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2 years ago

Given the figure, find the values of x and z.

Mathematics

2 answers:

matrenka [14]2 years ago

7 0

Answer:

$z = 62 \\ 6x + 52 = 180 - 62 \\ 6x = 66 \\ x = 11$

Slav-nsk [51]2 years ago

7 0

Answer:

x = 11 , z = 62

Step-by-step explanation:

62° and (6x + 52)° are adjacent angles on a straight line and sum to 180°

62 + 6x + 52 = 180

6x + 114 = 180 ( subtract 114 from both sides )

6x = 66 ( divide both sides by 6 )

x = 11

62° and z° are vertically opposite angles and are congruent , then

z = 62

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2 years ago

Read 2 more answers

The hypotenuse of a 30o-60o-90o triangle measures 4 square 3 inches. What is the length of the shorter leg?

Fofino [41]

Answer:

The shorter leg is $2\sqrt{3}$ inches

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The 30°-60°-90° is a special type of right-angled triangles

It has the following special side length:

The length of the side opposite to the 30° is $\frac{1}{2}$ the length of the hypotenuse

The length of the side opposite to the 60° is $\frac{\sqrt{3} }{2}$ of the hypotenuse

Now, we know that the lengths of the sides in a triangle are proportional to the angles

This means that the shortest side will be the one opposite to the smallest angles

In our case, the shortest side will be the one opposite to the 30° angle

We are given that the hypotenuse of the triangle is $4\sqrt{3}$ in

From the above:

Shorter leg = leg opposite to 30° = $\frac{1}{2} * hypotenuse = \frac{1}{2} * 4\sqrt{3} = 2\sqrt{2}$ inches

Hope this helps :)

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3 years ago

Rewrite the expression in the form 9^n (9^3) (9^12)

BartSMP [9]

Answer:

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3 years ago