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notsponge [240]
3 years ago
9

#6) Find the value of x. Be sure to show your work. ​

Mathematics
1 answer:
____ [38]3 years ago
7 0
The answer is x=70

My work below in the picture

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The question is below
Ad libitum [116K]

Answer:

£59.25

Step-by-step explanation:

Hello!

To solve this problem, we must:

  1. Solve for the length of the fence (aka height)
  2. Find the area of the lawn (trapezoid)
  3. Find the number of cans needed
  4. Find the price of all the cans

Area of a trapezoid, and why the formula works:

A trapezoid is a quadrilateral with one set of parallel sides known as bases. The other two sides are known as the legs.

To find the area of a trapezoid, we use the formula:

\frac{B_1 + B_2}{2}* h

This works because if we used the formula, we would be duplicating the trapezoid to form a rectangle with a side length of B1 + B2, and a height of h. Since the trapezoid is half of that, we divide by 2.

Solve for height:

The height is unknown but can be found using the Pythagorean Theorem.

The difference between the bases is the length of the bottom leg of the right triangle, and 17 is the hypotenuse.

Difference = 20 - 12 = 8

Hypotenuse = 17

  • 8² + fence² = 17²
  • 64 + fence² = 289
  • 225 = fence²
  • fence = 15

The height is 15

Solve for area:

Now we can solve for the area.

  • A = \frac{B_1 + B_2}{2} * h
  • A = \frac{12 + 20}{2} * 15
  • A = \frac{32}{2} * 15
  • A = 16 * 15 = 240

The area is 240

Cans:

The area of the lawn is 240 square meters. Each can cover 100 square meters.

  • 240 ÷ 100 = 2.4

Since we can't use part of a can, we round up to three whole cans.

The price of 3 cans :

  • 3 * 19.75
  • 59.25

£59.25

The Pythagorean Theorem:

The Pythagorean theorem is a very common geometry formula used to find the length of the hypotenuse in a right triangle, given the lengths of the two other bases.

The formula is : a^2 + b^2 = c^2

  • a is a leg
  • b is a leg
  • c is the hypotenuse

Images attached for your reference

7 0
2 years ago
Sandy cut three pieces of yarn to use for her art project one was 1ft 8in long one was 10 in long and one was 2 ft 6 in Long how
kogti [31]

Answer:

C. 5 feet

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Ian walked 4 miles in 90 minutes. Bob walked 7 miles in 2.5 hours. Are these rates in proportion? If no, who walked faster?
Yuliya22 [10]

Answer:

<h3>Bob walked faster than Ion.</h3>

Step-by-step explanation:

90/4=22.5

Ian - 1 mile in 22.5 minutes

2x60=120

60/2=30

120+30=150

150/7=21.43

Bob - 1 mile in 21.43

5 0
3 years ago
Read 2 more answers
What is the midpoint of (2,5) and (-5,6
Soloha48 [4]
(-3/2,11/2) is the midpoint
5 0
3 years ago
What is the slope of the line through the points (0,0) and (2,6)
Aneli [31]

Answer:

3

Step-by-step explanation:

The slope of a line can be found by dividing the amount that the line "rises" over a certain amount of "run". In this case, the line rises 6 units while moving 2 units to the right. 6/2=3, meaning that the slope of this line is 3. Hope this helps!

8 0
3 years ago
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