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denis23 [38]
3 years ago
11

Which of the following pairs of lines are perpendicular? How do you know?

Mathematics
1 answer:
Alexeev081 [22]3 years ago
7 0
Hi mate:
Here is your explanation......


Which of the following is perpendicular to 32=16y+64x

Possible Answers:
y=−x/4+7

y=4x+7

y=−4x+7

y=x+1/4

y=x/4+7

Correct answer:
y=x/4+7

Explanation:
Two lines are perpendicular if and only if their slopes are negative reciprocals. To find the slope, we must put the equation into slope-intercept form, y=mx+b, where m equals the slope of the line. We begin by subtracting 16y from each side, giving us 32−16y=64x. Next, we subtract 32 from each side, giving us −16y=64x−32. Finally, we divide each side by −16, giving us y=−4x+2. We can now see that the slope is −4. Therefore, any line perpendicular to 32=16y+64x must have a slope of 1/4. Of the equations above, only y=x/4+7 has a slope of 1/4.

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Answers:

Choice C)  1.5 + AB = 3.7

AB = 2.2  cm

====================================================

Explanation:

Segment AC can be cut into two smaller pieces AB and BC. The piece AB is of unknown length for now, while BC is 1.5 units long.

The expression AB+1.5 or 1.5+AB represents us adding those two smaller pieces together. Doing so will lead to the length of AC.

Therefore, 1.5 + AB = 3.7 is one valid equation to set up.

------------

To solve that equation, we subtract 1.5 from both sides to undo the addition operation done to AB.

1.5 + AB = 3.7

AB = 3.7 - 1.5

AB = 2.2

Notice how,

1.5 + AB = 1.5 + 2.2 = 3.7

to help confirm our answer.

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