I'd start by writing an equation for each of the right triangles. (Pythagorean theorem)
y² + 9² = z²
x² + z² = (4+9)²
4² + y² = x²
we want to find z so combine the equations by substituting the other variables x,y out.
substitute y² for (x² - 4²) in 1st equation.
(x² - 4²) + 9² = z²
now by rearranging the 2nd equation we can substitute x² for (13² - z²)
(13² - z²) - 4² + 9² = z²
169 - z² - 16 + 81 = z²
234 - z² = z²
234 = 2z²
234/2 = z²
117 = z²
√(117) = z
√(9*13) = z
3√(13) = z
13 goes in the box
ANSWER
The coefficient is 70.
EXPLANATION
The given binomial expression is

The specific term of a binomial expansion can be determined using the formula,

where

We substitute these values into the formula to get,

We simplify to get,

Hence the coefficient is 70.
15/20 and 16/20
4/5 or 16/20 is greater
The area of the triangle ABC is 207.5 square units.
Explanation:
The measurements of the sides of the triangle are
,
and 
We need to determine the area of the triangle ABC.
<u>Area of the triangle:</u>
The area of the triangle can be determined using the formula,

where
,
and 
Substituting these values in the above formula, we get,

Simplifying the values, we get,



Rounding off to the nearest tenth, we get,
Thus, the area of the triangle ABC is 207.5 square units.
It'd be easier to do #18 if y ou were to break it up:
14* (first term + 14th term)
Sum from n=1 to 14 of n = S = ---------------------------------
14 2
14(1+14)
= ---------------- = 7(15) = 105
2
The sum of twice that is 210. The sum of "1 from n=1 to n=14" is just 14.
The final sum is 210 + 14 = 224 (answer)