Equations (All Types)
Inequalities
Linear Functions
Systems
Exponents
100
Solve 5y+2=(10y+4)/2 for y
Infinite Solutions, or all real numbers
100
-3(x-3)≥5-4x
x≥-4
100
Write the general formulas for direct variation, slope-intercept form, point-slope form, and standard form.
f(x)=kx f(x)=mx+b y-y₁=m(x-x₁) Ax+By=C
100
−2x − y = −9, 5x − 2y = 18
(4,1)
100
[(4a²b)/(a³b²)][5a²b/2b⁴]
10a/b⁴
200
x²+7x-144=0
-16, 9
200
17-(4k-2)≥2(k+3)
k≤13/6
200
Write the equation 4.5x-2=y in standard and point-slope form.
Standard Form: 9x-2y=8 Point-slope Form: y+2=4.5(x-0) Equations may vary
200
−2x + 6y = 6, −7x + 8y = −5
(3, 2)
200
[(-2a³b²c⁰)/(3a²b³c⁷)]⁻²
(9b²c¹⁴)/4a²
300
Solve x=[-b+√(b²-4ac)]/2a for a
a=-c/(x²+xb)
300
Solve -3x+2≤x/2<14 and write the domain in interval notation.
4/7≤x<4 [4/7,4)
300
Give the equation of a line that is parallel and one that is perpendicular to the graph of y=4x-5
Answers may vary Parallel: y=4x Perpendicular: y=-1/4x
300
When an airplane flies into the wind, it can travel 3000 miles in 6 hours. When it flies with the wind, it can travel the same distance in 5 hours. Find the speed of the airplane in still air and the speed of the wind.
Speed of Plane = 550 mph Wind speed = 50 mph
300
Simplify ∛(x⁹y⁴z⁷) so that it is in exponential form.
x³y⁴/³z⁷/³
400
2x=√(2-2x)
1/2 (-1 is an extraneous root)
400
Solve |2x-7|-1≥0 and write the domain in interval notation.
x≥4, x≤3 (-∞,3] U [4,∞)
400
If a line has a y intercept of 5 and it passes through (1,7), what is its equation in slope intercept and point slope form?
y=2x+5, y-7=2(x-1)
400
You need 175 dollars to cover your weekly costs, and you work two jobs. Your job walking dogs earns 10.5 dollars per hour and your job tutoring earns 12 dollars per hour. You can also only work up to 25 hours. Write a system of inequalities and name three solutions for it.
x≥0 y≥0 10.5x+12y≥175 x+y≤25 Ex: (0,25) (5, 15) (15, 5)
400
A population of 100 frogs decreases at a rate of 15% annually. How many frogs will there be in 5 years?
Annually: f(x)=100(.85)ˣ After 5 years: 44 frogs
500
Solve (u+1)/(u+2)=-1/(u-3)+(u-1)/(u²-u-6) and find the excluded values.
u=2, 0 u≠3, 2
500
Solve -4|k+5|-3≤8. Write the domain in interval notation also.
All real numbers (-∞,∞)
500
A family is taking a road trip. In the car there is 7 pounds of food. The family decides to eat .75 pounds each day. Write an equation for this situation if y is the remaining food and x is the number of days. If the family has .25 pounds of food left after the trip is completed, how long was the trip?
y=7-.75x 9 days
500
Solve the system: y=-x²-2x-4, 7x+y=2
(2,-12),(3,-19)
500
Your 13,500 deposit earns 3.5% interest, and it is compounded semiannually. How much money will you have after 5 years?
$16,057.50
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