Consider the expression 2+5=7x3+9+3-1
(a) Simplify the expression above using the order of operations.
(b) Insert parentheses into the expression so that it simplifies to zero.
Simplify 3/5+6/15-18/25,5/6-2/3(3/4+7/8)
Give an example of a system of linear equations that has just one solution. Explain why the example you gave fits the criteria, and sketch a graph of it in the space below.
I'm thinking of a number between 1 and 35. 18 more than seven times the number is equal to the smallest three digit integer, whose digits sum to ten. What is the number?
Sherie works at a furniture store, where she makes a weekly salary of $525, plus a 15% commission on sales.
(a) Write an equation to determine Sherie's weekly income. Be sure to clearly define your variables.
(b) How much will she have to sell in order to make $800 in one week
(c) Suppose Sherie sells a couch for $2,895. How much will her commission be?
Tabitha has $4.35 in dimes and quarters. If the quantity of dimes is three more than twice the number of quarters, how many of each coin does she have? (Note: a dime is worth $0.10 and a quarter is worth $0.25 )
(a) Define the variables in this problem
(b) Write a system of two equations in two variables that represent this problem situation
(c) Solve the system you wrote using any method.
(d) Write your answer as a complete sentence.
Translate the following English statements to a mathematical equation or inequality. Then, solve them.
(a) The difference of four times a number and thirteen is at most 27
(b) Nine less than the square of a number is equal to zero
(c) The sum of a number and three is more than the difference of one half the number and 8
Determine if the lines given by the equations y=3x-5 and 6x-2y=7 are parallel, perpendicular, or neither. Justify your response.
Solve the systems (2/3)x+(2/5)y=10
(3/2)x-(1/3)y=-2 and {(11x+6y=17),(5x-4y=1):}
Solve each of the following equations by first factoring the polynomials, and then applying the zero product property.
(a) 9x^2-42x+49=0
(b) 2x^3+3x^2-8x-12=0 (use grouping)
(c) 2x^2-2=0
Solve each of the following equations by using the quadratic formula.
(a) 9x^2-12x+4=0
(b) 9x^2-12x+1=0
