Contestants in the Run-and-Bike-a-thon run for a specified length of time, then bike for a specified length of time. Jason ran at an average speed of 5.2 mi/h

and biked at an average speed of 20.8 mi/h,

going a total of 14.4 miles. Seth ran at an average speed of 10.4 mi/h and biked at an average speed of 18.2 mi/h,

going a total of 18 miles. For how long do contestants run and for how long do they bike? Round to the nearest hundredth if necessary.

Contestants run__hour and bike___hour.

They ran for 0.923 hrs and biked for 0.46 hrs

Step-by-step explanation:

First thing to do is write down the inequality of the question

5.2x + 20.8y = 14.4

10.4x + 18.2y = 18

Multiplying the whole equation by 10, so as to eliminate the decimal places, we have.

52x + 208y = 144

104x + 182y = 180

Multiplying the first equation by 2, we have

104x + 416y = 288, next we solve it simultaneously with the second equation

104x + 416y = 288

104x + 182y = 180

Subtract 2 from 1, and we have..

416y - 182y = 288 - 180

234y = 108

y = 0.46

Now, we go back and substitute for y in the earlier equation, so that

52x + 208(0.46) = 144

52x + 95.68 = 144

52x = 144 - 95.68

52x = 48.32

x = 48.32/52

x = 0.929

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

i got 10.28 but that rounds up to 10.3