+0

# Find the area of the region determined by the inequalities

0
100
3

Find the area of the region determined by the inequalities $$y \ge |x|$$ and $$y \leq -|x+1| + 4.$$

May 16, 2020

#1
0

Graphing would be one way to find out which areas are covered by the inequalities.

May 16, 2020
#2
0

I tried to graph it, but it's telling me my answer is wrong and I would like to see if anyone has an algebraic way of solving it. (or an explanation for the graphing method).

Guest May 16, 2020
#3
+111456
+1

Graphing  is definitely WAY easier  than an algebraic method

This shows  that  we really have the area of a simple region  (a rectangle)

https://www.desmos.com/calculator/xood3yofrf

One dimension of the rectangle  is   sqrt [( 1.5^2 + 1.5^2]  = 1.5sqrt (2)

And the other  is    sqrt [ 2.5^2 + 2.5^2]  = 2.5sqrt(2)

The area is   ( 1.5) (2.5) sqrt (2) * sqrt (2)  =  3.75 * 2  =    7

May 16, 2020