Weeks 2 & 3
Use the commutative property and the associative property to rewrite: 3 + (5 + 2)
Commutative: 3 + (5 + 2) or (5 + 2) + 3
Associative: (3 + 5) + 2 or (3 + 2) + 5
The sum of two numbers is negative 20. One number is 4 less than the other. Find the numbers.
x = -12 y = -8
Determine if the following lines are parallel, perpendicular, or neither:
3x - 2y = 6
y = 3/2x + 1
Parallel
A couple has a total household income of $84,000. One person earns $18,000 less than twice what the other earns. How much does each earn?
$34,000 and $50,000
Solve:
25 x 29
214
16,384
Use the distributive property to simplify: -4(x + 5)
-4x - 20
Joy and her classmates formed a study group. The number of girls in the study group was 4 more than twice the number of boys. There were 20 girls in the study group. How many boys were in the study group?
8 boys
Find the x and y-intercepts and the slope:
3x - 5y = 45
x-intercept: (15, 0)
y-intercept: (0, -9)
Slope: 3/5
Two angles are supplementary. The measure of the larger angle is 12 degrees more than 3 times the smaller angle. Find the measures of the angles.
42 degrees and 138 degrees
Solve:
(3x - y)(2x - 5y)
6x2 - 17xy +5y2
Solve and identify as conditional, identity, or a contradiction:
2(3x−5)=4(2x+7)
x = -19
Conditional
Jamie has $85 in their wallet all in $1 and $5 bills. There are 5 fewer $1 than $5. How many $1 and $5 bills are in the wallet?
10 $1 bills, 15 $5 bills
Find the equation of a line with slope m=3/7 and contains the point (-1, 4)
y = 3/7x - 7
A private jet can fly 1,044 miles in 3 hours with a tailwind but only 930 miles in 3 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.
Wind Sped: 19 mph
Solve:
y-6 x y4
1/y2
Solve:
(1/3)(9x − 3) = (1/4)(−2x + 5)
x = 9/14 = 0.642857...
The neighborhood association is overseeing a carnival and they just calculated their total proceeds for the weekend. The price for admission was $7 for children and $10 for adults. It was determined that the total amount of adults present was 25 less than 3 times the amount of children and the total amount of money collected for the weekend was $3635. How many children and adults attended the carnival?
105 children, 290 adults
Solve the system of equations:
2x - 3y = 12
-12y +8x = 48
(-∞, ∞), All Real Numbers
Greta wants to make 5 pounds of a nut mix using peanuts and cashews. Her budget requires the mixture to cost her $6 per pound. Peanuts are $4 per pound, and cashews are $9 per pound. How many pounds of peanuts and how many pounds of cashews should she use?
Peanuts: 3 pounds
Cashews: 2 pounds
Solve:
(3x2 - 4y3)(3x2 + 4y3)
9x4 - 16y3
Solve and write in interval notation:
2(3y + 2(y + 6)) > 3(5y − 12)
(-∞, 12)
Elliot has a landscape maintenance business. His monthly expenses are $1,100. IF he charges $60 per job, how many jobs must Elliot complete to earn a profit of at least $4,000 a month?
At least 85 jobs (greater than or equal to 85)
Jaqueline has been offered two options for her salary as a trainer at the gym. Option A would pay her $35,000 plus $10 for each training session. Option B would pay her $15,000 plus $30 for each training session. How many training sessions would make the salary options equal?
1000 sessions
LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50% solution. How much of the 25% and how much of the 50% solution should he mix to make the 30% solution?
120 mL of 25% solution
30 mL of 50% solution
Solve:
(x4 - 3x3 - 1000)/(x + 5)
x3 - 8x2 + 40x - 200