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dybincka [34]
4 years ago
10

Solve for x. 4 | x - 7 | + 2 | x - 7 | = 12

Mathematics
1 answer:
miv72 [106K]4 years ago
7 0

Answer: x = 9, 5

<u>Step-by-step explanation:</u>

4 | x - 7 | + 2 | x - 7 | = 12

6 | x - 7 | = 12      <em>added like terms</em>

  | x - 7 | = 2       <em>divided both sides by 6</em>

x - 7 = 2         or         x - 7 = -2     <em>removed absolute value sign</em>

    x = 9         or               x = 5     <em>added 7 to both sides of both equations</em>

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Write the equation of a line perpendicular to 5x−9y=−8 that passes through the point ​(−5​,8​).
Fantom [35]

Answer:  y = -(9/5)x - 1

Step-by-step explanation:

Rewrite the equation in standard form:  y = (5/9)x+(8/9).  [y=mx+b]

A line perpendicular to this would have a slope that is the negative inverse of the original slope (5/9), which would make it -(9/5).  The y-intercept would also change, but we don't know the value, yet.  For now, we'll use "b" for the y-intercept.  This results in a perpendicular line:

y = -(9/5)x + b

We can calculate b, the y-intercept, by using the point (-5,8) and solving for b.

8 = -(9/5)*(-5) + b

8 = (9) + b

b = -1

The line perpendicular to 5x−9y=−8 that passes through the point ​(−5​,8​) is

y = -(9/5)x - 1

7 0
3 years ago
Point R lies on the directed line segment from L (-8,-10) to M (4,-2) and partitions the segment in the ratio 3 to 5. What are t
Dvinal [7]

Answer:

R = (- 3.5, - 7 )

Step-by-step explanation:

Using the Section formula

x_{R} = \frac{3(4)+5(-8)}{3+5} = \frac{12-40}{8} = \frac{-28}{8} = - 3.5

y_{R} = \frac{3(-2)+5(-10)}{3+5} = \frac{-6-50}{8} = \frac{-56}{8} = - 7

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7 0
4 years ago
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3 years ago
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3 years ago
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