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OlgaM077 [116]
3 years ago
6

Please help me pleasssseeee <3

Mathematics
1 answer:
Sophie [7]3 years ago
8 0

Answer:

1st ans

(8x+19)=(9x+9)(vertically opposite angle)

19-9=9x-8x

x=10

2nd ans

(3x-31)=(x+59)(exterior alternate angle)

3x-x=59+31

2x=90

x=90/2

x=45

3rd ans

(5x-33)+(6x+4)=180(straight angle )

11x-29=180

11x=180+29

x=209/11

x=19

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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
3 years ago
Read 2 more answers
A batch of 40 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to custome
butalik [34]

Answer:

a) 658008 samples

b) 274050 samples

c) 515502 samples

Step-by-step explanation:

a) How many ways sample of 5 each can be selected from 40 is just a combination problem since the order of selection isn't important.

So, the number of samples = ⁴⁰C₅ = 658008 samples

b) How many samples of 5 contain exactly one nonconforming chip?

There are 10 nonconforming chips in the batch, and 1 nonconforming chip for the sample of 5 be picked from ten in the following number of ways

¹⁰C₁ = 10 ways

then the remaining 4 conforming chips in a sample of 5 can be picked from the remaining 30 total conforming chips in the following number of ways

³⁰C₄ = 27405 ways

So, total number of samples containing exactly 1 nonconforming chip in a sample of 5 = 10 × 27405 = 274050 samples

c) How many samples of 5 contain at least one nonconforming chip?

The number of samples of 5 that contain at least one nonconforming chip = (Total number of samples) - (Number of samples with no nonconforming chip in them)

Number of samples with no nonconforming chip in them = ³⁰C₅ = 142506 samples

Total number of samples = 658008

The number of samples of 5 that contain at least one nonconforming chip = 658008 - 142506 = 515502 samples

6 0
3 years ago
Four runners are training for long races. Noah Ran 5.123 miles. Andre ran 6.34 miles. Jada ran 7.1 miles. Diego ran 8 miles.
Korolek [52]
Jada ran 1.977 miles more than Noah
3 0
3 years ago
If a woman takes an early pregnancy test, she will either test positive, meaning that the test says she is pregnant, or test neg
k0ka [10]

Answer:

0.0098

Step-by-step explanation:

Probability of being pregnant:100/1000

=1/10.

98% chance:=98/100 ×1/10

=98/1000

Therefore the probability that she really is pregnant is: 0.098

3 0
3 years ago
A music store has 1,440 CDs. Each CD rack holds 90 CDs. How many racks does the store need to use to hold all the CDs?
Rufina [12.5K]

Answer:

16 cd racks

Step-by-step explanation:

1,440%90

6 0
3 years ago
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