Let's solve this problem using substitution. Given that x-y=8, x = 8 + y.
(Then x^2 = 64 + 16y + y^2)
This other equation is (x-2)^2 + (y-1)^2 = 25.
Easier to substitute 8 + y for x in (x-2)^2:
(8 + y - 2)^2 + (y-1)^2 = 25
(6 + y)^2 + (y-1)^2 = 25
36 + 12y + y^2 + y^2 - 2y + 1 = 25
Re-writing this in descending powers of y:
2y^2 + 10y + 36 + 1 = 25
Then 2y^2 + 10y - 12 = 0
Reduce by division by 2: y^2 + 5y - 6 = 0 = (y+3)(y+2) = 0
Then y=-3 and y=-2. From each of these we get x: x = 8 + y
So x = 8 - 3 = 5 and x = 8 - 2 = 6. There are common solutions.
Try (5, -3) and (6, -2). Do these points satisfy both of the given equations? If they do, you've shown that we have common solutions.
Answer:
The Aztecs made conquered people pay tributes, and asked cities, states, and countries to pay.
Hope this helps :)
10^1. 10^2. 10^3. 10^4. 10^5. Etc
6m (m+2) = 0 is the factored form
m=0, m=-2 is m
Steps are on paper
If you need more explanation, comment
Answer:
percentage change from 1960 to 1970 =( 0.11 ÷0.25 ) × 100
= 44 %
Percentage change from 1970 to 1980 =( 0.83 ÷ 0.36) × 100
= 230.55%
percentage change from 1980 to 1990 = ( 0.16 ÷ 1.19) × 100
= 13.44%
percentage change from 1990 to 2000 = (- 0.09 ÷ 1.35) × 100
= -6.667%
Step-by-step explanation:
Item : 1960 1970 1980 1990 2000
gallon: $0.25 $0.36 $1.19 $1.35 $1.26
change : 0.36 - 0.25 = 0.11
percentage change from 1960 to 1970 =( 0.11 ÷0.25 ) × 100
= 44 %
Percentage change from 1970 to 1980 =( 0.83 ÷ 0.36) × 100
= 230.55%
percentage change from 1980 to 1990 = ( 0.16 ÷ 1.19) × 100
= 13.44%
percentage change from 1990 to 2000 = (- 0.09 ÷ 1.35) × 100
= -6.667%
