Answers:
- Part A) There is one pair of parallel sides
- Part B) (-3, -5/2) and (-1/2, 5/2)
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Explanation:
Part A
By definition, a trapezoid has exactly one pair of parallel sides. The other opposite sides aren't parallel. In this case, we'd need to prove that PQ is parallel to RS by seeing if the slopes are the same or not. Parallel lines have equal slopes.
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Part B
The midsegment has both endpoints as the midpoints of the non-parallel sides.
The midpoint of segment PS is found by adding the corresponding coordinates and dividing by 2.
x coord = (x1+x2)/2 = (-4+(-2))/2 = -6/2 = -3
y coord = (y1+y2)/2 = (-1+(-4))/2 = -5/2
The midpoint of segment PS is (-3, -5/2)
Repeat those steps to find the midpoint of QR
x coord = (x1+x2)/2 = (-2+1)/2 = -1/2
y coord = (x1+x2)/2 = (3+2)/2 = 5/2
The midpoint of QR is (-1/2, 5/2)
Join these midpoints up to form the midsegment. The midsegment is parallel to PQ and RS.
Student's error is –5 < x.
Solution:
Step 1: Given inequality
31 < –5x + 6
Step 2: Subtract 6 from both sides of the inequality.
31 – 6 < –5x + 6 – 6
25 < –5x
Step 3: Multiply both sides by –1 to reverse the inequality.
25 × (–1) > –5x × (–1)
–25 > 5x
Step 4: Divide by 5 on both sides.
–5 > x
The correct answer is –5 > x.
Student's error is –5 < x.
The total amount of tax on her purchases to the nearest cent will be $9.97
<em><u>Explanation</u></em>
Marcella Heinz purchased office supplies for $107.64 and then she purchased an English-Spanish dictionary for $16.95
So, the total amount of her purchases 
On the total amount of the purchases, she paid state sales tax of 7.5% and the county tax of 0.5%
So, the <u>amount of the state sales tax</u> 
and the <u>amount of county tax</u> 
Thus, the total amount of tax on her purchases 
<em>(Rounded to the nearest cent)</em>
Answer:
21 3/4
Step-by-step explanation:
3 times 7 1/4 since the scale is 1:7 1/4. Good luck!! :)
4x+1=2x+7
-1 -1
4x=2x+6
-2x -2x
2x=6
2x/2- 6/2
X=3
