If Luke can now mow 10 yards in 5 hours, how many lawns can he mow in 8 hours?
2 answers:
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Problem 18
Answers:
~P -> Q: "if it is not fall, then the leaves change colors"
~P -> ~Q: "if it is not fall, then the leaves don't change colors"
P -> ~Q: "If it is fall, then the leaves don't change colors"
Q -> ~P: "If the leaves change colors, then it is not fall"
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Explanation:
Simply replace each letter with the corresponding definition. We replace each P with "it is fall" and each ~P with "it is not fall". The squiggly line means "not". The same idea applies with Q and ~Q.
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Problem 19
Answer: Choice A) 134
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Explanation:
AB = CD
8x = 4x+24
8x-4x = 24
4x = 24
x = 6
BC = 18x+26
BC = 18*6+26
BC = 134
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Problem 20
Answer: Choice C) x = 5 and y = 11
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Explanation:
(anglePQR)+(angleRQS) = 90
(12x-2)+(6x+2) = 90
18x = 90
x = 5
angle TQU = 90
10y-20 = 90
10y = 110
y = 11
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Problem 21
Answer: 99
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Explanation:
The remote interior angles add to the exterior angle (remote interior angle theorem)
(angle RPQ) + (angle PQR) = angle PRS
(3x-29) + (7x-42) = 6x-3
10x-71 = 6x-3
10x-6x = -3+71
4x = 68
x = 68/4
x = 17
angle PRS = 6x-3
angle PRS = 6*17-3
angle PRS = 99
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Problem 22
Answer: 116
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Explanation:
Refer to the diagram below.
Solve 105+x = 180 to get x = 75
Solve 135+y = 180 to get y = 45
Solve x+y+z = 180 to get z = 60
Solve z+82+p = 180 to get p = 38
Solve p+78+q = 180 to get q = 64
Solve q+r = 180 to get r = 116
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Problem 23
Answer: B) between 4 and 44 inches
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Explanation:
We use a variation of the triangle inequality theorem here.
If p is the missing side length, then
24-20 < p < 24+20
4 < p < 44
So,
4 < XY < 44
The side XY cannot be 4 inches and it cannot be 44 inches either.
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Problem 24
4 Answers: A, B, C, D
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Explanation:
Same idea as problem 23
24-10 < x < 24+10
14 < x < 34
So we'll select values between 14 and 34, excluding each endpoint. Those values are x = 16, 18, 24, 26
In other words, only 12 and 34 are non-answers.
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Problem 25
Answer: C) 84 degrees
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Explanation:
The given exterior angle is 152 degrees
Subtract that from 180 to get the adjacent interior angle 180-152 = 28
Now let's find the missing angle of triangle DEB
D+E+B = 180
28+68+B = 180
96+B = 180
B = 180-96
B = 84
This is the measure of angle DBE
This is also the measure of angle ABC because the two angles are vertical angles.
Vertical angles are always congruent.
Answer:
a) where "
" stands for the number of miles driven.
b) He can drive as far as 250 miles to keep the rental cost limited to $140.
Step-by-step explanation:
a) Robert wants to make sure that the addition of the costs coming from the car rental per week ($91) plus the amount paid for the coverage of "x" number of miles (which goes as $0.14 times x) does not exceed $140 (which is the same as saying that this total cost must be smaller than or equal to $140.
In math terms, such is written as:
where "x" stands for the number of miles driven.
b) the total number of miles (x) he is allowed to cover given the $140 restriction is obtained by solving for "x" (the number of driven miles) in the inequality of part a):
which tells us that the number of driven miles (x) has to be smaller or equal to 350 miles. Then he can drive as far as 250 miles to keep the rental cost limited to $140.