Algebra II Unit 1 test
Solve: 8x+2y-3z=-69 6x-4y+10z=-124 x-2y+z=-20
(-11,2,-5)
Solve by elimination (write solution as fraction, mixed number, and decimal to the 100th place): -6x+11y=28 3x-9y=11
(-373/21,-50,7), (-17 16/21,-7 1/7), (-17.76,-7.14)
Graph the feasible region represented by the system of inequalities (graph it on paper and give the 3 intersections): y≥x-2 y≤4 10x+5y≥-40
(6,4), (-6,4), (-2,-4)
Solve by graphing and verify your solution with substitution: y=(7/3)x-7 12x-8y=16
(6,7)
Optimize the system with intersections (6,4), (-6,4), (-2,-4) with the objective function ƒ(x,y)=11x-16y Then state the maximum and minimum
2, -130, 42 The maximum of 42 is at (-2, -4) The minimum of -130 is at (-6, 4)
(Thats a matrix)\/ [-5 6] [ 2 0]=D [13 6] What are the dimensions for matrix D
3x2
(Thats a matrix)\/ [-10 3 8] [ 5 2 0]=E What is the entry at e₂₁
5
(Those are matrices)\/ [ 1 0 -3] [ 6 9 2]=C [10 -3 4] [5 1] [0 -7]=A Perform A-C
Not possible; A is 2x2 and C is 3x3 and they must be the same dimensions
(Thats a matrix)\/ [1/2 -2/3] [3/4 5/6]=B Perform -72B
[-36 48] [-54 -60]
(Those are matrices)\/ [5 1] [0 -7]=A [24 -72] [ 2 3]=F Perform F+A
[29 -71] [2 -4]
(Thats a matrix)\/ [-5 6] [ 2 0]=D [13 6] What are the addresses for the number 6 in matrix D?
d₁₂ and d₃₂
Set up a system for the following: you invest $16,000 into three different accounts. The first account pays 3% interest, the second pays 5%, and the third is expected to pay 15%. You expect to make $840 in interest earnings the first year. You want to invest three times as much in the second-highest-paying account as you put in the highest-paying account
x+y+z=16,000 0.03x+0.05y+0.15z=840 y=3z
A gourmet restaurant sells two types of salad dressing, garlic and raspberry, in their gift shop. Each batch of garlic dressing requires 2 quarts of oil and 2 quarts of vinegar. Each batch of raspberry dressing requires 3 quarts of oil and 1 quart of vinegar. The chef has 18 quarts of oil and 10 quarts of vinegar on hand for making the dressings that will be sold in the gift shop that week. x = the number of batches of garlic dressing that will be made this week y = the number of batches of raspberry dressing that will be made this week Write a system of linear inequalities that models the situation Give the objective function if a batch of garlic dressing makes $24 and batch of raspberry dressing makes $38 If the vertices of the region are (0,6), (3,4), and (5,0), name the maximum income and the number of batches of garlic and raspberry dressing
x≥0 y≥0 2x+3y≤18 2x+y≤10 f(x,y)=24x+38y maximum income: $228 0 batches of garlic dressing and 6 batches of raspberry dressing