The repayment schedule is for a $1,300 loan at 7.5% for 6 months. what is the principal after the first payment?

First, you will need to calculate the monthly payment.
The loan payment formula is attached. 
(I'll leave it up to you to show the math).
Anyway, using a loan calculator, the monthly payment is 221.43
the monthly loan rate of 7.5% = rate / 1,200
.00625
Let's calculate the interest paid for the first payment

Interest Paid = Previous Balance * Monthly Interest Rate
Interest Paid = 1,300 * .00625
Interest Paid = $8.13

Now to calculate equity.
Equity = Monthly Payment -Interest Paid
Equity = 221.43 -8.13
Equity = 213.30

The equity (or what you own), is 213.30

The New Loan Balance (or the principal) is calculated by
New Balance = Previous Balance -Equity
New Balance (or principal) = 1,300 -213.30
= 1086.70

You might find this page VERY helpful:
http://www.1728.org/loanmath.htm

yes

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!