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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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X-5y=2 and 9x+8=15 solve by substitution
lozanna [386]
x-5y=2
Hence x=2+5y   (Equation I)
9x+8=15             (Equation II)
Substituting Equation I in Equation II
9(2+5y)+8=15
18+45y+8=15
26+45y=15
45y=-11
Hence y= - \frac{11}{45}

Substituting this in Equation in I to get X

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7 0
3 years ago
Can someone help me? Please show your work.
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We know that the perimeter of a rectangle can be represented by the expression 2l +2w, where l represents the length of the rectangle and w represents the width of the rectangle.

If we substitute in the values given in this problem, we get the expression:
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Another equivalent expression we can use to express the perimeter is w + w + l + l.

If we substitute in the values given in this problem into this expression, we get:

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Overall, we know that these expressions are equivalent and represent the same value (the perimeter of the rectangle), because if you combine like terms, both expressions simplify to 6x + 12.

Hope this helps!
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