33/100 * 48 =
33*48/100 =
1584/100 =
15.84
$48 - $15.84 = $32.16
Answer: C
Hey there!
We can solve systems two ways - substitution and elimination. It seems in this case that elimination is going to be easier.
Let's begin by multiplying the top equation by 3, and the bottom equation by 4:
3(5x - 4y = -24)
15x - 12y = -72
4(4x + 3y = 18)
16x + 12y = 72
Next, we'll add the two equations together to get rid of, or eliminate, the y variable and solve for the x variable:
(15x - 12y = -72) + (16x + 12y = 72)
31x = 0
x = 0
Next, we'll plug the value of the x variable into the top equation and solve for the y variable:
5(0) - 4y = -24
-4y = -24
y = 6
Therefore, x = 0 and y = 6.
Hope this helps!! :)
We may start by putting the given equation in slope-intercept from:
We can now easily identify the slope:
Since parallel lines have the same slope (as you already seem to know), any line with equation
is parallel to the given line. By choosing, for instance, , we get:
Answer:
D
Step-by-step explanation:
Complimentary measures
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