Linear Systems
Solve the linear system shown:
2x + 3y - 9 = 0
x - y - 2 = 0
What is P(3, 1)
Find the slope of the line segment joining M(3, 4) and N (-2, 5)
What is 5.1.
The vertex of the equation y = -5(x+8)(x-12)
What is V(2, 500)
Three sides of a garden are to be fenced with 100m of fencing, the fourth side being against the house. Write a quadratic equation in standard form for the Area in relation to the Width. Hint: width=w, length=100-?
What is A = -2w2 + 100w
In triangle ABC, angle B is 90o, angle A is 22o, what is the measure of angle C?
What is 68o.
Solve 3x+3y = -6
3x - y = -11
What is P(-13/4, 5/4)
What is the midpoint of the line segment joining
K(4, -2) and L (7, 13)
What is (5.5, 5.5)
Solve: 2x2 = 16 – 4x
What is (-4, 0) and (2, 0)
Computer software programs are sold for $20/each. Three hundred people are willing to buy them at this price. For every $5 increase in price, there are 30 fewer people willing to buy the software. Calculate the selling price that will produce the maximum revenue.
What is $35.
In right triangle ABC, a = 15 and c (hypotenuse) = 18cm. What is the degrees of A?
What is 43o
Two numbers differ by four. Twice the smaller, increased by the larger is 25. Find the numbers.
What are 7 and 11.
A line segment has one endpoint (3, 5) and midpoint (7, 10). Find the other endpoint.
What is (11, 15)
State the vertex of y = x2 + 2x - 8
What is (-1, -9)
A rocket is launched. The trajectory is modeled by h=-5t2 + 80t. What is the maximum height and the time it takes to reach it?
What is 320 m after 8 seconds.
Find b if B = 720 and a = 4.47 cm and c = 5.66 cm. Round to two decimal places.
What is b = 6.03 cm.
Eric invested $8000, part at 9% and the rest at 4%. After one year, the total interest earned was $420. How much did he invest at each rate?
What is $2000 and $6000.
Find the equation of the median from A for the triangle A(-10, -5), B(5, -2) and C(2, 10)
What is y = 2x/3 + 5/3
Rewrite the following equation in vertex form.
y = -3x2 - 30x - 25
What is y = -3(x + 5)2 + 50
Describe the transformations for the equation
y = 6(x - 6)(x+4)
What is y = 6(x-1)2 - 150
h = horizontal translation 1 unit to right
a = vertical stretch by a factor of 6
k = vertical translation 150 units down
Find M in triangle MAX if A = 75o, a = 52 cm and x = 41 cm.
What is 55o.
A vinegar-water solution is used to wash windows. If 1200 L of 28% solution are required, how much of a 16% and 35% solution should be used?
What is 480 L of 16% and 720 mL of 36% solution.
Find the equation of the altitude from C for the triangle A(3, 2), B(-6, -1) and C(-2, -8)
What is y = -3x - 14
Find the equation of the parabola, in standard form that passes through (5, 16) and has zeros (1, 0) and (7, 0).
What is y = -2x2+ 16x - 14
A uniform border on a framed photograph has the same area as the photograph. What are the outside dimensions of the border if the dimensions of the photograph are 25 cm by 20 cm?
What is 29.22 cm by 34.22 cm.
Two apartment buildings are 40 m apart. From the top of one building, the angle of elevation to the top of the second building is 10o and the angle of depression to the bottom of the second building is 65 degrees. How tall is each building? Round to 1 decimal place.
What is 85.8 m and 92.8 m.