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Chapter 6: Problem 66

Solve each proportion and check. \(\frac{x}{64}=-\frac{9}{16}\)

Short Answer

Expert verified
The solution to the equation is \(x = -36\).

Step by step solution

01

Cross multiplication

Cross multiply by multiplying the denominator of one fraction by the numerator of the other fraction. You get \(x \cdot 16 = -9 \cdot 64\).
02

Simplify equation

The equation simplifies to \(16x = -576\).
03

Solve for x

Divide both sides of the equation by 16 to solve for x. So, \(x = \frac{-576}{16}\).
04

Calculate x

After dividing -576 by 16, you find that \(x = -36\).
05

Check the solution

Check the solution by substituting -36 for x in the original proportion. After the substitution, you should get \(\frac{-36}{64} = \frac{-9}{16}\), which simplifies to \(\frac{-9}{16} = \frac{-9}{16}\). Since both sides of the equation are equal, this verifies that \(x = -36\) is the correct solution.

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Most popular questions from this chapter

The formula$$N=\frac{t^{2}-t}{2}$$describes the number of football games, \(N\), that must be played in a league with \(t\) teams if each team is to play every other team once. Use this information to solve Exercises 83-84. If a league has 36 games scheduled, how many teams belong to the league, assuming that each team plays every other team once?

Solve the equations using the quadratic formula. \(x^{2}+6 x-10=0\)

Solve each equation using the zero-product principle. \((x+11)(x-5)=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-9 x+81\)

When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.
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