Question

The total distance from Phoenix to Columbus is approximately 1820 miles. Given that the distance between Phoenix and Indianapolis can be represented by the expression 9x²+27 and the distance between Indianapolis and Columbus can be represented by the expression x²−7, determine the value of x in miles. If possible, leave the answer exact. Explain or show your process.

a.x=13
b.x=14
c.x=15
d.x=16

Answer 1

To determine the value of x in miles, you need to equate the total distance from Phoenix to Columbus to the sum of the distances between Phoenix and Indianapolis and between Indianapolis and Columbus. By simplifying the equation, you find that x = 3√20 miles.

Step-by-step explanation:

To determine the value of x in miles, we need to equate the total distance from Phoenix to Columbus to the sum of the distances between Phoenix and Indianapolis and between Indianapolis and Columbus.

The expression for the distance between Phoenix and Indianapolis is 9x²+27.

The expression for the distance between Indianapolis and Columbus is x²−7.

Therefore, the equation becomes: 9x²+27 + x²−7 = 1820.

Combining like terms, we get: 10x² + 20 = 1820.

Subtracting 20 from both sides, we have: 10x² = 1800.

Dividing both sides by 10, we get: x² = 180.

Taking the square root of both sides, we find: x = ±√180.

Since distance cannot be negative, we discard the negative solution. Thus, x = √180.

Simplifying √180, we get: x = √(9 × 20). Taking out the perfect square factor, we have: x = 3√20.

Therefore, the value of x in miles is 3√20.