If R is the midpoint of segment QS, QR = 8x-51 and RS = 3x-6, find QS

QS = 42 units

Step-by-step explanation:

8x - 51 = 3x - 6

5x = 45

x = 9

(8x - 51) + (3x - 6) = QS

72 - 51 + 27 - 6 = QS

42 = QS

QS = 42

Step-by-step explanation:

If R is the midpoint, the QR = RS

QR = RS

8x-51 = 3x-6

Subtract 3x from each side

8x-3x-51 = 3x-3x-6

5x -51 =-6

Add 51 to each side

5x -51+51 = -6+51

5x = 45

Divide by 5

5x/5 = 45/5

x = 9

RS = 3x-6

RS = 3*9-6

    = 27-6

    = 21

QS = QR + RS

     = RS +RS

     = 2RS

    = 2 *21

    = 42

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841