Chapter 1 & 2
Write an equation in slope-intercept form of the line that passes through the given points.
(-3,7), (2,8)
y - 8 = 2/5 (x - 2)
OR
y - 7 = 2/5 (x + 3)
Write the word sentence as an inequality:
A number n is no less than -3.
n ≥ -3
Solve the S.O.L.E. by substitution:
-2x + 3y = 9
y = 2x + 7
(-3, 1)
Find the domain and range of the function represented by (1, -5), (2, 3), and (4, 7).
Domain: 1, 2, 4
Range: -5, 3, 7
Solve the inequality, graph the solution.
3|4x + 2|≥ 6
x ≥ 0 or x ≤ -1
<====== -1 or 0 ======>
Determine the value of q when 4(3q - 2) = 16q
q = -2
Tell whether the given value is a solution of the inequality:
-3 ≤ k/2; k = -1
Yes, it is a solution of the inequality.
Solve the S.O.L.E. by elimination:
y = 5x - 8
y = -6x + 3
(1, -3)
Is the domain discrete or continuous?
INPUT, rabbits → 1, 2, 3, 4
OUTPUT, carrots → 1.5, 3, 4.5, 6
The domain is discrete, you can not have part of a rabbit.
4(3z - 2) = 16z
z = -2
You are 12 miles away from home. You start skateboarding home at a speed of 4 miles per hour.
a. Write an equation in standard form that represents your distance from home y after x hours.-------------------------------------------------------------------b. Find the x and y-intercept. What do they represent?
a. 4x + y = 12
b. y-intercept = 12, your distance from home. x-intercept = 3, how long it took you to get home.
Solve the inequality. Graph the solution.
3|4x + 2|≥ 6
x ≥ 0 or x ≤ -1
Without solving, determine whether the S.O.L.E. has one solution, infinitely many solutions, or no solution.
Y = 3x + 5
Y = 3x - 5
No solution
Use the table to write a linear function that relates y to x.
x → -1, 0, 1, 2
y → -4, 0, 4, 8
y = 4x
The position y(in meters) of a submarine after x minutes is y = -8x -12. Interpret the y-intercept and the slope.
The y-intercept, -12, is the depth (12 meters) at which the submarine starts at time 0. The slope -8 is the speed at which it descends, -8 meters per minute.
Which is steeper, a slide that rises 4 feet for every 3 feet of run, or a sliding pole that rises 5 feet for every 3 feet of run? Explain your reasoning.
A sliding pole that rises 5 feet for every 3 feet of run. This is because the pole has a steeper slope, 5/3 than the slide, 4/3.
The basketball team spends 20 minutes running laps and at least 15 minutes discussing plays. Practice lasts one hour and forty-five minutes. Write an inequality to represent the amount of time to work on other drills.
t ≤ 70, where t is time in minutes.
There are 27 red or blue marbles in a bag. The number of red marbles is 5 less than 3 times the number of blue marbles. How many red marbles are in the bag? How many blue marbles are in the bag?
19 red marbles, 8 blue marbles.
The function D=25 + 0.3x represents the daily rental charge D (in dollars) for x miles driven. Is the domain discrete or continuous?
The domain is continuous.
Solve the S.O.L.E. using any solution.
-x + 5y = 20
12y = 2x + 60
(30, 10)
The cost C (in dollars) of making n birthday cakes is represented by C = 24n +35. How many birthday cakes are made when the cost is $395? Explain your reasoning.
n = 15 birthday cakes made
An elevator can carry 800 pounds of weight.
a. One football player weighs 280 pounds and gets on the elevator. Write and solve an inequality representing the remaining weight that can be added.
b. Is it safe for two football players weighing the same amount to ride in the elevator? Explain.
a. y + 280 ≤ 705, y ≤ 425; up to 425 lbs
b. No; 470 > 425 which is outside the safe weight limit.
At a bakery, the price for 3 croissants and 2 glasses of iced tea is $14 and the price for 2 croissants and 4 glasses of iced tea is $12. How much does it cost for 1 croissant and 2 glasses of lemonade?
$6
You earn $8 per hour working at a library. The function p(x) = 8x represents the amount you earn for working x hours.
a. You work 15 hours. How much do you earn?
b. How many hours do you have to work to earn $200?
a. $120
b. 25 hours
Write an equation for the nth term of the arithmetic sequence. then find a25.
8, 11, 14, 17, ...
a25 = 80
an = 3n + 5