Using the rectangular route Mike rides 12 miles. If he rides diagonally the distance is √2²+10²=√4+100=√104.
The difference between the two routes is 12-√104=1.80 miles approximately.
<h3>Answer: 7 goes in the blank space</h3>
The range of values for x is 2 < x < 7
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Explanation:
The hinge theorem says that the larger the opposite side is, the larger the angle will be.
AD = 11, DC = 8
Since AD > DC, this means angle ABD > angle DBC.
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angle ABD > angle DBC
20 > 4x-8
20+8 > 4x-8+8 ... add 8 to both sides
28 > 4x
4x < 28 ... flip both sides and the inequality sign
4x/4 < 28/4 ... divide both sides by 4
x < 7
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At the same time, the angle 4x-8 cannot be 0 or negative.
So we say 4x-8 > 0. Let's solve this for x.
4x-8 > 0
4x-8+8 > 0+8 ... add 8 to both sides
4x > 8
4x/4 > 8/4 ... divide both sides by 4
x > 2
2 < x ... flip both sides and the inequality sign
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We have 2 < x and x < 7. Both of these combine to the compound inequality 2 < x < 7
We can pick any value between 2 and 7 as long as we dont pick x = 2 or we dont pick x = 7.
<em>x = 8</em>
Step-by-step explanation:
Add 1 to both sides.
Add 2x to both sides.
Divide 40 by 5.
x = 8
Answer:
7t
Step-by-step explanation:
Answer:
Thus # 2 is correct (5 (y + 4))/2
Step-by-step explanation:
Simplify the following:
(5 y (y^2 - 16))/(2 y (y - 4))
(5 y (y^2 - 16))/(2 y (y - 4)) = y/y×(5 (y^2 - 16))/(2 (y - 4)) = (5 (y^2 - 16))/(2 (y - 4)):
(5 (y^2 - 16))/(2 (y - 4))
y^2 - 16 = y^2 - 4^2:
(5 (y^2 - 4^2))/(2 (y - 4))
Factor the difference of two squares. y^2 - 4^2 = (y - 4) (y + 4):
(5 (y - 4) (y + 4))/(2 (y - 4))
Cancel terms. (5 (y - 4) (y + 4))/(2 (y - 4)) = (5 (y + 4))/2:
Answer: (5 (y + 4))/2