BRAiNLIES AND 10 POINTS What is the length of the third side of the window frame below?
10 inches
12 inches
16 inches
20 inches

20 inches

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Leg a = x

Leg b = 48

Hypotenuse c = 52

Step 2: Solve for x

20 inches

Step-by-step explanation:

Since this is a right triangle, we'll use the Pythagorean Theorem

a^2 + b^2 = c^2

48^2 + b^2 = 52^2

2304 + b^2 = 2704

subtract 2304 from both sides

b^2 = 400

b = 20

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.