LINEAR EQUATIONS
Does y=5x^4 represent GROWTH or DECAY
GROWTH because our a value (5) is greater than 1.
Find the difference of the polynomials:
(4x2-3xy+2y2)-(-6x2+7xy-2y2)
10x2-10xy+4y2
Which function would best be modeled by the scenario: The value of a baseball card decreases by 10% every year.
(Linear, Exponential, or Quadratic)
Exponential
A music streaming service charges a one-time activation fee of $15 and $10 per month for a subscription.
What is the constant and what is the variable?
$15 is the constant
$10 is the variable
What is the common ratio of the geometric sequence below and what would be the next number:
-5,-10,-20, -40, ...
r=2, next number would be -80
Factor: x² + 12x + 32
(x+4)(x+8)
How should the inequality below be graphed? (dotted or solid line, and shaded above or below)
y ≤ 2x – 4
Solid line, shaded below
Solve the equation:
25=(x+4)/5
First multiply the 5 out on both sides
125=x+4
Then subtract the 4 on both sides
Answer: x=121
Simplify: (x5)(x2)
x7
Find the product:
(4x-2)(5x+3)
20x2+2x-6
Write an explicit rule for the 15th term of the sequence: {5, 15, 45, 135…}.
(an=a1*r(n-1))
a15=5*(3)14
Create a LINEAR equation (y=mx+b) that has a slope of -2 and passes through the point (-3,1).
y=-2x-5
What are the transformations on the exponential function:
f(x)=3x+2-5
left 2 units (the +2 with x)
down 5 units (the -5 at the end)
Find the vertex of the parabola (use -b/2a):
2x2-12x+7=0
-(-12)/2(2)=3
2(3)2-12(3)+7= 18-36+7= -11
Answer: (3, -11)
How many solutions does the equation below have:
4x-5x+2=-x+4+7
-x+2=-x+11
2=11 (untrue statement)
NO SOLUTIONS
DAILY DOUBLE!!
A gym charges a one-time registration fee of $40 and $25 per month for membership.
a. Write a linear equation that models the total cost 𝐶 as a function of the number of months 𝑚.
b. In your equation, what does the number 40 represent? What does the number 25 represent?
a. C=25m+40
b. 40 represents the constant, the one-time fee. 25 represents the variable, the number that changes every month.
A rare comic book was purchased for $20. If the value of the comic book increases by 6.5% each year, how much will it be worth in 5 years? [use exponential growth formula: A=P(1+r)t ]
P=20;r=0.065;t=5
A=20(1+0.065)5
Answer: A=$27.40
Solve by factoring:
x2-5x-24=0
(x-8)(x+3)=0
x=8 and -3
Rearrange the equation in terms of y.
3m=ny+p
y=3m-p/n