Answer:
x ∈ (-∞, -1) ∪ (1, ∞)
Step-by-step explanation:
To solve this problem we must factor the expression that is shown in the denominator of the inequality.
So, we have:
So the roots are:
Therefore we can write the expression in the following way:
Now the expression is as follows:
Now we use the study of signs to solve this inequality.
We have 3 roots for the polynomials that make up the expression:
We know that the first two are not allowed because they make the denominator zero.
Observe the attached image.
Note that:
when 
when 
and
is always 
Finally after the study of signs we can reach the conclusion that:
x ∈ (-∞, -1) ∪ (1, 2] ∪ [2, ∞)
This is the same as
x ∈ (-∞, -1) ∪ (1, ∞)
Answer:
- asymptotes: x = -4, x = 4
- zeros: x = 0
Step-by-step explanation:
The vertical asymptotes of the rational expression are the places where the denominator is zero:
x^2 -16 = 0
(x -4)(x +4) = 0 . . . . . true for x=4, x=-4
x = 4, x = -4 are the equations of the vertical asymptotes
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The zeros of a rational expression are the places where the numerator is zero:
4x = 0
x = 0 . . . . . . divide by 4
Did you mean -10? If so that is -1 and 10. 10 and 9 is not possible to answer.
-1+10=9
-1*10=-10
Answer:
70 inches
Step-by-step explanation:
10 in x 7 in =70 inches
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Answer:
See below.
Step-by-step explanation:
Equation of parabola:
y = some expression in x^2
To translate the parabola vertically, substitute y with y - k.
The translation is k units vertically. If k is positive, the translation is up. If k is negative the translation is down.
Example 1:
original parabola: y = x^2 - 2x + 5
To translate it 3 units up, we need k = 3.
Substitute y with y - 5 to get
y - 3 = x^2 - 2x + 5
y = x^2 - 2x + 8 is the equation of the parabola translated 3 units up.
Example 2:
original parabola: y = 2x^2 + 4x - 6
To translate it 5 units down, we need k = -5.
Substitute y with y - (-5), or y = 5 to get
y + 5 = 2x^2 + 4x - 6
y = 2x^2 + 4x - 11
y = 2x^2 + 4x - 11 is the equation of the parabola translated 5 units down.
