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Elden [556K]
3 years ago
15

For the rational expression 2x^2-7x-15/x^2-25, do both of the following,

Mathematics
1 answer:
Mrrafil [7]3 years ago
3 0

Answer:

a. \frac{2x + 3}{x+5}

b. x ≠ -5 (Vertical asymptote) and x ≠ 5 (Hole)

Step-by-step explanation:

Factor the numerator (Grouping):

2x^2 - 7x - 15              

Two numbers that multiply to -30 and add to -7 = -3 and 10

[2x^2 - 10x] + [3x - 15]

(2x + 3)(x - 5)

Factor the denominator (Difference of Two Squares):

x^2 - 25 = (x +5)(x-5)

Factored Expression:

(x - 5) can be factored out of top and bottom as a hole-

\frac{(2x + 3)(x - 5)}{(x + 5)(x - 5)} = \frac{2x + 3}{x+5}

Variable Restrictions:

Denominator ≠ 0

x + 5 = 0\\x = -5

Vertical asymptote at x = -5 ⇒ x ≠ -5

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Given:
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Use polynomial long division to rewrite the following fraction in the form q(x)+r(x)d(x), where d(x) is the denominator of the o
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Step-by-step explanation:

p(x) = 2x^2+8x-12

d(x) = x + 1

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\\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  2x +6 \\ x  + 1 \sqrt{ {2x}^{2}  + 8x - 12}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  {2x}^{2}  + 2x \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \frac{  \: -  \:  \:  \:  \:  \:  \:  -  \:  \:  \:  \:  \: }{}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  6x - 12 \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 6x + 1 \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \frac{ -  \:  \:    -  \:  \:  \:  \:  \: }{}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  - 13

q(x)+r(x)d(x)

= 2x + 6 + (-13) * x + 1

= 2x + 6 -13 * x + 1

= 2x + 6 - 13x + 1

= (- 11x + 7)

6 0
3 years ago
Can someone help me with these probability questions?? i want to make sure that i solved these questions right.
kaheart [24]
When you say "I want to make sure that I solved them correctly,
the tasteful, less suspicious thing to do is to list YOUR solutions,
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1). HHH
HHT
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d). There are 3 ways that can happen.  3/8 = 0.375 = 37.5%

2). There are 16 possible outcomes.
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c). There's only 1 way that can happen, so it's 6.25% .
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e). There are 4 ways that can happen.  Prob = 4/16 = 25%
7 0
3 years ago
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