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olga2289 [7]
3 years ago
15

Find the values of x and y. Write your answer in simplest form.

Mathematics
2 answers:
agasfer [191]3 years ago
5 0

Answer:

y = 6√3 and x = 6

Step-by-step explanation:

this is a 30-60-90 triangle.  The side opposite the 30° angle corresponds to the side of length 1  in the most basic 30-60-90 triangle; the side opp. 60° to the side of length √3; and the hyp. to the side of length 2.

To find y, write and solve an equation of ratios, as follows:

adj side           adj side      (adjacent to the 30° angle)

    y                       √3

 hypo               hypo    then (cross multiplying):  2y = 12√3, and

    12                     2       y = 6√3

If the hypo here is 12 and the adj side (y) is 6√3, then we can use the Pyth. Theorem to find the third side (x):

[12]² = [6√3]² - x²  ↔ 144 = 36(3) - x²   ↔  36 = x².  So x = 6 here.

Lyrx [107]3 years ago
5 0

Answer:

x = 6

y ≈ 10. 40

Step-by-step explanation:

Using the SOHCAHTOA principle we can solve for x and y since the angle is known and it is a right angle triangle.

hypotenuse = 12

adjacent = x

opposite = y

cos 60° = adjacent/hypotenus

cos 60° = x/12

cross multiply

x = 12 cos 60°

x = 12 × 0.5

x = 6

Finding y

sin 60° = opposite/hypotenuse

sin 60° = y/12

cross multiply

y = 12 sin 60°

y  = 12 × 0.8660254038

y =  10.392304845

y ≈ 10. 40

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3 years ago
Mr. Nordman gets a commission of $2.30 on each pair of women's shoes he sells, and a commission of $3 on each pair of men's shoe
Alina [70]

Answer:

x ≥ 5

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Step-by-step explanation:

Lets the number of men's shoes he sells be x and women's shoes be y.

For each men's shoes , he gets a commission of $3 and for each women's shoe, he gets a commission of $2.30 .

He needs to sell atleast 10 women's shoes and 5 men's shoes.

Also he needs to make atleast $60 per week.

x ≥ 5

y ≥ 10

3x + 2.3y ≥ 60

These are are the 3 required inequalities.

Now we will see an example.

If he sells 20 womens shoes and 10 mens shoes , he will meet the requirements.

He will make a total profit = 2.3\times 20 + 3\times 10 =$76

8 0
2 years ago
Find the center and radius of (x + 9)^2 + (y + 6)^2 = 9.
VARVARA [1.3K]
You can do this by comparing your equation to the general form of equation of a circle

( x - a)^2 + (y - b)^2 = r^2       where (a,b) is the centre and r = radius:-
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4 0
3 years ago
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Am i doing this right????
Anna35 [415]
You are going in the right direction. For the distance of ST I get √136
√(-5-1)² + (6+4)² =
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3 0
2 years ago
In adjoining figure a circle is inscribed in the quadrilateral ABCD given that BC is equal to 38 cm cube is equal to 27 cm and B
lukranit [14]

<h3>Radius = 14cm</h3>

Step-by-step explanation:

Let O be the centre of the circle. Since P and S are the points of contact of tangents AD and DC respectively, OP ⊥ AD and OS ⊥ DC

Also, AD ⊥ DC (given), therefore, OPDS is a square.

BR = BQ = 27cm...(tangents from an external point to a circle are equal in length)

therefore, CR = CB - BR = (38 - 27)cm = 11cm

SC = CR = 11 cm...(tangents from an external point) therefore, DS = DC - SC = (25 - 11) cm = 14 cm.

therefore,

Radius of a circle = OP = DS = 14 cm...(therefore, OPDS is a square).

<h3>Hope it helps you!! </h3>
5 0
2 years ago
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