Linear Systems
Solve the linear system:
2x + 3y = 9
x - y - 2 = 0
What is (3 , 1)
The slope of the line segment joining the points
(3, 4) and (-2, 5).
What is -1/5
The vertex of the equation
y = -5(x+8)(x-12)
What is (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 terms of the Width.
What is A = -2w2 + 100w.
In triangle ABC, angle B is 90o, angle A is 22o.
Determine the measure of angle C.
What is 68o.
Solve the linear system:
3x + 3y = -6
4x - 7y = 3
What is (-1, -1)
The midpoint of the line segment joining the points (4, -2) and (7, 13).
What is (5.5, 5.5)
The solution of
2x2 = 16 - 4x
What is x = 2 and x = -4
The Revenue equation for the following scenario:
Antivirus 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.
What is R = (20 + 5x)(300 - 30x)
The measure of angle A in right triangle ABC, where
a = 15 and c = 18cm and c is the hypotenuse.
What is 43o.
A Tim Horton’s Wild Blueberry muffin has 90 more calories than a Vanilla Dip donut.
Four muffins and five donuts have a total of 2610 calories. Determine the number of calories in a muffin.
What is 340 calories.
The other endpoint of a line segment with one
endpoint at (3, 5) and midpoint at (7, 10).
What is (11, 15).
State the vertex of
y = x2 + 2x - 8
What is (-1, -9)
The maximum height of a rocket whose trajectory is modelled by
h(t)=-5t2 + 80t.
What is 320m.
The measure of side b in an acute triangle if
B = 72o, a = 4.47 cm, and c = 5.66 cm.
Round to two decimal places.
What is b = 6.03 cm.
Two integers differ by 4. Twice the smaller number plus the larger number equals 25. Find the numbers.
What are 7 and 11.
The equation of the median through A for the
triangle A(-10, -5), B(5, -2), C(2, 10).
y = 2/3 x + 5/3
The following equation in vertex form:
y = -3x2 - 30x - 25
What is y = -3(x + 5)2 + 50
The transformations for the equation:
y = 6(x - 6)(x+4)
Vertex form: y = 6(x - 1)2 - 150
vertical stretch by a factor of 6
horizontal translation 1 unit to right
vertical translation 150 units down
The measure of angle D in triangle DEF if
E = 75o, e = 52 cm and f = 41 cm.
What is D = 55o.
DAILY DOUBLE! (press space to see the question)
Eric invested $8000; some in a GIC paying 4% per year, another in a bond paying 9% per year. After one year he'd earned $420 in interest. How much did he invest at each rate?
The equation of the altitude through C for the
triangle A(3, 2), B(-6, -1) and C(-2, -8).
What is y = -3x - 14
DAILY DOUBLE! (press space to see the question)
Find the equation of the parabola, in standard form that passes through (5, 16) and has zeros (1, 0) and (7, 0).
The points of intersection of the parabolas
y = x2 - 4x + 7 and
y = -(x - 3)2 + 8
What are (1, 4) and (4, 7).
Two apartment buildings are 40 m apart. From the top of the shorter building, the angle of elevation to the top of the taller building is 10o and the angle of depression to the bottom of the taller building is 65o. Determine the height of each building to 1 decimal place.
What are 85.8 m and 92.8 m.