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Viktor [21]
3 years ago
9

What is the measure of P?

Mathematics
1 answer:
vesna_86 [32]3 years ago
4 0

Answer:

∠P = 111°

Step-by-step explanation:

∠P = 84 + 27

      = 111

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NASA launched another space probe, Voyager 2 on August 20, 1977. Voyager 2 is a bit slower than Voyager 1 only traveling 15.4 km
slava [35]

Using proportions, it is found that it will take Voyager 2 82,900 years from its location to travel to the second closest star.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the Voyager 2 travels 15.4 km/s. In kilometers per year, considering that one hour has 3600 seconds, the measure is given by:

15.4 x 365 x 24 x 3600 = 485,654,400 km/year.

The distance to Proxima Centauri in km is given by:

d = |1.93 x 10^10 km - 4.24 x 9.5 x 10^12 km| = 4.02607 x 10^13 km.

Hence the time in years is given by:

t = d/v =  4.02607 x 10^13/485,654,400 = 82,900.

It will take Voyager 2 82,900 years from its location to travel to the second closest star.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

6 0
2 years ago
Please help me :)<br><br><br> ty ty
WARRIOR [948]

Answer:

The slope is <u>steeper</u> and the line is shifted <u>flatter</u>.

Step-by-step explanation:

I have provided a graph to help illustrate the relationship between these two lines, (The red line is line A which is y = 2x + 4, and the blue line is line B which is y = 4x + 9).

As you can see, the slope does determine the steepness of the lines. This means that line A's slope is going up 2 units and over to the right 1 unit, whereas line B's slope is going up 4 units and to the right 1.

Therefore, if line A is to transform into line B, then its slope will be steeper.

Hope this helps you :)

Also, P.S. I don't know if there are supposed to be more options, so I apologize if flatter does not belong in the second box.

6 0
2 years ago
Find the exact value of sec theta if csc theta = -4/3 and the terminal side of theta lies in quadrant III
GREYUIT [131]

Answer:

-4 sqrt(7)/7

Step-by-step explanation:

csc theta = -4/3

csc theta = hypotenuse / opposite side

hypotenuse = 4  

opposite  = 3

Using the pythagorean theorem

a^2 + b^2 = c^2

3^2 + b^2 = 4^2

9+b^2 = 16

b^2 = 16-9

b^2 = 7

Taking the square root

sqrt(b^2) = sqrt(7)

b = sqrt(7)

We are in the third quadrant so only tan  and cot are positive

that means the x and y values are "negative"  so a = -3 and b = - sqrt(7)

sec theta = hypotenuse / adjacent

                = 4/ - sqrt(7)

rationalizing  

                   -4 sqrt(7)/ sqrt(7)* sqrt(7)

                = -4 sqrt(7)/7

           

3 0
3 years ago
Solving rational equations<br><br> solve for x: 3/x-4=7/x
KIM [24]

Solving the rational equation \frac{3}{x-4}=\frac{7}{x} the value of x is 7

Step-by-step explanation:

We need to solve rational equation: \frac{3}{x-4}=\frac{7}{x} and find value of x.

Solving:

\frac{3}{x-4}=\frac{7}{x}

Cross multiplying:

3(x)=7(x-4)\\Simplifying:\\3x=7x-28\\3x-7x=-28\\-4x=-28\\x=-28/-4\\x=7

So, value of x = 7.

Solving the rational equation \frac{3}{x-4}=\frac{7}{x} the value of x is 7

Keywords: Solving the rational equation

Learn more about Solving the rational equation at:

  • brainly.com/question/13168205
  • brainly.com/question/1757979
  • brainly.com/question/2456302

#learnwithBrainly

8 0
3 years ago
Read 2 more answers
Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights
Fed [463]

Answer:

a) 615

b) 715

c) 344

Step-by-step explanation:

According to the Question,

  • Given that,  A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 732 babies born in New York. The mean weight was 3311 grams with a standard deviation of 860 grams

  • Since the distribution is approximately bell-shaped, we can use the normal distribution and calculate the Z scores for each scenario.

Z = (x - mean)/standard deviation

Now,

For x = 4171,  Z = (4171 - 3311)/860 = 1  

  • P(Z < 1) using Z table for areas for the standard normal distribution, you will get 0.8413.

Next, multiply that by the sample size of 732.

  • Therefore 732(0.8413) = 615.8316, so approximately 615 will weigh less than 4171  

 

  • For part b, use the same method except x is now 1591.    

Z = (1581 - 3311)/860 = -2    

  • P(Z > -2) , using the Z table is 1 - 0.0228 = 0.9772 . Now 732(0.9772) = 715.3104, so approximately 715 will weigh more than 1591.

 

  • For part c, we now need to get two Z scores, one for 3311 and another for 5031.

Z1 = (3311 - 3311)/860 = 0

Z2 = (5031 - 3311)/860= 2  

P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772

  approximately 47% fall between 0 and 1 standard deviation, so take 0.47 times 732 ⇒ 732×0.47 = 344.

5 0
3 years ago
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