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3 years ago

It’s worth 10 points if you answer!

Mathematics

1 answer:

Maksim231197 [3]3 years ago

8 0

Answer:

m∠x = 10°

Step-by-step explanation:

Since we are dealing with a right triangle and its two sides and one angle, we can use trigonometry ratios. Remember them all with the acronym SohCahToa.

"o" is for opposite side, "a" is for adjacent side, "h" is for hypotenuse side.

The ratios are:

sinθ = opposite/hypotenuse

cosθ = adjacent/hypotenuse

tanθ = opposite/adjacent

θ means the "angle of reference", or the angle you know or want to find. This determines which side is adjacent (touching) or opposite (not touching). The hypotenuse (longest side) does not change.

In this triangle, θ = x. The sides we know are hypotenuse and opposite. Therefore, we will use the sinθ ratio.

sinθ = opposite/hypotenuse

sinx = CB/AB Substitute the labels in the diagram

sinx = 4/23 Substitute known values (side lengths)

x = sin⁻¹(4/23) Isolate 'x'. Use calculator to solve.

x = 10.015....° Exact answer

x ≈ 10° Round to the nearest degree

Therefore the measure of angle x (m∠x) is 10°.

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ladessa [460]

Mike has 4 times as many stamps as Andrew

Let Mike = M and Andrew = A, eq.1 will be M = 4A

However, if Mike gives Andrew 8 stamps, then the number of stamps Mike has is now twice the number of stamps Andrew has. This will give us another equation.

eq. 2 will be M-8 = 2 (A+8)

The expression on the left tells us that Mike gave away eight stamps, while the expression on the right tells us that whatever this new number is is equal to twice the total number of Andrew's stamps after receiving eight from Mike.
Simplifying this further gives us:

M-8 = 2A + 16
M = 2A + 16 + 8 = 2A + 24

Use 2A + 24 and substitute this for M in eq. 1. This gives us:

2A + 24 = 4A
24 = 4A - 2A
24 = 2A
12 = A, and therefore M = 48 (because M=4A)

To begin with, Andrew had 12 stamps and Mike had 48 stamps.
If only M-8 = 2A is used, this will only meet the condition given in situation 1 (M=4A) but not situation 2, wherein after giving away 8 stamps, Mike's stamps is twice as many as Andrew's. You can check it. :)

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