-5y)=-11*3

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Adds equation C and equation D

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<u>the answer Part 1) is the option A </u>

y=-2

Part 2)

we have

3x+y=6

y=-3x+6 ------> equation A

6x+2y=8

Simplify Divide by 2 both sides

3x+y=4

y=-3x+4 ------> equation B

the lines A and B are parallel lines, because the slope m is equal

so

The system has no solution

therefore

<u>the answer Part 2) is the option D</u>

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Part 3)

we have

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x-y=3

y=x-3  ------> equation B

substitute equation B in equation A

4x+2[x-3]=6

6x-6=6

6x=12

x=2

therefore

<u>the answer part 3) is the option D</u>

x=2

Part 4)

Let

x---------> The number of one-step equations

y---------> The number of two-step equations

we know that

x+y=1,120

x=1,120-y -------> equation A

3x-2y=1,300 ------> equation B

substitute equation A in equation B

3[1,120-y]-2y=1,300

3,360-5y=1,300

5y=3,360-1,300

5y=2,060

y=412

therefore

<u>the answer part 4) is  the option D</u>

y=412

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3 years ago
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