Answer:
She can buy no more than 22 decorations
Step-by-step explanation:
The costs for the party are food and decorations
Cost = food + decorations * costs per decoration
We can spend no more than 300
Food is 75
Decorations are 10 each
Let d= the number of decorations
300 >= 75 + 10 * d
Subtract 75 from each side
300-75 >= 75-75 + 10 * d
225 >= 10d
Divide each side by 10
225/10 >=10d/10
22.5 >=d
She can buy no more than 22 decorations
I will explain you and pair two of the equations as an example to you. Then, you must pair the others.
1) Two circles are concentric if they have the same center and different radii.
2) The equation of a circle with center xc, yc, and radius r is:
(x - xc)^2 + (y - yc)^2 = r^2.
So, if you have that equation you can inmediately tell the coordinates of the center and the radius of the circle.
3) You can transform the equations given in your picture to the form (x -xc)^2 + (y -yc)^2 = r2 by completing squares.
Example:
Equation: 3x^2 + 3y^2 + 12x - 6y - 21 = 0
rearrange: 3x^2 + 12x + 3y^2 - 6y = 21
extract common factor 3: 3 (x^2 + 4x) + 3(y^2 -2y) = 3*7
=> (x^2 + 4x) + (y^2 - 2y) = 7
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 7
=> (x + 2)^2 + (y - 1)^2 = 12 => center = (-2,1), r = √12.
equation: 4x^2 + 4y^2 + 16x - 8y - 308 = 0
rearrange: 4x^2 + 16x + 4y^2 - 8y = 308
common factor 4: 4 (x^2 + 4x) + 4(y^2 -8y) = 4*77
=> (x^2 + 4x) + (y^2 - 2y) = 77
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 77
=> (x + 2)^2 + (y - 1)^2 = 82 => center = (-2,1), r = √82
Therefore, you conclude that these two circumferences have the same center and differet r, so they are concentric.
2/15 and 3/5 share 15 as the least common denominator, hence, added up, it equals 11/15. Lindsay has 4/15 votes.
Answer:
The graph move up 5.
Step-by-step explanation:
When we add a constant to the end of a parabola, it shifts the graph up and down. Since the constant here is positive, the graph moves up by that number (5)
