In triangle abc, m∠abc = (4x – 12)° and m∠acb = (2x + 26)°. yin says that if x = 19, the triangle must be equilateral. is he correct? justify your answer

No, Yin is not correct. If  x = 19, the measure of angle ABC = 4(19) – 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.

Yin is incorrect because when the value of x is 19 both the angles is equal to but in equilateral triangle all the angles must be equal to and this can be determine by using the properties of equilateral triangle.

Given :

In triangle ABC, ABC = (4x – 12)° and ACB = (2x + 26)°.

In equilateral triangle all the three sides of the triangle are equal and all the interior angles are congruent to each other and equal to .

So, to prove that the given triangle ABC is an equilateral triangle than both the given angles must be equal to .

= 76 - 12

=

= 38 + 26

=

Therefore, Yin is incorrect because when the value of x is 19 both the angles is equal to but in equilateral triangle all the angles must be equal to .

For more information, refer the link given below:

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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!

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18