Bill wants to rent a car. rental comoany a cahrge $35 per day plus $0.10 per miles driven. rental company b charges $25 per day plus $0.15 per mile driven. aafter how many miles driven will the price charged by each company be the same?

1) Rental company A
f₁(x)=price charged.
x=number of miles

We have this function.

f₁(x)=0.1x+35

2)Rental company B.
f₂(x)= price charged.
x=number of miles.

We have this function.

f₂(x)=0.15x+25

The price charged by each company will be the same when f₁(x)=f₂(x), therefore:

0.1x+35=0.15x+25
0.1x-0.15x=25-35
-0.05x=-10
x=-10 / -0.05
x=200

the price charged will be the same after of 200 miles.

35 + 0.10m = 25 + 0.15m
35 - 25 = 0.15m - 0.10m
10 = 0.05m
10/0.05 = m
200 = mafter 200 miles driven, they will be the same

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.