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babunello [35]
2 years ago
12

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

Mathematics
1 answer:
algol132 years ago
4 0
Answers:
x = 24
y = 8√3
Explanation:

1) Since, the given triangle is a right triangle, and you have both an angle and the hypotenuse length, you can use some trigonometric ratios to find the variables.

2) The variables given represent:

x: adjacent-leg to angle 30°
y: opposite length to angle 30°

3) sine ratio:

sin 30° = opposite-leg / hypotenuse = y / (16√3)

⇒ y = 16√3 sin 30° = 16√3 × (1/2) = 8√3

4) cosine ratio

cos 30° = adjacent-leg / hypotenuse = x / (16√3)

⇒ x = 16√3 cos 30° = 16√3 (√3 / 2) = 16 × 3 / 2 = 24

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Step-by-step explanation: My teacher taught me this before so i know :)

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The length of a rectangle is 3 more than 3 times its width. The perimeter of the rectangle is 174 inches. What is the length of
saveliy_v [14]

Answer:

<em>l = w + 3cm</em>

<em>l = w + 3cmp = 2l + 2w = 58cm</em>

<em>l = w + 3cmp = 2l + 2w = 58cm </em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 </em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:l = (13cm) + 3cm = 16cm</em>

<em>l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:l = (13cm) + 3cm = 16cmStep-by-step explanation:</em>

I hope this helps you.

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2 years ago
A line has a slope of 7 and a y-intercept of -2
geniusboy [140]

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2 years ago
PLEASE HELP!!!!!!!!!<br> Make sure you show all your work for full points. What is o?
Pie

Answer:

  o = 54

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°. The definition of a linear pair tells you the two angles of a linear pair total 180°. Together, these relations tell you that an exterior angle of a triangle is equal to the sum of the remote interior angles.

In this geometry, the angle marked 78° is exterior to the left-side triangle. That means ...

  78° = o° +24°

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The value of 'o' is 54.

__

<em>Additional comment</em>

n° is the supplement of 78°, so is 102°.

m° is the difference between 102° and 22°, so is 80°.

6 0
2 years ago
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