rates
Sam B can type at a constant speed of 32 words/min. How many words can he type in five and a half minutes?
32 words / 1 minute
x words / 5min 30sec
32 * 5 = 160 words per 5 minutes
32 / 2 = 16 words per 1/2 minute aka 30 seconds
176 words
Fill in the blanks.
Slope is the ______ over the _____.
Slope is the rise over the run
8a + 4b can be classified as...
A linear binomial
3 : a = 23 : 7
Show all your solving steps. Answer as a fraction.
3/a = 23/7
23a = 21 <-- Cross Multiply
23a/23 = 21/23 <-- Isolate the variable
a = 21/23
Two weeks is equivalent to how many minutes?
Weeks -> Days -> Hours -> Minutes
2wk = 14 days
14 days * 24hrs/1 day = 336 hours
336 hours * 60 minutes/1 hour = 20,160 minutes
How many US dollar are needed to purchase a blanket if it costs 9,000 Argentine Pesos? Round to the nearest dollar.
9,000 = 117.27x
9,000/117.27 = 117.27x/117.27
76.745 = x --> so... at least $77 USD
What is slope intercept form?
y = mx + b
Complementary Angles have a sum of...
90 degrees
18 hikers take 4.7lbs of food. How many pounds of food will 5 hikers take? Round to the nearest tenth
18/4.7 = 5/x
18x = 23.5
18x/18 = 23.5/18
x = 1.31 --> 1.3 lbs of food
1.04 Euros can be exchanged for $1 USD
If Julianna exchanges 500 Euros, how many USD will she receive? Round to the nearest cent.
1.04 Euro / 1 USD = 500 Euro / x USD
1.04x = 500
1.04x/1.04 = 500/1.04
x = $480.77 USD
Solve the following and determine which statement is true.
A. 660 miles traveled on 20 gallons of gas
B. 850 miles traveled on 25 gallons of gas
1. A > B
2. B > A
3. A = B
4. There is not enough info to tell
Option #2 is correct b/c
A. 33mi / gal and B. 34mi / gal
B is greater bc you can travel more miles per 1 gallon
Identify m (as a fraction) and b in the following equation:
y = -x - 12
(slope) m = -1/1 or 1/-1
(y-int) b = -12
Simplify the following expression:
2h2 -7h + 2h2 - h - 6 + 4h - 9h - 19
4h2 - 13h - 25
1 pound is 16 ounces, how many pounds make up 435 ounces? Round to the nearest tenth.
1/16 = x/435
16x = 435
16x/16 = 435/16
x = 27.18 -> 27.2 pounds
Four yards of fabric costs $23. What is the cost per yard?
4x = 23
4x/4 = 23/4
x = $5.75 per yard
A car can travel 65km in 2hrs. What is the car's average mile per hour if 1km = 0.62 mi? Round to the nearest tenth.
65km / 2hr = x km / 1hr
32.5km per 1 hr
convert 32.5km to mi
32.5km / x mi = 1 1km /0.62 mi
x = 52.4 mi
Graph the following on your desk:
y = -3/2x - 4
y-int = -4
slope = rise 3 left 2 or down 3 right 2
Solve the following.
-3(x - 8) + x = -30
-3(x - 8) + x = -30
-3x + 24 + x = -30
-2x = -54
-2x/-2 = -54/-2
x = 27
Elizabeth reads 629 pages of a book in 4 days. How many pages will she be able to read in 8 hours? Round to the nearest page!
629 / 96 = x / 8 <-- converted 4 days into hrs
96x = 5032
96x/96 = 5032/96
x = 52.4 --> 52 pages in 8hrs
What is the equation of a line that passes through (-1, 3) and (0, 3).
y = -x + 3
1. 7 bags of candy will feed 19 students. How many bags of candy are required to feed 86 students? Round to the nearest bag.
2. Each bag weighs approximately 4.6 lbs. Each candy is individually wrapped and weighs 4.6 oz. How many candies are in 7 bags?
1. 7 / 19 = x / 86
19x = 602
x = 31.7 --> 32 bags
2. 4.6 lbs * 16 oz = 73.6 lbs
73.6 lbs * 16 oz / 1 lb = 1177.6 oz <-- # of oz in 1 bag
1177.6 / 4.6 = 256 pieces of candy in 1 bag
256 * 7 = 1792 candies in 7 bags
A line has a y-intercept of -5 and passes through the ordered pair (-3, -1). What is the equation of this line?
y = mx + b
y = mx - 5 <- given
(0, -5) and (-3, -1)
m = -4/3
y = -4/3x - 5
A pentagonal stage has an perimeter of 75 ft and an area of 845 ft2. Determine the apothem of the stage. Round to the nearest tenth if necessary.
845 = 1/2(a)(15)(5)
845 = 37.5a
845/37.5 = 37.5a/37.5
22.53 = a --> 22.5 ft
A train travels at a constant speed of 85mph. How far will it have traveled after 1 hour and 24 minutes?
85 mi / 1 hr = x mi / 1hr 24min
85mi / 60 min = x mi / 84 min
60x = 7140
60x/60 = 7140/60
x= 119 miles
William puts $500 into the bank. Each month he spends $75. Write the equation of a line to represent William's bank account.
y = -75x + 500
500 is positive because he initially puts in $500, which for his bank account, is positive because now it has money.
75 is negative because he is spending $75 each month which is a constant rate.