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Nana76 [90]
3 years ago
9

If you place a 38-foot ladder against the top of a 32-foot building, how many feet will the bottom of the ladder be from the bot

tom of the building? Round to the nearest tenth of a foot.
Mathematics
1 answer:
TEA [102]3 years ago
7 0

Answer: 20.5

Step-by-step explanation:

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What is the equation of the oblique asymptote?<br> h(x) = x² – 3x - 4/x + 2
NNADVOKAT [17]

Simplifying h(x) gives

h(x) = (x² - 3x - 4) / (x + 2)

h(x) = ((x² + 4x + 4) - 4x - 4 - 3x - 4) / (x + 2)

h(x) = ((x + 2)² - 7x - 8) / (x + 2)

h(x) = ((x + 2)² - 7 (x + 2) - 14 - 8) / (x + 2)

h(x) = ((x + 2)² - 7 (x + 2) - 22) / (x + 2)

h(x) = (x + 2) - 7 - 22/(x + 2)

h(x) = x - 5 - 22/(x + 2)

An oblique asymptote of h(x) is a linear function p(x) = ax + b such that

\displaystyle \lim_{x\to\pm\infty} h(x) - p(x) = 0

In the simplified form of h(x), taking the limit as x gets arbitrarily large, we obviously have -22/(x + 2) converging to 0, while x - 5 approaches either +∞ or -∞. If we let p(x) = x - 5, however, we do have h(x) - p(x) approaching 0. So the oblique asymptote is the line y = x - 5.

4 0
2 years ago
what is the slope intercept form of the linear equation with a graph that passes through (-2,2) and is perpendicular to the grap
qwelly [4]

Hey there!!

Steps to get into equation which is perpendicular:

  • Change the slope
  1. The slope of a perpendicular line is always negative reciprocal.
  • Take the point and get that into point-slope form.
  1. y - y = m ( x - x )
  • Convert this equation into slope-intercept form.

'm' is the slope.

We have the slope as 1/3

The perpendicular slope would be -3.

Point slope:

The point = (-2,2)

y - 2 = -3( x - (-2) )

y - 2 = -3(x+2)

y - 2 = -3x -6

Adding 2 on both sides:

y = -3x - 4

<em>Hence, the equation would be : </em>

<u><em>y = -3x - 4 </em></u>

Hope it helps!


7 0
3 years ago
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