The points a(0, 0), b(0, 4a - 5) and c(2a + 1, 2a + 6) form a triangle. if angle abc = 90, what is the area of triangle abc? (a) 102(b) 120(c) 132(d) 144(e) 156

A:102

Step-by-step explanation:

We are given that the points A(0,0),B(0,4a-5) and C(2a-+1,2a+6) form a triangle.

If angle ABC=

We have to find the area of triangle ABC

If angle ABC= 90 degree

From given below figure

Substitute the values then we get

B(0,17) and C (12,17)

Distance formula

AB=

BC=

BC= units

Area of triangle =

Substitute the values

Then we get

Area of triangle ABC=

Area of triangle ABC=102 square units

A: 102

step-by-step explanation: step 3 should really go to step seven, but anyway never mind.

1 ∠oln ≅ ∠lno

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!