Question

1. if 2x = 12, what is the value of 9x?
2. line k is defined by y = \frac{1}{4}x + 1. line j is parallel to line k in the xy - plane. what is the slope of j?
3. 6, 6, 8, 8, 8, 10, 21. which of the following lists represents a data set that has the same median as the data set shown? a) 4, 6, 6, 6, 8, 8 b) 6, 6, 8, 8, 10, 10 c) 6, 8, 10, 10, 10, 12 d) 8, 8, 10, 10, 21, 21
4. the length of the base of a certain parallelogram is 89% of the height of the parallelogram. which expression represents the length of the base of the parallelogram, where h is the height of the parallelogram? a) 89h b) 0.089h c) 8.9h d) 0.89h
5. for a camping trip a group bought x one - liter bottles of water and y three - liter bottles of water, for a total of 240 liters of water. which equation represents this situation? a) x + 3y = 240 b) x + y = 240 c) 3x + 3y = 240 d) 3x + y = 240

Explanation:

6.

Step1: Solve for x

Given $2x = 12$, then $x=\frac{12}{2}=6$.

Step2: Find the value of 9x

Substitute $x = 6$ into $9x$, so $9x=9\times6 = 54$.

Parallel lines have the same slope. The equation of line $k$ is $y=\frac{1}{4}x + 1$, which is in slope - intercept form $y=mx + b$ where $m$ is the slope. So the slope of line $k$ is $\frac{1}{4}$. Since line $j$ is parallel to line $k$, the slope of line $j$ is also $\frac{1}{4}$.

First, find the median of the data - set $6,6,8,8,8,10,21$. There are 7 numbers. The median is the 4th number when the data is arranged in ascending order, so the median is 8.
For option A: The data - set $4,6,6,6,8,8$ has 6 numbers. The median is $\frac{6 + 6}{2}=6$.
For option B: The data - set $6,6,8,8,10,10$ has 6 numbers. The median is $\frac{8 + 8}{2}=8$.
For option C: The data - set $6,8,10,10,10,12$ has 6 numbers. The median is $\frac{10+10}{2}=10$.
For option D: The data - set $8,8,10,10,21,21$ has 6 numbers. The median is $\frac{10 + 10}{2}=10$.

Answer:

54

7.