If you have changed the tires on your car, the original diameter is 24.5 inches, to a new diameter of 26 inches, how far have you actually gone if your odometer is reading 1500 miles?
a.1226 miles
b.1328 miles
c.1500 miles
d.1592 miles

Option d.1592 miles

Step-by-step explanation:

step 1

Find out the circumference for the original diameter of the tire

The circumference is equal to

we have

assume

substitute

The circumference represent the distance of one revolution of the tire

Find out the number of revolutions of the tire for a distance of 1,500 miles

1,500/(76.93/63,360)=1,235,408.81 rev

step 2

Find out the circumference for the new diameter of the tire

The circumference is equal to

we have

assume

substitute

Multiply by the number of revolutions in step 1

Round to the nearest whole number

Alternative Method

we know that

The ratio of the diameters of the tires is equal to the scale factor

To find out the new distance, multiply the scale factor by the original distance

so

Round to the nearest whole number

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15