Expressions, Equations, and Functions
4(6n + 7) when n = 6
172
Identify the slope and y-intercept: 6x+3y=18
What is m=-2;b=6
What is a sequence?
What is an infinite list of items that are in a specific order?
Solve:
Five friends equally split a restaurant bill that comes to $32.50. How much does each friend pay?
Each friend pays $6.50.
WORK
5x = 32.50
5x/5 = 32.50/5
x = 6.5 ~~~> $6.50
What property is shown: a(b+c)=ab+ac
Distributive Property
3 times the difference of a number m and 15 is equal to 30 (as an expression)
What is 3(m-15)=30.
What are is the X-intercept and the Y-intercept: -2x+5y=-20?
What is x-intercept=10; y-intercept=-4
What is the common difference.
Solve:
You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $164.00 total. How much did you earn per hour?
You earned $9.50 per hour.
WORK
4x + 8x + 50 = 164
12x + 50 = 164
12x + 50 - 50 = 164 - 50
12x = 114
12x/12 = 114/12
x = 9.5 ~~~> $9.50
What is the range of y = 7x?
All real numbers
Is x=8 a solution for 2x+10<4x-7?
What is no 26<25 does not work!
Solve for x: 16x-4=4(2x-3)
What is x=-1.
Write the explicit and recursive rules for the following sequence:
-12, 19, 50
What is t(n) = 31x - 43?
and t(1) = -12, t(n) = t(n - 1) + 31
Solve:
Two buildings have the same total height. One building has 8 floors with height, h. The other building has a ground floor of 16ft and 6 other floors with height, h. Write and solve an equation to find the height, h, of these floors.
8h = 16 + 6h
h = 8
WORK
8h = 16 + 6h
8h - 6h = 16 + 6h - 6h
2h = 16
2h/2 = 16/2
h = 8
Is this a function: {(1, 2), (2, 3), (2, 4)}
What is No
You buy apples at $2 per pound and oranges at $3.50 per pound. What is an expression for the total cost of fruit purchased? Also, what is the total cost of 7 apples and 4 oranges?
What is 2x+3.50y=c ; 28
Sketch a graph of the equation: y=-x+7
What is look at graph.
Write the recursive rule for the following sequence:
2.5, 15.63, 28.76
What is f(1) = 2.5.
f(n) = f(n-1) + 13.13
Solve
Online concert tickets cost $37 each, plus a service charge of $8.50 per ticket. The Web site also charges a transaction fee of $14.99 for the purchase. You paid $242.49. How many tickets did you buy?
You bought 5 tickets.
WORK
37t + 8.50t + 14.99 = 242.49
45.5t + 14.99 = 242.49
45.5t + 14.99 - 14.99 = 242.49 - 14.99
45.5t = 227.5
45.5t/45.5 = 227.5/45.5
t = 5 ~~~> 5 tickets
64(3/2) as an exponent as a radical.
(square root 64)3
A rectangular banner is 16 feet long and has an area of 80 square feet. What is the perimeter of the banner?
What is 42 feet.
Sketch a graph of the equation 4x - 2y = 16
What is look at graph (y = 2x - 8)
Write the explicit rule for the following sequence:
-2.7, 73.7, 150.1
What is t(n) = 76.4x - 79.1?
Solve
Pristine Printing will print business cards for $0.10 each plus a setup charge of $15. The Printing Place offers business cards for $0.15 each with a setup charge of $10. What number of business cards costs the same from either printer? BONUS: What would the cost be?
Printing 100 cards would cost the same from either business.
WORK
0.10n + 15 = 0.15n + 10
0.10n - 0.10n + 15 = 0.15n - 0.10n +10
15 = 0.05n + 10
15 - 10 = 0.05n + 10 - 10
5 = 0.05n
5/0.05 = 0.05n/0.05
100 = n ~~~>100 cards
BONUS answer: It would cost $25.00 to make 100 cards from either place.
WORK
0.10n + 15 = ??
0.10(100) + 15 = 25 ~~~>$25.00
0.15n + 10 = ??
0.15(100) + 10 = 25 ~~~>$25.00
Sketch a graph of the inequality: 3x - 6y < 24
See graph: y > 1/3x - 4