Linear Systems
Factoring
Solving
Trig
Analytic Geometry
Random
100
Determine the algebraic equation that would represent the following:
y=2x+5
y=-3x+1
one solution (they have different slopes)
100
Factor
y=49x^2-100w^2
(7x-10w)(7x+10w)
100
What is the x-intercept(s) of the function
y=8x^2-28x+24
(3/2,0) and (2,0)
100
A wheelchair ramp rises 0.8 m over a horizontal distance of 6 m. A larger ramp is designed with the same slope and rises 2.4 m. How long is the horizontal run of the larger ramp?
18m
100
Determine the coordinates of the midpoint Q(-3,-3) and R(-1,-7)
(-2,-5)
100
Solve by graphing
y=2x-1
y=-x+8
(3,5)
200
Solve by substitution.
x+4y=6
2x-3y=1
(2, 1)
200
Factor
4x(6-x)+10y(6-x)+(6-x)
(4x+10y+1)(6-x)
200
What are the x-intercepts
y=x^2-9
(3,0) and (-3,0)
200
Find the value of x. Round to one decimal.
x=15.9
200
Find the length of the line segment with endpoints J(2.1, 8.3) and K(-4.5, -4.7)
14.6
200
Solve by factoring.
3x^2-9x
x=0, x=3
300
Solve using elimination
3x+2y=2
4x+5y=12
(-2,4)
300
Factor
5x^2y^3-15x^2y^2+45xy^2+20xy
5xy(xy^2-3xy+9y+4)
300
What are the x-intercepts
y=x^2-5x
(0,0) and (5,0)
300
Determine the value of a
a=17
300
For the triangle with vertices A(-2, 0), B(8, 8) and C(4, -2)Classify the triangle as equilateral, isosceles or scalene
scalene (12,81, 10,77, and 6.32)
300
The perimeter of a rectangle is 90 cm. The length is 3 cm less than three times the width. Find the dimensions of the rectangle.
- Width = 12 cm
- Length = 33 cm
400
Maria had $10 000. She invested part of it in an account paying 4% per annum and remainder in bonds paying 5% per annum. If the total interest earned after 1 year was 440, how much did she invest in each account?
Maria invested $6000 at 4% and $4000 at 5%
400
Factor.
-12n^2+27m^2
-3(2n+3m)(2n-3m)
400
Solve for x
3/2(x-1)-4=1/2(x+5)
x=5
400
Solve for the missing angle.
103.9 degrees
400
A triangle has vertices L(-4,1), M(2,5), and N(6,-1)
Determine the if the triangle is a right angle triangle by finding slope!
mpq=2/3, mqr= -3/2 therefore it is a right angle triangle at angle Q
400
Solve using quadratic formula.
(x-2)^2+10=0
no solution
500
Maryam has a bottle of 5% acetic acid and a bottle of 10% acetic acid. How much of each would she use to make 250 mL of 8% acetic acid?
Maryam would mix 100 mL of the 5% acetic acid with 150 mL of the 10% acetic acid.
500
Solve
12x^3-75x
3x(2x-5)(2x+5)
500
Solve
(3x-5)/4 + (x+7)/6 = (5x+11)/12 +2
x=6
500
Two points, AAA and BBB, are located on opposite sides of a river. A surveyor stands at point CCC on the near bank and measures the following:
- ∠ACB=48∘
- ∠CAB=67∘
- BC=120
Determine the distance AB across the river
96.8m
500
The midpoint of line segment ABABAB is M(4,7)M(4,7)M(4,7). If A(1,3)A(1,3)A(1,3), determine the coordinates of BBB.
B(7,11)
500
A sporting goods store sells 90 ski jackets in a season for $200 each. Each $10 decrease in the price would result in five more jackets being sold. What is the max revenue?
The max revenue is $18050
Let:
- x = number of $10 decreases
- Price = 200−10x
- Quantity sold = 90+5x
- R(x)=(200−10x)(90+5x)