Solving Systems of Equations
Analytic Geometry
Quadratics
More Quadratics/Trigonometry
100
Write a system of equations for this situation: A lemonade stand makes a profit of 15 cents for each cup sold. The cost of buying the materials is $20. Write an equation for how much profit will be made at the end of the day. An orange juice stand across the street makes a profit of 25 cents for each cup sold. The cost of buying the materials is $30. Write an equation for how much profit will be made at the end of the day.
What is y= 0.15x-20 and y= 0.25x-30
100
Find the endpoint of line segment AB with point A (5,6) and midpoint (-2,-1).
What is (-9,-8)
100
In the equation y=x^2+k, what does k do to the graph of the parabola?
What is moves the graph up or down
100
Factor. 4x^2-81
What is (2x-9)(2x+9)
200
Explain how to solve a system using substitution, then explain how to solve a system using elimination.
What is: To solve using substitution, write one variable in terms of the other (ie. x=y+5) and substitute this into the second equation. Then solve for the remaining variable (y). To solve using elimination, add or subtract equations to eliminate one variable. For example, (y-5x=10) + (y+5x=5). Then solve for the remaining variable. So, 2y=15 and y=7.5.
200
Determine the equation of the line that right bisects a triangle with points A (2,3), B (-5, 4) C (1,6). The right bisector is perpendicular to line segment BC.
What is y=-3x-1
200
How will the graph of y=ax^2 be different from the graph of y=x^2?
What is y=ax^2 will be stretched or compressed depending on the value of a.
200
Factor. 16x^3y+18xy^3
What is 2xy(8x^2+9y^2)
300
Solve using substitution or elimination: 4x-y=-9 3y-2x=17
What is x= -1 and y=5
300
Find the distance between these two points. Point A (1, -7) and Point B (5, 2)
What is about 9.9
300
For this equation, state the vertex, axis of symmetry, stretch/compression factor and direction of opening. y=2(x+4)^2-5
What is vertex (-4,-5) axis of symmetry x=-4, stretch factor of 2 and opening upwards
300
Factor. y=(3x^2/2)-8x-6
What is (3x/2+1)(x-6)
400
There are litres of 1% milk and litres of 5% milk. These litres of milk are combined to get 10L of 4% milk. How many litres of 5% and 1% milk was there originally?
What is 7.5L (5%) and 2.5L (1%)
400
Find the length of the median of triangle ABC that passes through vertex A and line segment BC. A (3,2) B(5,-7) C (-3,-1).
What is sq. root of 40 or about 6.33
400
Identify the x-intercepts. y=(x-2)(x-14)
What is (2,0) and (14,0)
400
In a right triangle ABC with angle A equal to 90, find angle B and C so that sin(B) = cos(B).
What is B and C are 45 degrees
500
Solve: x-y=1 y-z=2 z+x=3
What is x=3, y=2, z=0
500
The line segment PQ has an endpoint P(2,8) . The midpoint, M, of PQ is on the y-axis and the other endpoint Q is on the x-axis. Find the coordinates of M and Q.
What is M (0,4) and Q (-2,0)
500
Identify the x-intercepts and axis of symmetry. y=4(x-1)(x+11)
What is (1,0) and (-11,0) x=-5
500
WITHOUT USING YOUR CALCULATOR, what is sin of 60 degrees? Answer will be in exact form.
What is (sq. root of 3)/2
M
e
n
u