In ΔBCD, \text{m}\angle B = (4x-14)^{\circ}m∠B=(4x−14) ∘ , \text{m}\angle C = (x-1)^{\circ}m∠C=(x−1) ∘ , and \text{m}\angle D = (6x+8)^{\circ}m∠D=(6x+8) ∘ . What is the value of x?X?

Step-by-step explanation:

The sum of angle in the triangle BCD is 180 degrees

Given;

<B = 4x  -14

<C = x - 1

<D = 6x + 8

Required

Find x

Since <B + <C + <D = 180, hence;

4x - 14 + x - 1 + 6x + 8 = 180

11x -7 = 180

11x = 180+7

11x = 187

x = 187/11

x = 17

Hence the value of x is 17

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!