Mathematics: Analyze the diagram below and complete the instructions that follow.Find the value of x and the value of y.

Analyze the diagram below and complete the instructions

shelbylynn17

17.03.2022

Step-by-step explanation:

Drawing a segment from the left side of the top base to the lower base, creates a right triangle on the left with legs 9 and x₁ and hypotenuse y

Using the tangent ratio in the right triangle and the exact value

tan45° = 1 , then

tan45° = $\frac{opposite}{adjacent}$ = $\frac{9}{x_{1} }$ = 1, so x₁ = 9 and

x = 7 + x₁ = 7 + 9 = 16

Using the sine ratio in the right triangle and the exact value

sin45° = $\frac{1}{\sqrt{2} }$ , then

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{9}{y}$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

y = 9 $\sqrt{2}$

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jessicap7pg75

25.10.2021

Step by step:

$4x - 3( - 2) = 18 \\ 4x + 6 = 18 \\ - 6 \: \: \: - 6 \\ 4x = 12 \\ x = 3 \\ \\$

(3, -2)

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