# Tutor profile: Carlyn T.

## Questions

### Subject: Pre-Calculus

Multiply (1+4i)(5+i). Write the answer in a+bi form.

1.) Similar to multiplying two binomials, multiply these two complex numbers by multiplying each term in the first parenthesis by each term in the second as follows: (1)(5) + (1)(i) + (4i)(5) + (4i)(i) 2.) Simplify: 5 + 1i + 20i + $$ 4i^2 $$ 3.) Simplify further by combining like terms: 5 + 21i + $$ 4i^2 $$ 4.) Since $$ i^2 $$ = -1, substitute to obtain the desired form, a+bi : 5 + 21i + 4(-1) 5.) Simplify: 5 + 21i - 4 6.) Combine like terms: 1 + 21i

### Subject: Pre-Algebra

Describe a real-world problem that could be solved with the expression (2+3)×6?

Josh ran 2 miles in the morning and 3 miles in the afternoon. He did this for 6 days. How many miles did he run?

### Subject: Algebra

7 - $$ \frac{10}{x} $$ = 2 + $$ \frac{15}{x} $$

1.) Begin by multiplying both sides of the equation by x to fix the problem of x's in the denominator. x(7 - $$ \frac{10}{x} $$ ) = x (2 + $$ \frac{15}{x} $$) 2.) Simplify by distributing the x to (multiplying it by) everything inside as follows: 7x - 10 = 2x + 15. 3.) Subtract 2x from both sides to isolate the variable on one side. 7x (-2x) - 10 = 2x (-2x) + 15 4. Simplify as follows: 5x - 10 = 15 5.) Add 10 to both sides to isolate the constant on one side opposite the variable. 5x - 10 (+10) = 15 (+ 10) 6.) Simplify as follows: 5x = 25 7.) Divide both sides by 5 to isolate the variable. $$ \frac{5x}{5} $$ = $$ \frac{25}{5} $$ 8.) Simplify as follows: x = 5