Solving Equations
2(x + 4) = 16
x=4
A line that rises from left to right has this type of rate of change.
positive rate of change
Find the positive zero of the following:
x2 - 64
x=8
When looking at a table when do you use an exponential equation vs. a linear equation
Exponential when you multiply
Linear when you add/subtract
The sum of two numbers is 104. Their difference is 68. What are the numbers?
86 and 18
2(x + 5) - 5x = -6x + 5
x= -2
What is the slope between (7, 4) and (-7, -1)
5/14
When looking for solutions of a quadratic function, what are you looking for on the graph?
x-intercepts (zeros, solutions or roots)
One is the answer for any exponential expression raised to this power.
zero
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt?
$30
5x - 2x + 8 = 3x + x - 12
x= 20
The function f(x) = 37x + 20 models the total cost for Rachel to be a member at a gym for x months. What can be interpreted from the y- intercept of the function?
The initial value is $20 (membership fee)
What is the value of the larger roots of the quadratic equation?
f(x) = 3x2 -14x + 15
x=3
Kelly is studying bacteria. She begins with 5 and realizes that they double each day. How many will she have in a week?
640
The number of each type of ticket sold in the following situation: Tickets to a football game cost $5.oo if purchased before the day of the game. They cost $7.50 if purchased at the game. For a particular game, 600 tickets were sold and the receipts were $3500.
400 advanced tickets, 200 game-day tickets
0.5(0.6x - 4) + 0.8 = 0.3(-0.2x + 0.12)
x= 1.73
Susan has 48 coins totaling $8.00 and the coins are all nickels and quarters.
Write a system of equations that can be used to determine the number of nickels, n, and quarters, q, that Susan has?
n + q = 48
.05n + .25q = 8
Hannah goes cliff diving and jumps off of a cliff. Her jump is modeled by the equation. (round to the nearest whole number)
What is the max height?
h(x) = -16x2 + 124x
240 ft
Cole buys a car for 10,000 in 2020. His car depreciates at a rate of 4.5% per year. In what year will his car be worth less than $5,000
2036
The dimensions of a rectangle whose perimeter is 78 inches, when the length of the rectangle is twice its width
26x13
The length of a rectangle is 3 more than 3 times its width. The perimeter of the rectangle is 174 inches. What is the length of the rectangle?
66 inches
What are the solutions to f(x) = 2x+3 and
g(x) = x2
x = -1 and x = 3
What is the GCF of 22x2 - 8x
2x
Eliza invests $450 in a savings account with 6.02% interest per year, but never adds any more money. Mary has $500 in a bank account and adds $50 each year. When will Eliza have more money than Mary?
22 years
The amount of money each child received when Mr. Vogel left $25,000 divided between his son and daughter, with the daughter receiving $5000 less than the son.
$15,000 for the son and $10,000 for the daughter