A. Long division
Multiply x-4 by x^2 to get x^3-4x^2. Subtract product
(x^3-7x-6) - (x^3-4x^2) = 4x^2-7x-6
Now multiply x-4 by 4x to get 4x^2-16x. Subtract product
(4x^2-7x-6) - (4x^2-16x) = 9x-6
Now multiply x-4 by 9 to get 9x-36. Subtract product
(9x-6) - (9x-36) = 30
Remainder = (x^3-7x-6)/(x-4) = 30
B. using the Polynomial Remainder Theorem
which says that if a polynomial f(y) is divided by a linear expression (x-a), the remainder equals f(a).
Here f(x)=x^3-7x-6, and (x-a)=(x-4)), i.e. a=4
according to the Polynomial Remainder Theorem,
Remainder = f(4) = (4)^3-7(4)-6 = 64-28-6 = 30 (as before)
Answer:
<em>9 sheep and 5 goats</em>
Step-by-step explanation:
s + g = 14
125s + 75g = 1500
125( 14 - g ) + 75g = 1500
1750 - 125 g + 75g = 1500
50g = 250
g = <em>5 goats</em>
s = <em>9 sheep</em>
Answer:
C is the correct answer
Step-by-step explanation:
A P E X
Here's a little known but very useful factoid:
If they're inversely proportional,
then their product is constant.
Here's how to use it:
-- We're told that Y = 8 when X = 7.
So when y=8 and x=7, their product is 56 .
-- If Y REALLY varies inversely as X, then
their product is ALWAYS going to be 56.
-- So when Y=4, X= (56/4) = 14 .
