Word/Phrase Definition
Absolute Value
The distance between zero and the point representing a real number on the number line
y = 6x − 11
−2x − 3y = −7
(2, 1)
How many mg of a metal containing 45% nickel must be combined with 6 mg of pure nickel to form an alloy containing 78% nickel?
4 mg
(1, −19), (−2, −7)
−4
−20 = −4x − 6x
{2}
Axis of Symmetry
The line that divides a graph into two symmetrical
parts that are mirror images or each other
2x − 3y = −1
y = x − 1
(4, 3)
7 L of an acid solution was mixed with 3 L of a 15% acid solution to make a 29% acid solution. Find the percent concentration of the first solution.
35%
(−4, 7), (−6, −4)
11 /2
8x − 2 = −9 + 7x
{−7}
Consistent System
A system of equations that has at least one solution
−3x − 3y = 3
y = −5x − 17
(−4, 3)
9 gal. of a sugar solution was mixed with 6 gal. of a 90% sugar solution to make a 84% sugar solution. Find the percent concentration of the first solution.
80%
(20, 8), (9, 16)
− 8 /11
p − 1 = 5 p + 3p − 8
{1}
Point-Slope Equation
A non-vertical line that contains a point (x1, y1) and
has a slope of m and is found in the format of y - y1 = m(x - x1)
y = −2
4x − 3y = 18
(3, −2)
A metallurgist needs to make 12.4 lb. of an alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of each should he use?
6.2 lb. of 60% gold, 6.2 lb. of 40% gold
(17, −13), (17, 8)
Undefined
p − 4 = −9 + p
No solution.
Inverse Variation
A non-linear relationship between two variables where
there is a non-zero number k; y = k/x
y = 5x − 7
−3x − 2y = −12
(2, 3)
Brand X sells 21 oz. bags of mixed nuts that contain 29% peanuts. To make their product they combine Brand A mixed nuts which contain 35% peanuts and Brand B mixed nuts which contain 25% peanuts. How much of each do they need to use?
8.4 oz. of Brand A, 12.6 oz. of Brand B
(19, 3), (20, 3)
0
−5(1 − 5x) + 5(−8x − 2) = −4x − 8x
{−5}