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Phantasy [73]
2 years ago
5

What is the equation of the oblique asymptote? h(x) = x² – 3x - 4/x + 2

Mathematics
1 answer:
NNADVOKAT [17]2 years ago
4 0

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.

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4vir4ik [10]

The required number will be 16

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Anti - Venom

5 0
3 years ago
A small half bath measures 42 inches by 48 inches.What is the square footage of the half bath?
Mkey [24]
A=LW, we are told that the dimensions are 42 and 48 so:

A=42*48

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3 0
3 years ago
Read 2 more answers
Two Parallel lines are cut by a transversal x and a transversal y so that x and y intersect at point Q as shown.
saw5 [17]

Answer:

- Angle 'a' is an alternating exterior angle with one angle in the triangle and therefore congruent to one angle in the triangle formed by lines m, x, and y.

- Angles 'b' and 'c' are vertical angles with the other two angles in the triangle and therefore congruent to two other angles in the triangle

Step-by-step explanation:

Vertical angles are angles that are equal to each other but in opposite direction. The angles b and c have vertical angles on the triangle Q while alternate exterior angles are equal angles that lie on different lanes cutting through an axis.

Angles on a plane can be congruent if they are vertical equals or alternating exterior angles.

8 0
3 years ago
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 150 nails an
densk [106]

Answer:

28 small

9 large

Step-by-step explanation:

4200 ÷ 150 = 28 small

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7 0
3 years ago
Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the num
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Answer:

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2/6(50)

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