Equations in one variable
12n + 9 = 6 - 3n
n = -0.2
When do you use a closed circle and when do you use an open circle if graphing an inequality?
Use a closed circle if the boundary point is part of the solution and an open circle if it is not.
V = IH solve for I
I = V/H
Is (8,1) a solution of 3x + 5y = 15?
No
What are three ways a function can be represented and how can you recognize a function?
A function can be represented by a graph, mapping diagram, table, or equation. In a function each value of the domain is paired with exactly one value in the range.
2r - 6 + 5r = 3 - r + 7
r = 2
9y + 4 ≥ -2(1 - 3y)
y ≥ -2
A = P + Prt solve for t
t = (A - P)/Pr
Is (0,-8) a solution of 6x - 3y = 24?
Yes
f(n) = 2n - 2; What are the first four terms in the sequence? Assume that the domain is the set of whole numbers greater than 0.
(1,0) (2,2) (3,4) (4,6)
4(2x - 3) = x - 12 + 7x
Infinitely many solutions
2b - 15 > 5b
b < -5
kn + mp = q; solve for p
p = (q - kn)/m
Is (0,5) a solution of 2(x + 1)2 + 3y = 15?
No
Find the 6th term in the sequence. f(n) = n2 + 3
6z = 4(1/2z - 8)
z = -8
3(x - 4) > 5(x + 2) - 2x
No solution
A = 1/2(a + b)h; solve for h
h = 2A/(a + b)
2x + y = 4; What are 3 ordered pair solutions for this equation?
Answers vary some examples are: (-2, 8) (-1, 6) (0, 4) (1, 2) (2, 0) (3, -2) (4, -4)
A vertical line is shown on a coordinate plane. Is it a function or not? Why?
Not a function. The domain is paired with more than one output for the range.
6 - 2r + 1 = 3r - 5(r - 2)
No solution
Write an inequality for the following problem and solve: Alexis received an 85, 89, and 92 on three tests. How many points does she need to score on her next test in order to have an average of at least 90?
(85 + 89 + 92 + x) ÷ 4 ≥ 90
x ≥ 94
SA = 2∏r2 + 2∏rh; solve for h
h = (SA - 2∏r2)/2∏r
2x + 2y = 36; What are the ordered pair solutions if x is equal to 2, 4, 6, 8, and 10?
(2,16) (4,14) (6,12) (8,10) (10,8)
Given the functions f(x) = 2x - 4 and g(x) = x + 2 find the value of x for which f(x) = g(x).
x = 6