The polynomial remainder theorem states that the remainder upon dividing a polynomial

by

is the same as the value of

, so to find

you need to find the remainder upon dividing

You have
..... | 2 ... 14 ... -58
-10 | ... -20 ... 60
--------------------------
..... | 2 ... -6 .... 2
So the quotient and remainder upon dividing is

with a remainder of 2, which means

.
Option B: 4.0 cm is the value of w
Explanation:
It is given that
,
,
and 
Using the law of sines, we have,

Substituting the values, we have,

Cross multiplying, we get,

Simplifying, we have,

Dividing both sides by 0.515, we have,

Thus, the value of w is 4.0 cm
Hence, Option B is the correct answer.
David will finish first, because if you divide Brad's miles by 2 to his miles in a 1/4 of an hour are 5.95 miles. This means David went 6.2 miles in the same time that Brad went 5.95. Therefore, David will finish first.
<u>ΔACB</u> <u>ΔCDA</u>
AC² + BC² = AB² AD² + CD² = AC²
BC² = AB² - AC² BC² + CD² = AC² (AD=BC is given)
BC² = AC² - CD²
AB² - AC² = AC² - CD² (both sides were = to BC²)
AB² + CD² = 2AC²
(3)² + (√2)² = 2AC² (AB=3 and CD=√2 were given)
9 + 2 = 2AC²
11 = 2AC²
= AC²
= AC
= AC
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