Distance and Midpoints
Find the distance from A = (1,2) to B = ( -2,-3).
square root of 34
Solve the system of linear equations for y:
2x - y = 2
4x + y = 1
(A) y = 1
(B) y = 0
(C) y = -1
(D) y = -2
(E) y = -3
y = -1
Solve the quadratic equation by factoring:
8z^2 + 20z + 1 = 7z^2 + 33z - 39
z = 8 or 5
Find the slope of the line passing through (−6, −5) and (8, −5).
M=0
4x − 3y = 5
3x + 4y = 10
(a) x = 1, y = 2
(b) x = 2, y = 1
(c) x = 1, y = 1
(d) x = 1, y =− 1
(e) No Solution.
(b) x = 2, y = 1
Find the coordinates of the midpoint of A = (1, 1) and B = (−2, −3).
(A) (-1/3, 1)
(B) (-1/2, 2)
(C) (1/2, -1)
(D) (-1/2, 1)
(E) (-1/2, -1)
(E) (-1/2, -1)
Solve for y:
2x - 3y = 2
3x - y = 3
(A) y = 2
(B) y = 3
(C) y = 4
(D) y = 5
(E) y = 0
(E) y=0
Solve the inequality and express your answer in interval notation:
3|z + 3| ≥ 9
(-infinity, -6] Union [0, infinity)
h(x) =− 8 − (8/3x)
Slope: -8/3
y-intercept: (0, -8)
Let f(x) = 3x^2 − 12x + 11. Find the coordinates of the vertex of the parabola.
(a) V = (− 2, − 1)
(b) V = (2, 1)
(c) V = (2, − 1)
(d) V = (− 2, 1)
(e) V = (3, 7)
(c) V = (2, − 1)
Solve the following linear equation.
5(4w − 3) =− 9(9 − w)
w=-6
Find the equation of the line in slope-intercept form that passes through the point (0, −9) with a slope of 4.
y=4x-9
Solve the quadratic equation using the quadratic formula:
5z^2 + 12z = 10z - 3
No real solution
Let f(x) = − 2x^2 + 4x + 11. Which statement is correct?
(a) f has a maximum value of 13 at x = 1.
(b) f has a maximum value of 11 at x = 1.
(c) f has a minimum value of 13 at x = 1.
(d) f has a minimum value of 9 at x = 1.
(e) f has a minimum value of 10 at x =− 1.
(a) f has a maximum value of 13 at x = 1.
Determine the implied domain of the following function. Express your answer in interval notation.
f(x) =11/(x−3)
x=3
Given (x subscript 2, 7) and (− 8, y subscript 1) find x subscript 2 and y subscript 1 such that the midpoint between these two points (6,8).
x=20
y=9
Solve the absolute value equation:
|−3z − 9| = 0
z=-3
Consider the following inequality. Solve the inequality and express your answer in interval notation.
5z − 6 ≥ 1 + 7z
(-infinity, -7/2]
Find the linear function with the following properties.
f(0) = 8
Slope of f =− 8
f(x) = -8x+8
2.) Two lines have equations y = 5/2x-1 and 2x + 5y = 5.
Choose the correct statement.
(a) The lines are parallel.
(b) The lines have two common points.
(c) The lines have the same y-intercepts.
(d) The lines are perpendicular.
(e) The lines are not perpendicular.
(D) The lines are perpendicular
Given the following function. Express your answer in
interval notation.
f(x+h)−f(x)/h.
f(x) =− 3x + 6
H =-3
Find the equation of the line in slope-intercept form that passes through the following point with the given slope. Simplify your answer.
Point: (9, − 11); Slope: 32
y= 3/2x-49/2
Factor the following polynomial by grouping.
8x^2 − 8x + 5xy − 5y
(8x+5y) (x-1)
Find the equation of the line passing through Q(0, 5) and perpendicular to the line
3x − 2y = 3.
(a) y = 2/3x - 5
(b) y = -2/3x + 5
(c) y = 2/3x + 5
(d) y = 1/2x + 5
(b) y = -2/3x + 5
Find the domain of the function f(x).
f(x) = The square root of 1 − 2x
(a) (− ∞, −1/2]
(b) (− ∞,1/2)
(c) (− ∞, 1/2]
(d) (1/2, ∞)
(e) (−1/2, ∞)
(c) (− ∞, 1/2]