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QveST [7]
3 years ago
11

A shelf is built on a wall, as shown below. What is the value of x?

Mathematics
1 answer:
sp2606 [1]3 years ago
8 0

Answer:

Step-by-step explanation:

Given:

A shelf is built on a wall. The angles of the triangle are given as (x + 3)°, (2x - 18)° and 90°

We need to determine the value of x.

Value of x:

By triangle sum property, the angles in a triangle always add up to 180°

Thus, we have;

Simplifying, we get;

Subtracting both sides by 75, we get;

Dividing both sides of the equation by 3, we get;

Thus, the value of x is 35.

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I'm going to separate this into sections so it makes more sense for you to read. For the problems with π where you have to round, ask your teacher where to round, unless your textbook specifies it:

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To calculate area of squares, you multiply l • w. It's a square, so all sides are equal, and since we know that one side = 10 cm, the area is 10 • 10 = 100

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To find the area of a circle, you must follow the formula πr^2. In this case, the diameter is 10. The radius is half the diameter, so to substitute the values you must find 10 ÷ 2 = 5. So the radius is 5 cm. From there you can substitute r for 5, ending up with π • 5^2.    5^2 = 25, so the area is 25π, or about 78.54, depending on where the question wants you to round.

D – An approximate round (to the nearest hundredth it is 21.46 cm^2)

To find the area of the shaded region, just subtract the circle's area from the square's area, or 100 – 25π ≈ 21.46. Again, though, ask your teacher about where to round, unless your textbook specifies it.

E – dπ      (diameter • pi)

F – 10π cm^2 or an approximate round like 31.42 cm^2

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