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Chapter 11: Problem 2

$$x^{2}+8 x=-7$$ $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x & 0 \end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
Quantity B is greater.

Step by step solution

01

Rearrange the Equation

First rearrange the equation to standard quadratic form \(ax^2 + bx + c = 0\). So for our equation, we'll write it as \(x^{2}+8 x + 7 = 0\)
02

Factoring the Quadratic Equation

Here, we need to factor this quadratic equation. We are basically looking for two numbers that add up to 8 and multiply to 7. These numbers are 7 and 1. So, our factored equation becomes \((x+7)(x+1) = 0\)
03

Solving for x

Set each factor to zero and solve for x. Doing so gives the solutions \(x+7=0\) implies \(x=-7\) and \(x+1=0\) implies \(x=-1\)
04

Comparing Quantities

Now, we can compare these two solutions of \(x\) which are Quantity A with 0 which is Quantity B. As we can see, both solutions \(x = -7\) and \(x = -1\) are less than 0. So Quantity B is greater.

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Most popular questions from this chapter

If \(x=3 a\) and \(y=9 b,\) then all of the following are equal to \(2(x+y)\) EXCEPT a. \(3(2 a+6 b)\) b. \(6(a+3 b)\) c. \(24\left(\frac{1}{4} a+\frac{3}{4} b\right)\) d. \(\frac{1}{3}(18 a+54 b)\) e. \(12\left(\frac{1}{2} a+\frac{3}{4} b\right)\)

A merchant sells three different sizes of canned tomatoes. A large can costs the same as 5 medium cans or 7 small cans. If a customer purchases an equal number of small and large cans of tomatoes for the same amount of money needed to buy 200 medium cans, how many small cans does she purchase? a. 35 b. 45 c. 72 d. 199 e. 208

$$11 x+14 y=30 \text { and } 3 x+4 y=12$$ $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x+y & (x+y)^{-2} \end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

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If \(a\) is multiplied by 3 and the result is 4 less than 6 times \(b,\) what is the value of \(a-2 b ?\) a. -12 b. \(-\frac{4}{3}\) c. \(-\frac{3}{4}\) d. \(\frac{4}{3}\) e. 12
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