Matrices
Solve by substitution/ addition- elimination
2𝑥 − 3𝑦 = −4
2𝑥 + 𝑦 = 4
x = 1
y = 2
Solve for x
x2 - 4x + 24
2 +/- 2 root 5 i
Y = (x - 2)2 - 1
Opens:
Vertex:
Y-int:
X-int:
Up, (2,-1), (0,3), (3,0)(1,0)
Write in its equivalent exponential/log form:
8 = log5M
58 = M
Find the next four terms:
an = 3a(n-1) a1= 5
5, 15, 45, 135, 405
Solve for x and y
5𝑥 − 4𝑦 = 9
𝑥 − 2𝑦 = −3
y = 4
x = 5
Solve for x
x1/2 = 4
x = 16
-2(x - 7)(x + 3)3
Find the zeros:
Find the multiplicity for each zero and its behavior:
End behavior:
(-3,0)(7,0), 3,1 rises left rises right
Solve without a calculator:
ln e7
7
Give the first three terms:
an = 20 / (n+1)!
10, 10/3, 5/6
Perform the operation:
3 6 0 -1
-1 -3 + 6 0
-5 -1 2 3
3 5
5 -3
-3 2
Identify if the following is a function and give domain and range:
(-3, -1) , (2, 1) , (6, -5)
Yes, it is a function
domain: -3, 2, 6
range: -1, 1, -5
Solve by synthetic division:
X2 + 14x + 45 / (x + 9)
(x+9) and (x+5)
Solve by using like bases:
5 2x - 3 = 125
x = 3
Find the 9th term if a1 = 6 and d = -5
-34
Perform the operation:
-5 -5 -2 -3
-1 2 x 3 5
-5 -10
8 13
Is y a function of x?
x2 + y2 = 49
no, two outputs
Find the horizontal asymptote:
x / x - 2
x = 2
Solve:
log6 (x + 5) + log6 x = 2
x = 4
Give the 10th term for the following sequence: 12, 9, 6, 3
-15
Perform the operation:
0 5 -4 4
-3 1 x -2 -4
-5 1
-10 -20
10 -16
18 -24
determine the inverse function:
f(x) = 2x + 7
1/2 x - 7/2 = f-1(x)
X2 - x - 20 > 0
Find the x- intercepts
Write solutions that satisfy the given equation (positive or negative values)
x = 5, x = -4
(-infintiy, -4) U (5, infinity)
Solve:
5x = 134
X = ln 134/ ln5
Find the sum of the infinite series:
0.54545454...
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