$81! 70 + 11 = 81, therefore dan payed $81
Answer: ![\frac{x^{20}}{y^{15}}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B20%7D%7D%7By%5E%7B15%7D%7D)
This is the same as writing (x^20)/(y^15)
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Work Shown:
![\left(x^{-4}y^3\right)^{-5}\\\\\left(x^{-4}\right)^{-5}*\left(y^3\right)^{-5}\\\\x^{-4*(-5)}y^{3*(-5)}\\\\x^{20}y^{-15}\\\\\frac{x^{20}}{y^{15}}](https://tex.z-dn.net/?f=%5Cleft%28x%5E%7B-4%7Dy%5E3%5Cright%29%5E%7B-5%7D%5C%5C%5C%5C%5Cleft%28x%5E%7B-4%7D%5Cright%29%5E%7B-5%7D%2A%5Cleft%28y%5E3%5Cright%29%5E%7B-5%7D%5C%5C%5C%5Cx%5E%7B-4%2A%28-5%29%7Dy%5E%7B3%2A%28-5%29%7D%5C%5C%5C%5Cx%5E%7B20%7Dy%5E%7B-15%7D%5C%5C%5C%5C%5Cfrac%7Bx%5E%7B20%7D%7D%7By%5E%7B15%7D%7D)
In the second step, I used the rule that (a*b)^c = (a^c)*(b^c)
In step 3, I used the rule (a^b)^c = a^(b*c)
In the last step, I used the rule a^(-b) = 1/(a^b)
Think of this as a triangle. The height is 3 miles and the side is 4. It's a 3,4,5 triangle. You are using the Pyhtagorean Theorem to find the hypotenuse, or the diagonal distance. 3 squared plus 4 squared equals the perfect square of the distance. So, 9 plus 16 equals 25. Square root that, and you get 5. So, the diagonal distance is 5 miles.
Team A: 15 points
Team B: 3 points
Team A has twelve more points than Team B:
A = B + 12
Team A has five times as many points as Team B:
A = B × 5
A = 5B
substitute "A" with "B + 12" to solve for B:
A = 5B
(B + 12) = 5B
B + 12 = 5B
12 = 5B - B
12 = 4B
3 = B
Team B has 3 points
now substitute "B" with 3 to solve for A:
A = 5B
A = 5(3)
A = 15
Team A has 15 points
Check your answer by inputting both values into either equation:
A = 5B
(15) = 5(3)
15 = 15 ✔
A = B + 12
(15) = (3) + 12
15 = 15 ✔
2x - 2y = 12
-2x - 3y = -22
solution could be (x,2)
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2x - 6y = 10
x + 8y = 5
solution could be : (5,y)
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3x - y = -5
x + 4y = 7
solution could be : (x,2)
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x + y = 2
2x + y = 13
solution could be : neither....is this one written correctly ?