A dishwasher is priced at $475. There are two options offered to reduce the price: either a 15% discount off the price or a rebate of $75. Which is the better choice, and what is the extra amount saved?

Rebate ; $3.75

Step-by-step explanation:

15% of 475

15/100 × 475 = 71.25

Rebate > 71.25

Difference:

75 - 71.25

3.75

Rebate, $3.75

Step-by-step explanation:

15% Off:

We want to find 15% of 475, so we can multiply 15% by 475 to find the discount

Convert 15% to a decimal by diving by 100 or moving the decimal place over 2 spots to the left

15/100=0.15

0.15* 475

71.25

Rebate:

75.00

Extra Amount Saved:

We want to find the difference between the discount and the rebate, so we can subtract

75-71.25

3.75

The rebate is the better choice, because 75.00 is greater than 71.25, and you will save $3.75 using the rebate

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!

69.64%

step-by-step explanation: