Linear Equations
Find the slope between these 2 points
(2,5) & (8,17)
2
Simplify:
sqrt72
6sqrt2
Simplify:
(x^7*x^-3)/x^2
x^2
Expand and simplify:
(x-7)(x+4)
x^2-3x-28
Solve for x:
x^2-7x+12=0
x=3,4
Is this a function? Explain
{(1,4),(2,7),(3,7),(4,9)}
Yes because no repeated x-value corresponding to multiple y-values
Find the linear equation between these 2 points (Write your answer in slope-intercept form)
(-3,7), (5,-9)
y=-2x+1
Simplify:
3sqrt50-2sqrt18+sqrt8
11sqrt2
Expand this log:
log((3x^4sqrty)/z^2)
log3+4logx+1/2logy-2logz
Factor Completely:
x^2-9x+20
(x-4)(x-5)
Solve for x:
3/x+2/x=5
x=1
Find the inverse function of:
f(x)=3x-8
f^-1(x)=(x+8)/3
Find the line that is parallel to
3x-2y=8
and goes through the point
(4,-5)
y=3/2x-11
Simplify:
i^34
-1
Write this into ONE log:
2logx+1/2logy-log5
log((x^2sqrty)/5)
Find Vertex and Line of Symmetry of:
f(x)=2x^2-12x+7
(3,-11)
x=3
Solve for x:
2^(x+1)=16
x=3
Given f(x) and g(x), what is (f o g)(x)?
f(x)=2x+3
g(x)=x^2-4
(fog)(x)=2x^2-5
Find the line that is Perpendicular to
4x+3y=12
and goes through the point
(-6,2)
y=3/4x+13/2
Rationalize the numerator & simplify:
(sqrt5-2)/3
1/(3(sqrt5+2)
A population of bacteria is initially 2,500. The population grows continuously at a rate of 6% per hour.
How many bacteria will there be after 8 hours?
Round your answer to the nearest whole number.
4,040 bacteria
Find x-intercept and y-intercept of:
f(x)=x^2-5x-14
(7,0),(-2,0)
(0,-14)
Solve for x:
log_2(x)+log_2(x-2)=3
x=4
Is this function one-to-one? Explain
f(x)=x^2-6x+8
It is a Quadratic, so fails H.L.T and thus not being one-to-one.
The line L passes through the points (-4, 9) and (2, -3). Find the line M that is perpendicular to line L and passes through the point: (6,8).
y=1/2x+5
Rationalize Denominator:
7/(3-sqrt5)
(21+7sqrt5)/4
An investment of $4,000 is placed into an account earning 5.2% annual interest, compounded monthly.
How much money will be in the account after 7 years?
Round your answer to the nearest cent.
$5,751.77
Write the quadratic in vertex form:
f(x)=3x^2-18x+11
f(x)=3(x-3)^2-16
Solve for x:
sqrt(x+4)=x-2
x=5
Find Center and Radius of:
x^2+y^2-6x+8y-11=0
C:(3,-4)
r = 6
The line L passes through the points (-3, 8) and (5, -4). Line M is perpendicular to Line L. Find the x-intercept of line M.
(-9/2,0)
Simplify and write the answer in a+bi form:
((3+2i)(4-5i))/(2-i)
51/5+8/5i
An investment is placed into an account that earns 4.8% annual interest compounded continuously. After 12 years, the account contains $9,850.
How much money was originally invested?
Round your answer to the nearest cent.
$5,537.10
Find vertex, Axis of Symmetry, x-intercept(s), and y-intercepts of:
f(x)=2x^2-20x+37
vertex: (5,-13)
x=5
x: (5+-(sqrt26)/2,0)
y: (0,37)
Solve for x (Double points if you solve by completing the square):
3x^2-8x-5=0
x=(4+-sqrt31)/3
Solve this system:
x^2+y^2=25
x^2-y^2=7
(4,3),(4,-3),(-4,3),(-4,-3)