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3 years ago

Find the value of the variable and MN if N is between M and Q. Round to the nearest hundredth if necessary.

1 answer:

Rudiy273 years ago

3 0

Answer:
MN = 4 units

Explanation:
1- getting the value of m:
We are given that:
NQ = 4m and NQ = 12
This means that:
12 = 4m
$\frac{4m}{4} = \frac{12}{4}$
m = 3

2- getting MQ:
We are given that:
MQ = 5m + 1
We have calculated that:
m = 3
Therefore:
MQ = 5(3) + 1 = 15 + 1 = 16 units

3- getting MN:
We are given that point N is located somewhere between points M and Q.
This means that:
line MQ can be divided into two portions: MN and NQ
This also means that:
length of MQ = length of MN + length of NQ

We have calculated that:
MQ = 16 units
We are given that:
NQ = 12 units
Therefore:
16 = length of MN + 12
length of MN = 16 - 12
length of MN = 4 units

Hope this helps :)

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From the given information,

a. The length of the belt is 180.28 ft

b. The height of the window from the ground is 100 ft

c. The length of the ramp needed is 141.42 ft

<h3>What is the Pythagorean theorem's formula?</h3>

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the triangle. I.e., (hypotenuse)² = (opposite)² + (adjacent)²

<h3>Calculation:</h3>

It is given that,

The height of the silo is 150 feet

The distance from the belt to the silo is 100 feet

With the given measurements, a right-angled triangle is formed.

a. Finding the length of the belt:

From the diagram,

The height of the silo, sh = 150 ft

The base distance, sb = 100 ft

So, the length of the conveyor belt is the hypotenuse (bh) of the triangle formed.

On applying the Pythagorean theorem,

bh² = sb² + sh²

⇒ bh² = (100)² + (150)²

⇒ bh² = 32500

⇒ bh = √32500 = 50√13

∴ bh = 180.28 ft

Thus, the length of the belt is 180.28 ft.

b. Finding the height of the window from the ground:

It is given that the angle of elevation from the lower end of the belt(b) to a window(w) on the side of the silo is 45°.

This creates a special right-angled triangle. I.e.,

The angles of the new triangle are 90°- 45°. So, the third angle also becomes 45° (Since the sum of angles in a triangle is 180°)

So, the new triangle has angles of 90°- 45°- 45°

Thus, the new triangle is said to be an isosceles right angled triangle.

So, the two legs of the triangle are equal. I.e., sb = sw = 100 ft

Therefore, the height of the window from the ground(sw) is 100 ft

c. Finding the length of the ramp(bw) to the window:

Since we have

sw = 100 ft and sb = 100 ft

On applying Pythagora's theorem,

bw² = sb² + sw²

⇒ bw² = (100)² + (100)²

⇒ bw = √20000 = 141.42 ft

Therefore, the length of the ramp to the window is 141.42 ft.

Learn more about the Pythagorean theorem here:

brainly.com/question/343682

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