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28 shaded triangles

Step-by-step explanation:

First, we have 0 shaded triangles.

Then we have 1 shaded triangle

then we have 3 shaded triangles

then we have 6 shaded triangles

In each new triangle, we add a base with a larger number of triangles.

In the base of the fourth triangle we have 3 triangles, then in the next triangle we have a base of 4 triangles, then we have 4 + 3 + 2 +1 triangles = 10 triangles.

in the sixth triangle the base has 5, so here we have 5 + 4+ 3 + 2 +1 = 15 triangles

in the seventh the base has 6 triangles, so here we have 15 + 6 = 21 shaded triangles

and in the height triangle, the base has 7 triangles, then we have 28 shaded triangles

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.

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!