1. suzette ran and biked for a total of 34 mi in 3.5 h. her average running speed was 6 mph and her average biking speed was 12.5 mph. let x = total hours suzette ran. let y = total hours suzette biked. use substitution to solve for x and y. show your work. check your solution. (a) how many hours did suzette run? (b) how many hours did she bike?

in this problem we have two unknown variables x and y.

to solve this we must to form two equations.

first we will calculate average speed for total distance

let v= speed(velocity)   d=distance 34miles t=total time x+y=7/2h

v=d/t= 34/(7/2)= 68/7 mph

let d1= total distance suzette ran d1= v1*x = 6x

let d2= total distance suzette bike d2= v2*y= (25/2)y

v1=6mph and v2=25/2 mph

formula for calculating average speed is v=(d1+d2)/x+y

when we replace all we know we get   68/7=(6x+(25/2)y)/(7/2) =>

68/7= 2(6x+(25/2)y)/7 we will multiply whole equation with number 7 and get

68= 2(6x+(25/2)y) => 68= 12x+25y => 12x+25y=68

we know that   x+y=7/2 => x=(7/2)-y we replace this in upper equation and get

12((7/2)-y)+25y=68 => 42-12y+25y=68 => 13y=68-42 => 13y=26 => y=2 h

when we back in x=(7/2)-y and replace y we get

x=(7/2)-2=3/2 h=1.5 h x=1.5h

(a) suzette ran x=1.5h

(b) suzette bike y=2h

good !

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

the anwser is d) 75°

step-by-step explanation: