HURRY QUICKLY SOMEONE PLEASE HELP ME ANSWER THIS QUESTION (10 POINTS)
2 answers:
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Answer:
1, 5, 2, 4, 3, 7, 6
Step-by-step explanation:
After dividing by the leading coefficient, each equation can be put into the form ...
x² + y² + ax +by +c = 0
Subtracting c and separately completing the square for x-terms and y-terms, we get ...
x² + ax + (a/2)² + y² + by + (b/2)² = -c + (a/2)² + (b/2)²
(x +a/2)² + (y +b/2)² = r² = (a/2)² + (b/2)² -c . . . . . rewrite in standard form
Ordering by the square of the radius length will match the ordering by radius length, so we just need to compute (a/2)² +(b/2)² -c for each given equation. I find it convenient to let a calculator or spreadsheet do this calculation (see attached).
In the order the equations are given, the square of the radius is ...
3, 18, 45, 23, 5, 117, 46
So the order of the equations from smallest radius to largest is ...
1, 5, 2, 4, 3, 7, 6
<u><em>Answer:</em></u>
The coordinate pair that represents this solution is (20 , 240)
<u><em>Explanation:</em></u>
<u>We are given that:</u>
1- Equation that represents amount paid on football team based on number of purchased footballs is:
y = 40 + 10x
2- Equation that represents amount paid on baseball team based on number of purchased baseballs is:
y = 200 + 2x
Now, Logan wants to spend the same amount of money on both teams. This means that the y value in both equations should be equal
He also wants to buy the same number of balls for the two teams. This means that the x value in both equations should also be equal.
Therefore, we would be getting the point of intersection between the two equations.
<u>To do this, we will start by equating the two equations and solving for x as follows:</u>
40 + 10x = 200 + 2x
10x - 2x = 200 - 40
8x = 160
x = 20
<u>Then, we will use the x to substitute in any of the two equations:</u>
<u>Substituting in the first equation:</u>
y = 40 + 10x = 40 + 10(20) = 240
<u>Substituting in the second equation (as a check):</u>
y = 200 + 2x = 200 + 2(20) = 240
<u>Based on the above calculations:</u>
If Logan bought 20 balls for each team, he will be spending $240 on each
Solution set is (20, 240)
Note: the graphical solution is attached.
Hope this helps :)
