<span><u><em>Answer:</em></u>
Player A had 122, while player B had 110.
<u><em>Explanation:</em></u>
<u>This is solved by:</u>
<u>1- setting Player A = x and Player B = x -12. </u>
<u>2- adding both of those, setting equal to 232:</u>
x + x - 12 = 232
<u>3- solving. </u>
x + (x - 12) = 232.
2x - 12 = 232.
2x = 244.
x = 122. </span>
Answer:
Step-by-step explanation:
16 rotations
500/32 = 15.625
15.625 rounded = 16
Therefore, the answer is 16 rotations.
Why:
500 and 32 are both given to you in distance. By divided 500 by 32 will give you how many times the shorter distance can fit into the longer distance. This will then give you the amount of rotations in the greater distance.
Once you have the answer, it asks for you to round to the nearest rotation. 15.625 rounds to 16 because 6 is in the tenths place. And we all know a number 5 or greater rounds up. So, 16 is the correct answer.
Answer: the cost of one apple is $1
Step-by-step explanation:
Let x represent the cost of one apple.
Let y represent the cost of one Pomegranate.
Donata bought 3 Apples and 5 Pomegranates at the local supermarket for a total of $16.50. This means that
3x + 5y = 16.5 - - - - - - - - - - - - -1
Meaghan bought 6 Apples and 11 Pomegranates at the same store for a total of $35.70. This means that
6x + 11y = 35.7- - - - - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 1, it becomes
6x + 10y = 33
6x + 11y = 35.7
Subtracting, it becomes
- y = - 2.7
y = 2.7
Substituting y = 2.7 into equation 1, it becomes
3x + 5 × 2.7 = 16.5
3x + 13.5 = 16.5
3x = 16.5 - 13.5 = 3
x = 3/3 = 1
1)
here, we do the left-hand-side
![\bf [sin(x)+cos(x)]^2+[sin(x)-cos(x)]^2=2 \\\\\\\ [sin^2(x)+2sin(x)cos(x)+cos^2(x)]\\\\+~ [sin^2(x)-2sin(x)cos(x)+cos^2(x)] \\\\\\ 2sin^2(x)+2cos^2(x)\implies 2[sin^2(x)+cos^2(x)]\implies 2[1]\implies 2](https://tex.z-dn.net/?f=%5Cbf%20%5Bsin%28x%29%2Bcos%28x%29%5D%5E2%2B%5Bsin%28x%29-cos%28x%29%5D%5E2%3D2%0A%5C%5C%5C%5C%5C%5C%5C%0A%5Bsin%5E2%28x%29%2B2sin%28x%29cos%28x%29%2Bcos%5E2%28x%29%5D%5C%5C%5C%5C%2B~%20%5Bsin%5E2%28x%29-2sin%28x%29cos%28x%29%2Bcos%5E2%28x%29%5D%0A%5C%5C%5C%5C%5C%5C%0A2sin%5E2%28x%29%2B2cos%5E2%28x%29%5Cimplies%202%5Bsin%5E2%28x%29%2Bcos%5E2%28x%29%5D%5Cimplies%202%5B1%5D%5Cimplies%202)
2)
here we also do the left-hand-side
![\bf \cfrac{2-cos^2(x)}{sin(x)}=csc(x)+sin(x) \\\\\\ \cfrac{2-[1-sin^2(x)]}{sin(x)}\implies \cfrac{2-1+sin^2(x)}{sin(x)}\implies \cfrac{1+sin^2(x)}{sin(x)} \\\\\\ \cfrac{1}{sin(x)}+\cfrac{sin^2(x)}{sin(x)}\implies csc(x)+sin(x)](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B2-cos%5E2%28x%29%7D%7Bsin%28x%29%7D%3Dcsc%28x%29%2Bsin%28x%29%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2-%5B1-sin%5E2%28x%29%5D%7D%7Bsin%28x%29%7D%5Cimplies%20%5Ccfrac%7B2-1%2Bsin%5E2%28x%29%7D%7Bsin%28x%29%7D%5Cimplies%20%5Ccfrac%7B1%2Bsin%5E2%28x%29%7D%7Bsin%28x%29%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B1%7D%7Bsin%28x%29%7D%2B%5Ccfrac%7Bsin%5E2%28x%29%7D%7Bsin%28x%29%7D%5Cimplies%20csc%28x%29%2Bsin%28x%29)
3)
here, we do the right-hand-side
