Answer:
Each goal gives 5 points and a penalty costs 7 points.
Step-by-step explanation:
Let a penalty cost = x points
And a goal gives = y points
Ben makes 7 goals and 2 penalties ending the game with 21 points,
7y - 2x = 21 --------(1)
Alyssa makes 10 goals and 8 penalties ending the game with (-6) points,
10y - 8x = -6
5y - 4x = -3 --------(2)
Equation (1) multiplied by 2, then subtracted from equation (2),
(5y - 4x) - 2(7y - 2x) = -3 - 2(21)
5y - 4x - 14y + 4x = -3 - 42
-9y = -45
y = 5
From equation (1)
7(5) - 2x = 21
35 - 2x = 21
2x = 35 - 21
2x = 14
x = 7
Therefore, each goal gives 5 points and a penalty costs 7 points.
hi!
so the original equation is (x^2 -121) / x+ 11.
Those two equations look similar...
well, we know that the top equation looks like a^2 - b^2, and that equation iis equivalent to this equation: (a+b)(a-b).
So if we factor that out, we get:
( (x + 11) * (x-11) )/ (x + 11)
we can cancel the x+11 on the top and the x+11 on the bottom out.
that leaves us with x-11.
Hope this helped!
A=113.1 IN with the little 2 above the IN
The area is the product of length and width, which is to say that the length and width are factors of the area.
Assuming the dimensions are integers, you want factors of 84 that differ by 5.
... 84 = 1×84 = 2×42 = 3×28 = 4×21 = 6×14 = 7×12
The last of these pairs differ by 5, so ...
- the length is 12 inches
- the width is 7 inches.
He had 40 pencils left after he gave away 8, so originally he had 40 + 8 pencils, which is 48.
Now, he bought 4 packages, which had a total of 48 pencils, so divide 48 by 4, which is 12. He had 12 pencils in each package.
To determine the solution arithmetically, first add 8 to 40, then divide 48 by 4.
To determine the solution algebraically, set up and solve the equation 40 = 4x - 8.
Each package contained 12 pencils.
Hope this helps
