What is the solution to the following equation 4(-2x+3)=10x-15

1 answer:

3 0

$4(2x + 3) = 10x - 15 \\ \\ 1. \: - 8x + 12 = 10x - 15 \\ 2. \: 12 = 10x - 15 + 8x \\ 3. \: 12 = 18x - 15 \\ 4. \: 12 + 15 = 18x \\ 5. \: 27 = 18x \\ 6. \: \frac{27}{18} = x \\ 7. \: \frac{3}{2} = x \\ 8. \: x = \frac{3}{2}$

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The diameter of a tire is 2.5 ft. Use this measurement to answer parts a and b. Show all work to receive full credit

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Answer:

The answer is below

Step-by-step explanation:

The diameter of a tire is 2.5 ft. a. Find the circumference of the tire. b. About how many times will the tire have to rotate to travel 1 mile?

Solution:

a) The circumference of a circle is the perimeter of the circle. The circumference of the circle is the distance around a circle, that is the arc length of the circle. The circumference of a circle is given by:

Circumference = 2π × radius; but diameter = 2 × radius. Hence:

Circumference = π * diameter.

Given that diameter of the tire = 2.5 ft:

Circumference of the tire = π * diameter = 2.5 * π = 7.85 ft

b) since the circumference of the tire is 7.85 ft, it means that 1 revolution of the tire covers a distance of 7.85 ft.

1 mile = 5280 ft

The number of rotation required to cover 1 mile (5280 ft) is:

number of rotation = $\frac{5280\ ft}{7.85\ ft\ per\ rotation}=672\ rotations\\\\\\$