I'll focus on problem 19 and problem 22
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Problem 19
Answers:
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Explanation:
The horizontal lines are parallel. Note the arrow markers along the interior portion of the lines. These similar markers tell us how the lines pair up to be parallel to one another.
Since the horizontal lines are parallel, this means the angles in question are congruent. They are corresponding angles.
x+15 = 102
x = 102-15
x = 87
Which leads to
x+15 = 87+15 = 102
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Problem 22
Answer: y = 27
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Explanation:
We have a pair of alternate exterior angles. They are congruent due to the parallel lines.
Let's solve for y.
7y-55 = 3y+53
7y - 3y = 53+55
4y = 108
y = 108/4
y = 27
Answer:
0
Step-by-step explanation:
She will likely finish the graduation sessions in less time.
Answer:
k = -9.
Step-by-step explanation:
As the triangle is right-angled at Q, by Pythagoras:
PR^2 = PQ^2 + RQ^2
So, substituting the given data and using the distance formula between 2 points:
(7 - 1)^2 + (k - 4)^2 = (-4-4)^2 + (-3-1)^2 + (7 - (-3))^2 + (k - (-4))^2
36 + (k - 4)^2 = 64 + 16 + 100 + ( k + 4)^2
(k - 4)^2 - (k + 4)^2 = 180 - 36
k^2 - 8k + 16 - (k^2 + 8k + 16) = 144
-16k = 144
k = -9.
They will be greater for both of these answers because 5 is a larger number than -2 and -2 is a larger number than -5 and it comes before -5 on the number line
