Melia put the $20 her grandmother gave her for her tenth birthday into her piggy bank. each week after that she added her $1.50 allowance to the bank. a. write an equation to represent the mount of money is in melia's piggy bank after n weeks. b. on her 18th birthday, melia breaks open her piggy bank to use the money to buy supplies for college. how much does melia have to spend? show your work. (there are 52 weeks in a year)

Step-by-step explanation: We are given that Melia put $20 initially in piggy bank.

Each week amount added in piggy bank = $1.50.

Let us assume total number of weeks be n Melia added amount in piggy bank and get y amount after n weeks.

a) Therefore, total amount after n weeks = Initial amount + 1.50 times n weeks.

y= 20+ 1.50n.

b) On 18th birthday, there would be total 8 years after 10th birthday.

And in 8 years there would be 52 × 8 = 416 weeks.

So, in order to find the total amount after 8 years or 416 weeks, we need to plug n= 416 in the equation we got in a part.

Therefore,

y = 20+ 1.50(416)

y = 20 + 624 = 644.

step-by-step explanation:

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!