Question

question #6 solve the equation. remember to check for extraneous solutions. $\frac{2x - 1}{2x^{2}}=\frac{2}{2x^{2}}$ $x=\frac{3}{2}$ $x = 3$ $x=\frac{1}{2}$ $x = 1$ question #7 six ounces of mixed nuts containing 18% peanuts were mixed with 12 ounces of another kind of mixed nuts which contain 72% peanuts. what percent of the new mixtures will be peanuts? round your answer to the nearest hundredth. 60% 58% 35% 54%

Explanation:

Question #6

Step1: Cross - multiply (since denominators are equal)

Since the denominators of the fractions $\frac{2x - 1}{2x^{2}}$ and $\frac{2}{2x^{2}}$ are the same ($2x^{2}
eq0$, i.e., $x
eq0$), we can set the numerators equal to each other. So, $2x−1 = 2$.

Step2: Solve for x

Add 1 to both sides of the equation $2x−1 = 2$. We get $2x=2 + 1$, which simplifies to $2x=3$. Then divide both sides by 2, so $x=\frac{3}{2}$.

Step3: Check for extraneous solutions

The original equation has a denominator of $2x^{2}$. When $x = \frac{3}{2}$, $2x^{2}=2\times(\frac{3}{2})^{2}=2\times\frac{9}{4}=\frac{9}{2}
eq0$. So $x=\frac{3}{2}$ is a valid solution.

Step1: Calculate the amount of peanuts in each mixture

For the first mixture, which is 6 ounces and 18% peanuts, the amount of peanuts is $0.18\times6 = 1.08$ ounces. For the second mixture, which is 12 ounces and 72% peanuts, the amount of peanuts is $0.72\times12=8.64$ ounces.

Step2: Calculate the total amount of the new mixture and peanuts in it

The total amount of the new mixture is $6 + 12=18$ ounces. The total amount of peanuts in the new mixture is $1.08 + 8.64 = 9.72$ ounces.

Step3: Calculate the percentage of peanuts in the new mixture

Let $p$ be the percentage of peanuts in the new mixture. We use the formula $p=\frac{\text{amount of peanuts}}{\text{total amount of mixture}}\times100\%$. So $p=\frac{9.72}{18}\times100\%=0.54\times100\% = 54\%$.

Answer:

$x=\frac{3}{2}$

Question #7