LINEAR SYSTEMS
Solve the system.
−4x − 2y = −12
4x + 8y = −24
(6, −6)
24a − 22 = −4(1 − 6a)
No solution
Write each as a fraction.
58%
29/50
x2 − 42x + c
441
Complete the square and factor.
x^2+bx+81
(x+9)(x+9)
Solve the system
−3x + 7y = −16
−9x + 5y = 16
(−4, −4)
−3(4x + 3) + 4(6x + 1) = 43
4
Write each as a percent. Use repeating decimals when necessary.
210%
2 1/10
a^2 + 22/13a + c
121/169
Complete the square and factor.
x^2-bx+289
(x-17)(x-17)
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?
2 fancy shirts and 5 plain shirts
10(x + 3) − (−9x − 4) = x − 5 + 3
−2
A logistics company purchases a server rack for $25,000. Due to technological obsolescence, the value of the server depreciates by 20% in the first year, by another 15% of its new value in the second year, and by a final 10% of its remaining value in the third year. What is the value of the server rack at the end of the third year?
$15,300
y^2 - 5/14y + c
25/784
Complete the square and factor.
x^2+19x+c
(x+19/2)(x+19/2)
All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7 students each and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles total?
8 vans and 7 buses
12(2k + 11) = 12(2k + 12)
No solution
A boutique clothing store buys a designer winter coat from a distributor for $150. The store marks up the price by 60% for retail display. After two months on the floor, the coat hasn't sold, so the manager applies a 30% clearance discount to the retail price. Finally, an employee uses a 10% employee coupon on the clearance price to buy it. How much does the employee pay for the coat?
$151.20
x^2+bx+196
28
Complete the square and factor.
x^2+2/5x+c
(x+1/5)(x+1/5)
Solve the system.
2x + 8y = 6
−5x − 20y = −15
Infinite number of solutions
At a local cinema, tickets cost $12 each for adults and $8 each for children. For a Saturday afternoon screening, 3 times as many children as adults attended, with an extra 20 children. If the total ticket sales for that screening reached $1,240, how many adults attended?
30 adults
A wildlife preserve records a starting population of 1,500 deer. In year one, the population increases by 12%. In year two, a harsh winter causes the population to decrease by 15%. In year three, conservation efforts cause the population to rebound with an increase of 20%. What is the final deer population size at the end of year three?
1,714 deer
p^2-bp+121/4
-11
Complete the square and factor.
x^2+7x+c
(x+7/2)(x+7/2)