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. (m^2 + m - 12) / (m^2 - 16)
2. Since p and q vary inversely, we have the equation p * q = k, where k is a constant. Given that p = 14 when q = 4, we can solve for k:
14 * 4 = k
k = 56
Now, when q = 8:
p * 8 = 56
p = 7
3. ((x^2 - 49) / (x - 2)) * ((x^2 - 5x + 6) / (x^2 + 4x - 21))
4. Since Malik's weekly pay varies directly with the number of hours he works, we can write a direct variation equation as follows: pay = k * hours. Given that his weekly pay is $229.50 when he works 17 hours, we can solve for k:
229.50 = k * 17
k = 13.50
Now, when Malik works 23 hours:
pay = 13.50 * 23
pay = $310.50
5. y = (x + 1) / (x^2 - 6x - 7)