Linear Systems
Solve Algebraically:
x + 2y -3z = -3
2x + 4y - 6z = 7
5x + 4y - z = 5
No Solution
Write a system of linear equations with the solution: (3,8,-2).
Solve Algebraically:
y - 2x^2 = 6
y + x = 12
(-2,14) and (1.5,10.5)
Write a general formula for the following sequence:
0, 1, 4, 9, 16, 25....
(n - 1) ^ 2
Write a general formula for the following sequence:
212, 182, 152, 122, 92...
242 - 30n
OR
212 - 30(n-1)
Solve Algebraically:
2x + 3y - z = 29
6x - 4y - 6z = 40
-4x + 8y + 4z = 0
(29, 40, 0)
A hawk travels North along the shore. It travels 64 miles with the wind in 2 hours. It then turns around and travels 60 miles against the wind in 4 hours. Find the windspeed and how fast the hawk could fly without any wind.
Hawk: 23.5 mph
Wind: 8.5 mph
Find two numbers whose sum is 1 and whose product is -42.
7 and -6
Write a general formula for the following sequence:
2, 8, 32, 128, 512....
2 * 4^(n-1)
Write a general formula for the following sequence:
-1, 5, -25, 125, -625, 3125....
-1 * (-5)^(n-1)
Solve Algebraically:
2x - 9y + 12z = 5
7x + 12y - 3z = 24
-4x + 3y - 6z = -11
(5/2, 2/3, 1/2)
A pharmacist wants to mix a 25% vinegar solution with pure vinegar in order to create 10mL of a 70% vinegar solution. How much pure vinegar and how much 25% solution should she use?
6mL pure vinegar
4mL 25% solution
Solve Algebraically:
2xy + x^2 = -4
4xy + 7x^2 = 12
(-2, 2) and (2, -2)
A puppy named Clifford's weights after each day is listed below.
Day 1: .8lbs Day 2: 2.3lbs
Day 3: 3.8 lbs Day 4: 5.3 lbs
Assuming this pattern will hold, how much will Clifford weigh after 2 years? Round to the nearest pound.
1,094 lbs
Find the sum of this infinite series:
9, 8, 64/9, 512/81, ...
81
Solve Algebraically:
6x + 2y - 8z = 16
3x + y - 4z = 8
-9x -3y + 12z = -24
{(x,y,z) | 3x + y - 4z = 8}
Phil wants to borrow $1,000,000 to invest in a circus. He borrows some from bank 1 which has 5% interest. He borrows the rest from bank 2 which has 3.5% interest. How much does he borrow from each bank if he owes $43,475 after one year?
$565,000 from bank 1
$435,000 from bank 2
Find the dimensions of a computer monitor whose perimeter is 60inches and whose area is 216 square inches.
12 inches by 18 inches
Find the sum:
9 + 13 + 17 + 21 + ... + 77
774
Find the sum of the first 63 terms in this sequence:
1, 1.5, 2.25, 3.375, 5.0625.....
{I'm sorry, but I really like sequences that make really big numbers.}
248,187,163,837
Solve Algebraically:
x + y + z = 2
-2x - 3y - z = -8
3x + 4y + 2z = 1-
(-2z - 2, z + 4, z)
Pam wants to mix 5 ounces of a paint that is 40% red with a paint that is 80% red. How much of the 80% paint should she use if she wants to create a paint that is 64% red.
{Note: IDK if paint works like this, I just wanted an example different from our usual chemical solutions.}
2.5 ounces.
A closed box has a length of 10 cm. If it's surface area is 480 square centimeters, and it's volume is 700 cubic centimeters, find the dimensions of the box.
{Maybe throw away this question, tricky/weird}
One side will equal 7 cm, the other will be 10cm.
How many terms are in this sequence?
16,777,216 8,388,608 4,194,304 ... 2
22
Find the sum, do not round until your final answer, sorry about the decimals, consider it a fun challenge:
6 + 7.5 + 9.375 + 11.71875 + ... + 44.70348358154
199.52