Erratic Quadratics
The product of two binomials is
x2 + 8x + 16. What are those factors?
(x + 4) and (x + 4)
The water level of Lake Okeechobee is currently 34 feet and is receding at a rate of 0.5 foot per day. Write an equation to represent the water level, L, after d days. In how many days will the water level be 26 feet?
L = 34 - 0.5d
16 days
Solve for x
g = 6x
x = g/6
Amanda rented a bike from Shawna's Bikes. They charged her $2 per hour, plus a $10 fee. Amanda paid less than $27. Write an inequality to represent the situation, then solve the inequality to find the maximum number of hours Amanda rented the bike.
10 + 2h < 27 ; h < 8.5
27 > 2h + 10 ; 8.5 > h
The elephant population in northwestern Namibia and Etosha National Park can be predicted by the expression 2649(1.045)b, where b is the number of years since 1995. What does the value 2646 represent?
The predicted number of elephants in the park in 1995.
A rectangular garden has a length that is 3 feet longer than its width. Let w represent the width of the garden, in feet. The entire garden is surrounded by a 2-foot wide cement walkway. Write an algebraic expression to represent the area of the garden and the cement walkway then simplify the expression.
(w + 4)(w + 7)
w2 +11w + 28
Chara charges a flat fee of $3, plus $5 per hour to babysit. Write an equation for the cost, C, after h hours of babysitting. What do the slope and y-intercept represent and how much money will Chara make for 5 hours of babysitting?
C = 3 + 5h
The y-intercept represents the $3 Chara charges as an initial fee before her hourly rate. The slope represents the $5 she charges each hour.
Chara will make $28 babysitting for 5 hours.
Solve for x
u = x - k
x = u + k
Trinity had $500 in a savings account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food and entertainment. Write an inequality that represents Trinity’s situation. How many weeks can Trinity withdraw money from her account and stay within her budget?
500 - 25w > 200
200 < 500 - 25w
Trinity can withdraw from her account no more than 12 weeks and remain within her budget.
Write an expression and solve. Find a bank account balance if the account starts with $100, has an annual rate of 4%, and the money left in the account for 12 years.
100 * 1.0412
$160.10
A ball was thrown upward into the air. The height, in feet, of the ball above the grown t seconds after being thrown can be determined by the expression -16t2 + 40t + 3. What is the meaning of the 3 in the expression?
The initial height the ball was thrown from.
Attorney A charges a fixed fee of $250 for an initial meeting and $150 per hour for each hour worked after that. Attorney B charges a fixed rate of $150 for the initial meeting and $175 per hour for each hour after that. For how many hours will the cost to see the attorneys be the same and what would that cost be?
4 hours
$850
Solve for a
12am = 4
a = (4/12)(m) or a = (1/3)(m)
The eighth grade class is putting on a talent show to raise money. It cost $700 to rent the banquet hall that they are going to use. If they charge $15 for each ticket, how many tickets do they need to sell in order to raise at least $1000? Write an inequality that represents the situation. How many tickets do they need to sell to meet their goal?
15t - 700 > 1000
1000< 15t - 700
They need to sell at least 114 tickets.
Write an expression and solve. In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?
285 * 1.759
43872 subscribers
When (2x - 3) is subtracted from 5x2 what is the result.
5x2 - 2x + 3
A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. Write a system of equations to represent this situation then solve to determine the "base rate" for the empty bus and the cost to transport each person?
The base rate is $120
The charge per person in $2
Solve for a
u = ak/b
a = ub/k
More than 450 students went on a field trip. Ten buses were filled and 5 more students traveled in a car. Write and solve an inequality to represent the situation. Solve the inequality to find the minimum number of people on each bus.
450 < 10s + 5
10s + 5 > 450
There had to be a minimum of 45 students on each bus.
Write an expression to represent the situation and solve. Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds?
128 * 0.55
4 participants will remain after 5 rounds.
What is 3(x2 - 1) - (x2 - 7 + 10)
2x2 + 7x -13
The city's water reservoir currently contains 55 gallons of water before the officials decide to fill it. Water flows into the reservoir at a rate of 8 gallons per minute. Write an equation model this situation and tell what the volume will be 2.5 hours after they begin filling the reservoir.
V = 55 + 8m
1,255 gallons
Solve a
g = (1 + 2a)/a
a = 1/(g-2)
Kevin has $25. MP3 downloads cost $0.75 each. How many songs can he download and still have at least $13 left to spend? A. Write an inequality that represents Kevin’s situation. B. How many downloads can Kevin purchase?
13 < 25 - 0.75d
25 - 0.75d > 13
At most 16 downloads
Write an expression and solve. An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours?
400 * .716
51.24 mg