Show your work
1. m^2 + m -12/m^2-16
2. Suppose p and q vary inversely and p=14 when q=4. Find p when q=8.
3. x^2- 49/x - 2 • x^2 - 5x + 6/x^2+ 4x-21
4. Malik’s weekly pay varies directly to the number of hours he works as a lifeguard. His weekly pay is $229.50 when he works 17 hours. What is his weekly salary when he works 23 hours? Note: Write a direct variation equation representing this situation and use this equation to answer the question.
5. y= x + 1/x^2 - 6x - 7
1. To simplify the expression m^2 + m - 12/m^2 - 16, we can first factor the denominator as (m+4)(m-4) to get:
(m^2 + m - 12)/((m+4)(m-4))
Factor the numerator as (m+4)(m-3) to get:
((m+4)(m-3))/((m+4)(m-4))
(m - 3)/(m - 4)
2. If p and q vary inversely, it means that p = k/q where k is a constant. Given that p=14 when q=4, we can find k:
14 = k/4
k = 56
Now, we can find p when q=8:
p = 56/8
p = 7
3. To simplify the expression x^2-49/x - 2 • x^2 - 5x + 6/x^2+ 4x-21, we can first factor all the denominators:
(x^2-49)/(x) - 2 • (x^2-5x+6)/(x^2+4x-21)
(x+7)(x-7)/(x) - 2 • (x-3)(x-2)/(x-3)(x+7)
(x-7) - 2(x-2)/(x)
(x-7 - 2x + 4)/x
(-x - 3)/x
4. Since Malik's weekly pay varies directly with the number of hours worked, we can write a direct variation equation as:
weekly pay = (hourly pay rate) * (number of hours)
Given that his weekly pay is $229.50 when he works 17 hours, we can find the hourly pay rate:
229.50 = hourly pay rate * 17
hourly pay rate = 229.50/17
hourly pay rate ≈ $13.50
Now, we can find his weekly salary when he works 23 hours:
weekly pay = $13.50 * 23
weekly pay = $310.50
5. To simplify the expression y=x+1/x^2-6x-7, we can first factor the denominator:
y=x+1/((x-7)(x+1))
y=x+1/(x^2-6x-7)
y=x+1/((x-7)(x+1))