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Dmitrij [34]
2 years ago
10

A triangle has a 60° angle, and the two adjacent sides are 12 and "12 times the square root of 3". Find the radius of a circle w

ith the same vertex as a center, if the arc in the triangle bisects the area of the triangle.
Mathematics
1 answer:
shusha [124]2 years ago
5 0

The radius of a circle with the same vertex as a center is 12 units

<h3>Application of Pythagoras theorem;</h3>

To get the radius of the circle, we need to determine the diameter of the circle first:

According to SOH CAH TOA:

sin\theta = \frac{opp}{hyp} \\sin60 = \frac{12\sqrt{3}}{hyp} \\hyp =\frac{12\sqrt{3}}{sin60} \\hyp =\frac{2\times12\sqrt{3}}{\sqrt3}} \\hyp = 24 = diameter

Determine the radius of the circle

Radius = dismeter/2

Radius = 24/2

Radius = 12

Hence the radius of a circle with the same vertex as a center is 12 units

Learn more on radius of a circle here: brainly.com/question/24375372

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6 0
3 years ago
Priya is hosting a poetry club meeting this week and plans to have fruit punch and cheese for the meeting. She is preparing 8 ou
Korvikt [17]

Answer:

i) Number of people in club = 12

ii) 96 ounces of fruit punch for 12people

iii) 24 ounces of cheese for 12 people

iv) Priya's budget for poetry club meeting in dollars = $7.87

Step-by-step explanation:

We are not given the options for the equations that could represent the quantities and constraints in this situation. We can tell we are to represent the information given above.

Number of people in the club = 12

8 ounces of fruit punch per person

For 12 people = 12×8 = 96 ounces of fruit punch

2 ounces of cheese per person

For 12 people = 12×2 = 24 ounces of cheese

A package of cheese = 16 ounces

The costs for 1package = $3.99

The costs for 16 ounces of cheese = $3.99

The cost for 24 ounces of cheese = (24×3.99)/16 = 5.985

The cost for 24 ounces of cheese = $5.99

One-gallon jug of fruit punch = 128 ounces

The cost of One-gallon jug of fruit punch = $2.50

The costs of 128 ounces of fruit punch = $2.50

The costs for 96 ounces of fruit punch = (96×2.5)/128 = 1.875

The costs for 96 ounces of fruit punch = $1.88

Priya's budget for poetry club meeting in dollars = $5.99 + $1.88 = $7.87

Cost per item for x number of people:

y = x(2.5/128) + x (3.99/16)

y = x(0.0195) + x(0.2494)

Cost equation for Priya's budget:

y = 96x(2.5/128) + 24x (3.99/16)

y = 96x(0.0195) + 24x(0.2494)

Since the total number of people to attend the meeting is 12, the constraint = 0≤x≤12

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3 years ago
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Answer:

is a sas theorem.

Step-by-step explanation:

7 0
3 years ago
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AURORKA [14]

Step-by-step explanation:

<em>In the second column, we can see that every value of n is being added by 6. </em>

  • Thus, the expression is n + 6.

<em>Now, let's substitute the value of n in each column to verify each column. Then, using the expression, let's find the value of n + 6 where n = 28.</em>

<u>When n is 12:</u>

  • n + 6 = 18
  • 12 + 6 = 18
  • 18 = 18

<u>When n is 15:</u>

  • n + 6 = 21
  • 15 + 6 = 21
  • 21 = 21

<u>When n is 21:</u>

  • n + 6 = 27
  • 21 + 6 = 27
  • 27 = 27

<em>Thus, the expression is proven correct. Now, let's find n + 6 when n is 28.</em>

<u>Finding n + 6 when n is 28:</u>

  • n + 6 = x
  • 28 + 6 = x
  • 34 = x

Thus, the missing value in the table is 34.

4 0
2 years ago
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