In Sync
Determine the slope of the line that contains the points (2, -5) and (5, -14).
m=-3
Solve the inequality.
-x/2 > -3
x<6
Find the median of the data below.
75, 62, 65, 90, 77, 76, 89, 64, 72, 68, 95
75
How do we define "parallel lines" mathematically?
Lines which have the same slope but different y-intercepts, such that they never intersect
Simplify
a-2/b4
1/a2b4 ; a and b cannot be 0
A moose runs at a constant speed such that after 2 hours, the moose travels 40 miles. After 4 hours, she travels 80 miles. After 6 hours, she travels 120 miles, and after 8 hours, she travels 160 miles.
What is her rate of change?
20 miles per hour
Solve this inequality and graph it on a number line.
x-6>-2
x>4
Include a number line
Half of the data in a box and whisker plot are between which components of the graph?
The first and third quartiles
How do we define "perpendicular lines" mathematically?
Lines that have opposite, reciprocal slopes, causing them to intersect at a right angle
Imagine, if you will, a giraffe is standing next to Mr. Randall. Let's assume Mr. Randall is 6ft tall and casts a shadow that is 4 ft long at this time of day. The average giraffe stands around 18 ft tall. Therefore, how long must the shadow of the giraffe be by the relationship of similar triangles?
12 ft
Solve the system of equations below.
y=2/5x-2
4x-10y=-20
Parallel lines are independent; there are no solutions.
Solve this inequality and graph it on a number line.
-x/3<2
x>-6
Include a number line
Mr. Overman is playing an intense game involving two dice, six bottles of orange juice, and the tooth of an albino crocodile. In order to win on his next turn, he must roll at least one odd number and a sum of 7. Can he win? Why or why not?
Yes! These are inclusive events, so they could happen at the same time.
Ex: He rolls a 3 and a 4. 3 is odd, and the sum is 7.
Identify the constant of variation if y=10 when x=2, given that y varies directly with x. Then, write the equation of this variation.
k=5
y=5x
Simplify
2√xy - 8√xy
-6√xy
Solve this system of equations with elimination.
6x-4y=-8
3y=3x+9
(2,5)
A sporting goods store has a 25% discount on a $35.00 pair of boxing gloves. What is the discount and the new price?
Discount: $8.75
Price: $26.25
What is the probability of rolling doubles (two identical numbers) or rolling a sum of 6 on two dice?
5/18
Tommy Falcon is riding his skateboard across town to visit a friend. His speed varies inversely with his travel time. If he is riding at 15 mph, it will take him 3 hours to get to his friend's house. How long will it take if he slows down to 9 mph?
5 hours
Simplify
6-2[(5-2)2+7]
-26
A magician's prop has a perfectly square top. The area of this prop top measures 32 square feet. Find the length of one side of this contraption.
4√2 ft
A standard 8x8 square chess board has side length of 8p inches (where p is the length of a single space on the board). What is the area of the chess board?
64p2 in2
A car travels at 40 mph. What is its rate of change in miles per minute?
2/3 miles per minute
Determine whether these two lines are parallel.
y=2/5x+6
-2x+5y=30
They have the same slope, but they are actually the same exact line!
Simplify
(5x+1)(-3x+2)
-15x2+7x+2