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gogolik [260]
3 years ago
14

What value of x would make rq tangent to Circle P at point Q?

Mathematics
2 answers:
Novay_Z [31]3 years ago
7 0
If Q is tangent to circle P, that means that it is perpendicular to the radius at the point of tangency.  This means that ΔPRQ would be a right triangle.  We can use the Pythagorean theorem to solve this.
9² + 12² = (x+9)²
We use x+9 because the unknown segment x would combine with the radius, 9, to give that side of the triangle (the hypotenuse).
81 + 144 = (x+9)(x+9) ---- remember that squared means multiplied by itself
225 = (x+9)(x+9)
Multiply the right hand side:
225 = x² + 9x + 9x + 81
225 = x² + 18x + 81
Subtract 225 from both sides:
225 - 225 = x² + 18x + 81 - 225
0 = x² + 18x - 144
Use the Quadratic Formula to solve:
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}
\\
\\x=\frac{-18 \pm \sqrt{18^2-4(1)(-144)}}{2(1)}
\\
\\x=\frac{-18 \pm \sqrt{324--576}}{2}
\\
\\x=\frac{-18 \pm \sqrt{324+576}}{2} = \frac{-18 \pm \sqrt{900}}{2}
This gives us
x=\frac{-18 \pm 30}{2} = \frac{-18+30}{2} \text{ or } \frac{-18-30}{2}
Since -18 - 30 = -48, and a negative number doesn't make sense in this situation, we have 
x = (-18+30)/2 = 12/2 = 6.

marta [7]3 years ago
4 0

The answer is x= 6

have a nice day =)

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Usimov [2.4K]

Answer:

x=2/3 or x=1

I had this before

Is the right answer

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5 0
3 years ago
Round to the nearest tenth wa hit is the perimeter of the triangle
klio [65]

Answer:

D. 11.8 cm

Step-by-step explanation:

This triangle is a 30°-60°-90° triangle. There is a shortcut to find the lengths of the sides of a 30°-60°-90° triangle. The longest side is the hypotenuse. The longest side is double the shortest side or, the shortest side is half the longest side. Here the longest side is 5, so the short leg (shortest side) is 2.5

The other shortcut is that the longer leg is the

short leg×sqroot3

Here, the short leg is 2.5, so the long leg is 2.5×sqroot3

Perimeter is all the sides added together.

5 + 2.5+ 2.5×sqrt3

Do the times first.

5 + 2.5 + 4.3

= 11.8

6 0
2 years ago
Quadrilateral WXYZ is on a coordinate plane. Segment XY is on the line x − 3y = −12, and segment WZ is on the x − 3y = −6. Which
Nostrana [21]

Answer:

Equation shown

Step-by-step explanation:

Eq(1): x-3y=-12

X=-12+3y

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Eq(2): x-3y=-6

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4 0
3 years ago
Read 2 more answers
Determine el área del siguiente rectángulo
Arte-miy333 [17]
English ⬇️

So, 8*8=64, and is expressed as 64 square feet. A square has all sides equal. So, since one side is 8 feet long the other sides also have the same length. Area of a rectangle is length multiplied by the width.

Answer?= 8

Spanish ⬇️

Entonces, 8 * 8 = 64, y se expresa como 64 pies cuadrados. Un cuadrado tiene todos los lados iguales. Entonces, dado que un lado mide 8 pies de largo, los otros lados también tienen la misma longitud. El área de un rectángulo es la longitud multiplicada por el ancho.

hola no puedo hablar español así que tuve que traducir espero que esto sea bueno y la respuesta es 8 ¡buena suerte!
5 0
3 years ago
Approximately 1,870,000 oz of gold went into the manufacturing of electronic equipment in a certain country in 1 year. This was
Alexxandr [17]

Answer: 17000000 ounces of gold were mined in that country that year.

Step-by-step explanation:

Let x represent the number of ounces of gold that were mined in that country that year.

Approximately 1,870,000 oz of gold went into the manufacturing of electronic equipment in a certain country in 1 year. This was 11% of all the gold mined in that country that year. This means that

11/100 × x = 1870000

0.11x = 1870000

x = 1870000/0.11

x = 17000000

7 0
3 years ago
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