Liza y Abby planean extender sus mantas en un parque para un picnic con sus amigos. El parque está lleno de gente, así que extienden sus mantas como se muestra en el diagrama. 5.7 pies5.7 \text{ pies} 5.7 pies 4 pies4 \text{ pies} 4 pies 2 pies2 \text{ pies} 2 pies 5 pies5 \text{ pies} 5 pies 6 pies6 \text{ pies} 6 pies Determina el área total area que Liza y Abby tienen para su picnic.

Step-by-step explanation:

The question in English is basically find the area of the pink and blue area shown. The image is attached. This is Liza and Abby's blanket spread and we want the area of the whole shown.

Solution:

We want area of pink rectangle PLUS the blue region, which is a sum of lower rectangle and top triangle (if we cut it in this way).

First, area of pink rectangle:

Area = length * height

Area = 5 * 5.7

Area = 28.5

Now, the blue region, if broken down, lower portion is rectangle and upper portion is a triangle (we DISREGARD the overlapping region, of course!)

Lower Rectangle Area = length * height = 4 * 2 = 8

Upper triangle Area = 0.5 * base * height = 0.5 (4) * (6-2) = 0.5 * 4 * 4 = 8

So, blue region area = 8 + 8 = 16

Total Area = 28.5 + 16 = 44.5 sq. ft.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )