Linear Equations
How many solutions does the linear system y = 3x + 5 and 5y = 25 + 15x have?
Infinite
What two integers add to -10 and multiply to 24
-4, -6
What is the y-intercept for the function
y = -2x2 + 3x - 5
(0, -5)
What are the x - intercepts for the quadratic relation
y = x2 - 8x + 12
x = 2 and x = 6
Triangle ABC is similar to triangle PQR with <A = <P, <B = <Q, and <C = <R. Which Side of triangle PQR corresponds to side AB?
PQ
Does this pair of lines have a P.O.I
y - x = 5
-5x + 5y = 9
No
Expand and Simplify
-2(3x - 5)(x - 4)
-6x2 + 34x - 40
What are the correct values of a, h, and k for the relation
y = -2 (x + 9)2 - 16
a = -2
h = -9
k = -16
What is the axis of symmetry for the function
y = -2 (x + 4)(x - 6)
x = 1
Triangle KLM ~ triangle STR where <K = <S, <L = <T, and <M = <R. If l = 24, k = 30, m = 15 and t = 16, how long is side S?
s = 20
Solve the linear system by elimination
3x + 5y = -11
2x + 3y = -9
(-12, 5)
x2 - 8x + 15
(x - 3)(x - 5)
State the transformations applied to the function
y = -1/3 (x - 1)2 + 5
Reflection over the x-axis
Vertical compression by a factor of 1/3
Horizontal shift 1 unit right
Vertical shift 5 units up
Solve by factoring
x2 + 9x + 14 = 0
x1 = -7
x2 = -2
Find angle E
e = 11km
f = 12km
d = 13km
E = 59
Solve the linear system by substitution
x + y = 3
4x + 3y = 10
(1, 2)
5r2 + 7r - 6
(r + 2)(5r - 3)
Convert to vertex form by completing the square
y = x2 + 2x + 7
y = (x + 1)2 + 6
Solve by quadratic formula
-3x2 + 2x + 3 = 0
x1 = -0.7
x2 = 1.4
Find side y
Y = 48
Z = 25
x = 36cm
y = 28cm
Tia had $10 000 to invest. She invested part of it in a term deposit paying 4% per annum and the remainder in bonds paying 5% per annum. If the total interest earned after one year was $440, how much did she invest in each account?
Tia invested $6000 at 4% and $4000 at 5%
Find all the values of b so that the expression x? + bx - 20 can be factored.
b = -1 + 20 = 19
b = 1 - 20 = -19
b = -2 + 10 = 8
b = 2 - 10 = -8
b = -4 + 5 = 1
b = 4 - 5 = -1
A natural bridge is a stone arch formed over a river or stream. The longest natural bridge in the world is Rainbow Bridge in Utah which spans a total length of 84m and has a maximum height of 88m. Determine an equation to represent the path of the bridge.
y = -22/441 (x - 42)(x + 42)
A picture that measures 10 cm by 5 cm is to be surrounded by a mat before being framed.
The width of the mat is to be the same on all sides of the picture. The area of the mat is to be twice the area of the picture. What is the width of the mat?
The width of the mat is 2.5cm
Two surveyors, Alice and Bob, need to determine the height of a steep cliff. They stand 50 m apart where they each have a clear view of the cliff and each other. Bob measures an angle of elevation of 61• from the base of the cliff to its highest point. He also measures the angle between Alice and the base of the cliff as 72°. Alice measures the angle between Bob and the base of the cliff as 38° . How tall is the cliff?
The cliff is 59.1m tall