6. Alicia and Margaret did jumping jacks.
Alicia : (1, 30) (2,60) (3,90) (4,120) (5,150) (6,180) (7,210) (8,240)
Margaret :(4,100) (8,200)
Which choice best describes the difference between
the rates at which the girls did jumping jacks?
H. Margaret did 5 more jumping jacks per minute
than Alicia.
I. Alicia did 5 more jumping jacks per minute than
Margaret.
J. They did the same number of jumping jacks per
minute.
H. Margaret did 5 more jumping jacks per minute than Alicia.
Explanation:
To find the rates at which the girls did jumping jacks, we divide the total number of jumping jacks by the corresponding time intervals.
For Alicia:
- (1,30) gives a rate of 30 jumping jacks per minute
- (2,60) gives a rate of 30 jumping jacks per minute
- (3,90) gives a rate of 30 jumping jacks per minute
- (4,120) gives a rate of 30 jumping jacks per minute
- (5,150) gives a rate of 30 jumping jacks per minute
- (6,180) gives a rate of 30 jumping jacks per minute
- (7,210) gives a rate of 30 jumping jacks per minute
- (8,240) gives a rate of 30 jumping jacks per minute
So, Alicia did 30 jumping jacks per minute consistently.
For Margaret:
- (4,100) gives a rate of 25 jumping jacks per minute
- (8,200) gives a rate of 25 jumping jacks per minute
So, Margaret did 25 jumping jacks per minute consistently which is 5 less than Alicia. Hence, choice H is correct.
7. What is the slope of the line? Explain: I found the slope by _____________
______________________________________________.
I knew it was positive/negative (circle one)
because it is _______________________________
______________________________________________.
4. How many solutions does the
equation have?
8 + 3(x − 6) = −2 + 3x − 4
R. one solution
S. infinite solutions
T. no solutions
Work:
5. How many solutions does the
equation have?
8 + 2(x − 6) = −2 + 2x − 2
S. one solution
T. infinite solutions
U. no solutions
Work:
Graphing Linear Equations Unit Rate, Slope from a Graph, Write Linear Equation from a Graph, Graph Linear
Equations, Write an Equation in Slope-Intercept Form
L. -4
M. 2
N. -2
7. To find the slope of a line, you need to determine the change in y-values divided by the change in x-values between two points on the line. The formula for finding slope is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Once you plug in the coordinates of the two points, simplify the expression to find the slope.
You would know if the slope is positive or negative based on whether the line is sloping upwards from left to right (positive slope) or downwards from left to right (negative slope).
4. To find the solutions to the equation 8 + 3(x - 6) = -2 + 3x - 4, you first simplify the equation:
8 + 3x - 18 = -2 + 3x - 4
3x - 10 = 3x - 6
-10 = -6
The equation becomes -10 = -6, which is not true. Since the equation results in a false statement, there are no solutions. The answer is T. no solutions.
5. To find the solutions to the equation 8 + 2(x - 6) = -2 + 2x - 2, you first simplify the equation:
8 + 2x - 12 = -2 + 2x - 2
2x - 4 = 2x - 4
Since the equation simplifies to 2x - 4 = 2x - 4, it is an identity where both sides are equal. This means that the equation is true for all values of x, resulting in infinite solutions. The answer is S. infinite solutions.