Question

What is the simplified form of the product Start fraction x squared plus eight x plus fifteen over x minus four end fraction times start fraction x squared minus sixteen over two x plus six end fraction ?

Answer 1

Divide: Left Parenthesis negative 7 x plus x-squared plus 15 Right Parenthesis divided by Left Parenthesis negative 3 plus x Right Parenthesis

Answer 2

Sarah picks a bushel of apples in 45 min. Andy picks a bushel of apples in 75 min. How long will it take them to pick a bushel together?
A. about 14 min
B. about 28 min
C. about 40 min
D. about 60 min

Answer 3

We can factor the first fraction as (x+3)(x+5)/(x-4), and the second fraction as (x-4)(x+4)/(2x+6).

Then, we can simplify by cancelling out common factors:

(x+3)(x+5)/(x-4) * (x-4)(x+4)/(2x+6)

= (x+3)(x+5)/(2x+6) * (x+4)

= (x+3)(x+5)/(2(x+3)) * (x+4)

= (x+5)/2 * (x+4)

= (x+5)(x+4)/2

Therefore, the simplified form of the product is (x+5)(x+4)/2.

Answer 4

We can use long division to divide polynomial expressions.

_____________
-3 + x | x^2 + (-7x + 15)
-x^2 + 3x
-----------
-4x + 15
-(-4x + 12)
---------
3

Therefore, (x^2 + (-7x + 15)) / (−3 + x) = x - 4 + (3 / (-3 + x)).

The final answer can also be expressed as (x-4) - 3/(x-3) or (x-4) + 3/(3-x).

Answer 5

Let's use the formula:

1/t = 1/t1 + 1/t2

where t is the time it takes for both Sarah and Andy to pick a bushel together, and t1 and t2 are the times it takes each of them individually.

Plugging in the values:

1/t = 1/45 + 1/75

Now we can simplify by finding a common denominator:

1/t = (5/225) + (3/225)

1/t = 8/225

Solving for t:

t = 225/8

t ≈ 28.125

So it would take Sarah and Andy approximately 28 minutes to pick a bushel of apples together.

Therefore, the answer is B. About 28 min.