Linear Systems
Solve the linear system shown:
2x + 3y - 9 = 0
x - y - 2 = 0
(3, 1)
Find the slope of the line segment joining M(3, 4) and N (-2, 5)
5.1.
The vertex of the equation y = -5(x+8)(x-12)
(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.
A = -2w^2 + 100w
In triangle ABC, angle B is 90 degrees, angle A is 22 degrees, what is the measure of angle C?
68 degrees.
Solve the linear system:
3x+3y = -6
3x - y = -11
(-3.25, 1.25)
What is the midpoint of the line segment joining K(4, -2) and L (7, 13)
(5.5, 5.5)
Find the solutions for the equation
2x^2 = 16 – 4x
(-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.
$35.
In right triangle ABC, a = 15 and c (hypotenuse) = 18cm. What is the measure of A?
43 degrees
Two numbers differ by four. Twice the smaller, increased by the larger is 25. Find the numbers.
7 and 11.
Fully factor the expression
2x^2 - 8x +3
2(x-3)(x-1)
State the vertex of
y = x^2 + 2x - 8
(-1, -9)
A rocket is launched. The trajectory is modelled by h(t)=-5t^2 + 80t. What is the maximum height and the time it takes to reach it?
320 m after 8 seconds.
Find b if B = 72 degrees and a = 4.47 cm and c = 5.66 cm. Round to two decimal places.
b = 6.03 cm.
The perimeter of a volleyball court is 54 m. The difference between the length and width is 3 m. Find the dimensions.
12 m and 15 m
Fully factor the expression
10x^2 + 19x + 6
(5x+2)(2x+3)
Rewrite the following equation in vertex form.
y = -3x^2 - 30x - 25
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 = 75 degrees, a = 52 cm and x = 41 cm.
55 degrees.
Ms. O'Brien travels a total of 320 km in 3 hours. For part of the trip she is on the highway travelling 120 km/h and the other part is on city roads travelling 60 km/h. Find how long she was on the highway.
2 hours and 15 minutes
A line segment has one endpoint (3, 5) and midpoint (7, 10). Find the other endpoint.
(11, 15)
Find the equation of the parabola, in standard form that passes through (5, 16) and has zeros (1, 0) and (7, 0).
y = -2x^2+ 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?
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 10 degrees 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.
85.8 m and 92.8 m.