The age of Noelle’s dad is 6 less than 3 times Noelle’s age. The sum of their ages is 74. Find their ages

Noelle: 20 Dad: 54

Step-by-step explanation:

The age of Noelle's Dad is 6 less than 3 times Noelle's age looks like this:

d=3n-6

While the sum of their two ages is 74, looks like this:

n+d=74

The system is:

{d=3n−6

{n+d=74

Now, substitute the first equation into the second equation and solve for n.

n+(3n−6)=74

4n-6=74

Add 6 to both sides

4n=80

Divide both sides by 4

n=20 (< Noelle's Age!)

Now plug n into the second equation

d=3(20)-6

d=60-6

d=54 (< Noelle's Dad's Age!)

87%

step-by-step explanation:

apex answer

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!