For the rational expression 2x^2-7x-15/x^2-25, do both of the following,
1 answer:
Answer:
a.
b. x ≠ -5 (Vertical asymptote) and x ≠ 5 (Hole)
Step-by-step explanation:
Factor the numerator (Grouping):
Two numbers that multiply to -30 and add to -7 = -3 and 10
Factor the denominator (Difference of Two Squares):
=
Factored Expression:
(x - 5) can be factored out of top and bottom as a hole-
Variable Restrictions:
Denominator ≠ 0
Vertical asymptote at x = -5 ⇒ x ≠ -5
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In order to answer this question, the figure in the first picture will be helpful to understand what a right triangle is. Here, a right angle refers to .
However, if we want to solve the problem we have to know certain things before:
In the second figure is shown a general right triangle with its three sides and another given angle, we will name it :
- The side <u>opposite to the right angle</u> is called The Hypotenuse (h)
- The side <u>opposite to the angle
</u> is called the Opposite (O)
- The side <u>next to the angle
So, going back to the triangle of our question (first figure):
- The Hypotenuse is AB
- The Opposite is BC
- The Adjacent is AC
Now, if we want to find the length of each side of a right triangle, we have to use the <u>Pythagorean Theorem</u> and T<u>rigonometric Functions:</u>
Pythagorean Theorem
(1)
Trigonometric Functions (here are shown three of them):
Sine: (2)
Cosine: (3)
Tangent: (4)
In this case the function that works for this problem is cosine (3), let’s apply it here:
(5)
And we will use the Pythagorean Theorem to find the hypotenuse, as well:
(6)
(7)
Substitute (7) in (5):
Then clear BC, which is the side we want:
Finally is approximately 13 cm
