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Elis [28]
3 years ago
13

Line RS bisects PQ at point R, Find RQ if PQ = 14 cm

Mathematics
1 answer:
Dovator [93]3 years ago
6 0
If PQ is 14, each segment, PR and RQ will be 7.
14 = PR + 7.
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PLEASE WILL GIVE 50 POINTS PLEASE ANSWER ​
leva [86]

Answer:

AB = 75

BC = 60

AC = 45

m∠A = 53°

m∠B = 37°

m∠C = 90°

Step-by-step explanation:

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Given:

\sf \tan(A)=\dfrac{60}{45}

Therefore:

  • side opposite angle A = BC = 60
  • side adjacent angle A = AC = 45

To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:

a^2+b^2=c^2

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ AC² + BC² = AB²

⇒ 45² + 60² = AB²

⇒ AB² = 5625

⇒ AB = √5625

⇒ AB = 75

To find m∠A:

\implies\sf \tan(A)=\dfrac{60}{45}

\implies\sf A=\tan^{-1}\left(\dfrac{60}{45}\right)

\implies\sf A=53^{\circ}\:(nearest\:degree)

m∠C = 90° (as it is a right angle)

The interior angles of a triangle sum to 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 53° + m∠B + 90° = 180°

⇒ m∠B = 180° - 53° - 90°

⇒ m∠B = 37°

4 0
2 years ago
What is the solution to the system?<br> 8x + 4y = 12<br> y = -2x + 3
elena-s [515]

Answer:

Step-by-step explanation:

use substitution and solve this 8x+4(-2x+3)=12

with the 4 distributed its

8x-8x+12=12

then you can cancel out the 8x and -8x and switch the 12 over into a -12 canceling out the 12s making it x=0

6 0
3 years ago
Susan ate 1 5/6 cups of popcorn on Monday night. She at 2 3/4 of popcorn on Thursday night. How many cups of popcorn did Susan e
Shtirlitz [24]

Answer: 4 7/12 cups of popcorn

Step-by-step explanation:

5 0
3 years ago
Can someone please help me?! Marking Brainliest!!!!!
irga5000 [103]

Answer:

5\sqrt{2}

Step-by-step explanation:

The formula for the length of a vector/line in your case.

L = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} = \sqrt{[4 - (-1)]^2 + [2 -(-3)]^2} = \sqrt{5^2 + 5^2} = \sqrt{50} = 5\sqrt{2}

3 0
3 years ago
Read 2 more answers
The larger of two numbers is five more than twice the smaller number. The sum of the two numbers is 38. Find the numbers.
Damm [24]

Answer:

I would set this up as:

let: lesser number = x

     greater number = 2x + 5

Restating the word problem:

lesser number + greater number = 38

        x           +  2x + 5             = 38

Solving:  3x + 5 = 38

                  - 5     -5

             ---------------

              3x      =  33

              ---          ---

               3            3

               x        =  11

Substitution for the greater number:

        2(11) + 5

          22    + 5

              27

8 0
3 years ago
Read 2 more answers
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