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just olya [345]
3 years ago
13

Assume that lines that appear to be tangents are tangents. O is the center of the circle.

Mathematics
1 answer:
scoray [572]3 years ago
8 0

Answer: the value of x is 45

Step-by-step explanation: its a little bit bigger than the 40 on the right

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100 POINTS + BRAINLIST
mojhsa [17]

Problem 1

Since point P is the tangent point, this means angle OPT is a right angle

angle OPT = 90 degrees

Let's use the Pythagorean theorem to find the missing side 'a'

a^2 + b^2 = c^2

a^2 + 7^2 = 12^2

a^2 + 49 = 144

a^2 = 144 - 49

a^2 = 95

a = sqrt(95)

a = 9.7467943

a = 9.7

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

Let's use the sine and arcsine rule to find angle y

sin(angle) = opposite/hypotenuse

sin(y) = 7/12

y = arcsin( 7/12 )

y = 35.6853347

y = 35.7

The value of y is approximate. Make sure your calculator is in degree mode. Arcsine is the same as inverse sine or \sin^{-1}

====================================================

Problem 2

Focus on triangle OHP. This may or may not be a right triangle. The goal is to test if it is or not.

We use the converse of the Pythagorean theorem to check.

Recall that the converse of the Pythagorean theorem says: If a^2+b^2 = c^2 is a true equation, then the triangle is a right triangle. The value of c is always the longest side. The order of a and b doesn't matter.

In this case we have

  • a = 7
  • b = 13
  • c = 16

Which leads to

a^2 + b^2 = c^2

7^2 + 13^2 = 16^2

49 + 169 = 256

218 = 256

We get a false equation at the end, since both sides aren't the same number, which means the original equation is false.

We don't get a^2 + b^2 = c^2 to be true, therefore this triangle is not a right triangle.

Consequently, this means angle OPH cannot possible be 90 degrees (if it was then we'd have a right triangle). Therefore, point P is not a tangent point.

You follow the same basic idea for triangle OQH and show that point Q is not a tangent point either. Or you could use a symmetry argument to note that triangle OPH is a mirror reflection of triangle OQH over the line segment OH. This implies that whatever properties triangle OPH has, then triangle OQH has them as well for the corresponding pieces.

7 0
2 years ago
Read 2 more answers
–9x + 9y = 9<br> y = –7<br><br> (<br> , <br> )
Y_Kistochka [10]

Answer:

x=-8

(-8,-7)

Step-by-step explanation:

–9x + 9y = 9

–9x + 9(-7) = 9 (y=-7)

-9x-63=9

Both side +63

-9x=63+9

-9x=72

Both side divide   -9

x=-8

y=-7

(-8,-7)

6 0
2 years ago
13. A cone with a radius of 3 inches and a height of 7 inches has the same radius as a cylinder. If the cylinder's volume is two
Ghella [55]

Answer:

Step-by-step explanation:

r = 3 in

h = 7 in

volume of cone = ⅓πr²h = 21π in³

cylinder has radius r = 3 and height h.

volume of cylinder = πr²h = 9πh in³

volume of cylinder is two times the volume of cone

9πh = 2×21π

9h = 42

h = 42/9 = 4⅔ in

3 0
2 years ago
Definitions given.
Yuki888 [10]

The pitch of the roof is given by the ratio of the rise to the run of the roof, which is the slope of the rafter

The \ pitch  \ of  \ the \  roof  \ is \ \mathbf {\dfrac{6}{13}}

Please find attached the simple <u>diagram of the house</u> with all measurements labeled

The reason the above value for the pitch and the diagram are correct are as follows:

The given parameters are;

Width of the section of the house on which the gable of the roof is to be placed = 50 feet

Length of the over hang on the sides of the roof = 1 foot each

Total span of the roof = 52 feet

Horizontal length of each rafter, the run = 26 feet

The height of the ridge above the top of the frame, the rise = 12 feet

Required:

  • To find the pitch of the roof
  • To draw a diagram of the house showing measurements

Solution:

Pitch = \dfrac{Rise}{Run}

  • Pitch  \ (slope) \ of \ roof =  \dfrac{12}{26} =\dfrac{6}{13}

Please find attached the <u>diagram</u> of the house showing the measurements for the roof parameters and the section of the house where the gable roof is to be placed

Learn more about finding the slope of a line here:

brainly.com/question/18990889

brainly.com/question/17105217

brainly.com/question/20987659

8 0
2 years ago
Angle A = 7x + 40 degrees
sashaice [31]
It equals 0.0192727261287227 mathamatics
8 0
3 years ago
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