1.1/1.2
Express in interval form and graph
-6 < x < 3
Express in inequality form and graph
[5, infinity)
(-6, 3) and x>=5
Multiply
(y+(3-y^2))(y-(3-y^2))
-y^4 + 7y^2 - 9
Solve for x
7x - 6 = 4x +9
5
Solve the inequality
3x-2 > -11
(-3, infinity)
Solve graphically and algebraically
2/x + 1/2x = 7
5/14
Find the distance between -1/3 and 4/5
12/15 + 5/15 = 17/15
Factor
4t^2 - 13t -12
(4t + 3) (t-4)
Solve for x
absvalue (x-7)=4
3, 11
solve the absolute value inequality and graph
8 - absvalue(2x-1) >= 6
[-1/2 , 3/2]
Sketch a graph, find x and y intercepts and test for symmetry
y= - sqrt(4-x^2)
see attached Desmos on board
Perform indicated operation
4-2/3 / (6/7-1/14)
140/39
Rationalize the denominator
sqrt (5) / (sqrt(7) + sqrt(2))
sqrt(35) - sqrt(10) / 5
Solve
1/x + 2/x-1 = 3
3 +- sqrt(6) / 3
Solve the inequality and graph
3/(x-1) - 4/x >= 1
[-2,0) U (1,2]
Find the equation of a line that passes through (1, -6) and perpendicular to x + 2y = 6
y=2x-8
Evaluate each expression
(1/2)^(-3) x 5/12
root 4(4) times root 4(324)
10/3
6
Perform indicated operations
x^2 + 2x -3 / x^2 + 8x + 16 divided by x -1 / 3x+12
3(x+3) / (x+4)
The hypotenuse of a right triangle has length 20cm . The sum of the lengths of the other two sides is 28cm. Find the lengths of the other two sides of the triangle.
12cm 16cm
Find the area of the right triangle
A(2,2) B(-3,-1) C(-3,-3)
10
Write an equation that expresses the statement.
A is jointly proportional to the square roots of x and y
A=k sqrt(xy)
Simplify each expression
(9x^3 y / y^(-3))^(1/2) times (x^3/ y^(1/2)
3 x^(9/2) y^(3/2)
Simplify
(1/x+2) + (1/x^2 - 4)- (2/x^2 - x -2)
x^2 - 2x - 5 / (x-2)(x+1)(x+2)
Henry and Irene working together can wash all the windows of their house in 1 h 48 min. Working alone, it takes Henry 1 1/2 h more than Irene. How long does it take each person working alone to wash all windows.
Irene 3h Henry 4 1/2 h
Find the equation of the circle
Center (7, -3) ; Tangent to the x-axis
(x-7)^2 + (y+3)^2 = 9
Hookes Law states that the force needed to keep a spring stretched x units beyond its natural length is directly proportional to x. Here the constant of proportionality is called the spring constant.
a) write hooke's law as an equation
b) If a spring has a natural length of 10cm and a force of 40N is required to maintain the spring stretched to a length of 15cm , find the spring constant.
c) What force is needed to keep the spring stretched to a length of 14cm?
a) F=kx
b) 8
c) 32N