Mathematics, 21.11.2019 17:31 azimgd1612

Can any one me with this it is gemo.

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Answer from: deena7

Area of the shaded region in the figure below (As):
As=Total area of the circle - area of the sector of 120º +area of the triangle

1)We calculate the total area of this circle
Area of a circle=πr²
r=radius=9 cm

Area of a circle=π(9 cm)²=81π cm²

2)We calculate the area of the sector of 120º
Area of the sector=(120º/360º)πr²=(1/3)π(9 cm)²=(81/3)π cm²

3) we calculate the area of the triangle
1) we calculate the base of this triangle by cousine theorem:
a²=b²+c²-2bc(cos Ф)
a²=(9 cm)²+(9 cm)²-2(9cm)(9 cm)cos 120º=243 cm
a=√243 cm

2)we calculate the height of this triangle by Pythagoras theorem:
a²=b²+c²
This triangle can be divided in two right triangles:
hypotenuse=9 cm
leg 1=√243/2 cm
leg 2=height

(9 cm)²=(√243 /2 cm)²+height²
height²=√(81 cm²-60.75 cm²)=20.25 cm
height=√20.25 cm=4.5 cm

Area of the triangle=(base x height) / 2=(√243 cm * 4.5 cm)/2=20.25√3 cm²

As=Total area of the circle - area of the sector of 120º +area of the triangle
As=81π cm²-81/3 π cm²+20.25√3 cm²=54π+20.25√3 cm²

c (54π+20.25√3) cm²

Answer from: Quest

well my understanding of this question is they want you to use the y=14.1x -2.3 and put the coordinates they gave you onto the line segment of y=14.1x -2.3

step-by-step explanation:

Answer from: Quest

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

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

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

g(x)

g(2)

=2x

=2⋅2

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!

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