Write each phrase as an algebraic expression.
1. 12 more than a number
2. The quotient of a number and 9
3. 4 times a number cubed decreased by 7
4. 15 less than a number squared
5. 3 more than 5 times the number of dogs
6. The product of 5 and y added to 3
7. 4 times the number of cows plus 2 times the number of ducks

0if x and y vary inversely and y=6 as x=7, what is the constant of variation?

If m∠abc = 70°, what is m∠abd? justify your reasoning.  using the addition property of equality, 40 + 70 = 110, so m∠abd = 110°.  using the subtraction property of equality, 70 − 30 = 40, so m∠abd = 30°.  using the angle addition postulate, 40 + m∠abd = 70. so, m∠abd = 30° using the subtraction property of equality.  using the angle addition postulate, 40 + 70 = m∠abd. so, m∠abd = 110° using the addition property of equality.

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?