Question

5.
a. andre received and spent money in the following ways last month. for each example, write a positive or negative number to represent the change in money from his perspective.
i. his uncle gave him $25 as a present.
ii. he earned $18 dollars tutoring.
iii. he spent $10 on a book.
b. what does 0 mean in this situation?
6.
a. plot and label these four points in the coordinate plane.
$a=(2, 3), b=(-2, 1), c=(4, -5), d=(-3, -5)$
b. find the distance between c and d.

Explanation:

Step1: Represent money gain as positive

i. $+25$
ii. $+18$

Step2: Represent money spent as negative

iii. $-10$

Step3: Define 0 in this context

0 means no change in Andre's money (no money gained or spent).

Step4: Identify point coordinates for plotting

Points: $A=(2, 3)$, $B=(-2, 1)$, $C=(4, -5)$, $D=(-3, -5)$
(Note: Plotting instructions: For $A$, move 2 right on x-axis, 3 up on y-axis; for $B$, 2 left on x-axis, 1 up; for $C$, 4 right on x-axis, 5 down; for $D$, 3 left on x-axis, 5 down, then label each point.)

Step5: Calculate distance between C and D

Since $C=(4, -5)$ and $D=(-3, -5)$ share the same y-coordinate, use horizontal distance formula: $|x_2 - x_1|$
$\text{Distance} = |4 - (-3)| = |7| = 7$

Answer:

1. a.

i. $25$
ii. $18$
iii. $-10$

1. b. 0 means Andre did not gain or spend any money (no change in his total money).
2. a. (Plot the points as described: $A$ at (2,3), $B$ at (-2,1), $C$ at (4,-5), $D$ at (-3,-5) on the coordinate plane)
3. b. $7$