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Tomtit [17]
3 years ago
8

Angle measures and segment lengths. Algebra Find the value of each variable.

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
6 0

(9)

<em>x</em> ° = 1/2 (130° - 30°) = 50°

(due to a theorem about intersecting secants/tangents)

(11) The labeled angle subtends a minor arc of meaure 120°, which means the larger arc has a measure of 360° - 120° = 240°. Then

<em>x</em> ° = 1/2 (240° - 120°) = 60°

(due to the same theorem)

(13) The labeling here is a bit confusing. I'm not sure what the 70° is referring to. It occurs to me that it might be info from a different exercise, so that <em>y </em>° is the measure of the angle made by the tangent to the circle with a vertex of the pentagon, and <em>x</em> ° is the measure of each arc that passes over an edge of the pentagon.

Each arc makes up 1/5 of the circle's circumferece, so

<em>x</em> ° = 360°/5 = 72°

The pentagon is regular, so each of its interior angles have the same measure of 108°. (Why 108°? Each exterior angle measures 360°/5 = 72°, since the exterior angles sum to 360°. Interior and exterior angles are supplementary, so the interior angles measure 180° - 72° = 108° each.)

The angles formed by the tangent to the circle are supplementary, so that

<em>y</em> ° + 108° + <em>y</em> ° = 180°

2<em>y</em> ° = 72°

<em>y</em> ° = 36°

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Answer:

Sin J =\frac{|KL|}{|JL|}

Step-by-step explanation:

In Right Triangle JKL, with Right angle at K

sin \theta =\frac{Opposite}{Hypotenuse} \\

Opposite =|KL|

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Sin J =\frac{|KL|}{|JL|}

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What's the answer to this math problem 3x+2/5 =7
yan [13]
3x+2/5=7

3x+2/5=35/5

3x=35/5-2/5

3x=33/5

x=(33/5)/3

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x=(33/5)*(1/3)

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Find the distance between the two numbers on a number line. Write your answer as a fraction in simplest form. - 7/9, - 2/9 The d
Nesterboy [21]

The distance between the two points on the number line is of \mathbf{\frac{5}{9}} units.

-------------------------------------------

  • The distance between two numbers on the number line is given by the <u>subtraction of the greater by the smaller number.</u>
  • The greater number is -\frac{2}{9}
  • The smaller is -\frac{7}{9}.
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-\frac{2}{9} - (-\frac{7}{9}) = -\frac{2}{9} + \frac{7}{9} = \frac{-2 + 7}{9} = \frac{5}{9}

Thus, distance of \mathbf{\frac{5}{9}} units.

A similar problem is given at brainly.com/question/10795861

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How many pounds each of dried fruit selling for $3.00 per pound and $3.80 per pound must be mixed to make a mixture of 80 pounds
allochka39001 [22]

Answer:

The quantity of dried fruit of $ 3 per pound is 30 pounds

The quantity of dried fruit of $ 3.80 per pound is 50 pounds  .  

Step-by-step explanation:

Given as :

The price of one dried fruit = $ 3.00 per pound

The price of other dried fruit = $ 3.80 per pound

The total quantity of mix dried fruit = 80 pounds

The price of sell for mix dried fruit = $ 3.50 per pound

Let The quantity of dried fruit of $ 3 per pound = x pounds

And The quantity of dried fruit of $ 3.80 per pound = y pounds

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Or, 3 x + 3.8 y = 3.5 x + 3.5 y

Or, 3.8 y - 3.5 y = 3.5 x - 3 x

or, 0.3 y = 0.5 x

Or, y = \frac{0.5}{0.3} x

I.e y =  \frac{5}{3} x

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I.e x = 80 - y

Or, x = 80 - \frac{5}{3} x

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Now, y =  80 - x

∴ y = 80 - 30

I.e y = 50

So,The quantity of dried fruit of $ 3.80 per pound = y = 50 pounds

Hence The quantity of dried fruit of $ 3 per pound is 30 pounds

And The quantity of dried fruit of $ 3.80 per pound is 50 pounds  .  Answer

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Step-by-step explanation:

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