Answer:
x = 4 ± 5i
Step-by-step explanation:
Just use the quadratic formula (ax²+bx+c=0) like you would for every other quadratic equation. Substitute i² for -1 when you get the square root of a negative number.
a = 1
b = -8
c = 41
Solution is x = (8 ± √(64-4·41)) / 2
x = 4 ± (√-100) / 2
x = 4 ± (√-25·4)/2
x = 4 ± √-25
x = 4 ± √(25i²)
x = 4 ± 5i
Let g = graph paper and r = ruler
1st equation: 5g + 30r = 40
2nd equation: 12g + 20r = 44
Multiply the 2nd equation by -1.5 to cancel out the r's
2nd equation: 12g + 20r = 44 x -1.5 = -18g - 30r = -66
Now add the 1st equation to that:
-18g + 5g = -13g
30r -30r = 0
40 -66 = -26
The new equation becomes -13g = -26
Divide both sides by -13
g = -26 / -13
g = 2
This means each pack of graph paper cost $2.
Now replace g with 2 in the first equation to solve for the cost of a rule:
5(2) + 30r = 40
Simplify:
10 + 30r = 40
Subtract 10 from each side:
30r = 30
Divide both sides by 30:
r = 30 / 30
r = 1
Each rule cost $1.
Answer:
The remainder is 2.
Step-by-step explanation:
Use modular arithmetic.
If the remainder is x then 8^33 mod 6 = x.
8^3 = 512 = 2 mod 6
8^6 = (8^3 * 8^3) mod 6 = (2*2) mod 6 = 4 mod 6
8^30 mod 6 = (8^6)^5 mod 6 = 4^5 mod 6 = 1024 mod 6
= 4 mod 6.
Finally 8^33 mod 6 = (8^3 * 8^30) mod 6 = (2 * 4) mod 6
= 8 mod 6 = 2.
Answer:
B. -21a-15
Step-by-step Explanation:
Answer:
pints: 2 4 7 10 12
quarts: 0 2 4 5 12
Step-by-step explanation:
