Stephen was thinking of a number. Stephen divides by 7, then adds 8 to get an answer of 12. What was the original number?

Which sum or difference identity would you use to verify that cos (180° - ∅) = -cos ∅? a. sin (α -β) = sin α cos β – cos α sin β b. cos (α -β) = cos α cos β – sin α sin β c. cos (α -β) = cos α cos β + sin α sin β d. sin (α + β) = sin α cos β + cos α sin β

1. which of the following algebraic equations is equivalent to ? x^n = a a^n = x a^x = n x^a = n 2. 16^1/4= 1/2 2 4 3. (-36)^1/2= -6 1/6 no real number 4. 8^2/3= 4 8 16√2 )^5/2= 7,776 1/7,776 no real number 6. m ^ the square root of a^2m simplified is: 7. the square root of 3^3 times the square root of 2 simplified and in radical form is:

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24