Step-by-step explanation:
<u>1. Divide 8 1/3 by 2 to find the value of x:</u>
<u>Turn</u><u> </u><u>8</u><u> </u><u>1</u><u>/</u><u>3</u><u> </u><u>into</u><u> </u><u>an</u><u> </u><u>improper</u><u> </u><u>fraction</u><u>:</u>
<u>Find the reciprocal (opposite) of 2/1, then multiply:</u>
x = 25/6 or 4 1/6
<u>2. 8.1 can be put over 1</u><u>:</u>
<u>Turn</u><u> </u><u>2</u><u> </u><u>1</u><u>/</u><u>3</u><u> </u><u>into</u><u> </u><u>an</u><u> </u><u>improper</u><u> </u><u>fraction</u><u>:</u>
<u>Find</u><u> </u><u>the</u><u> </u><u>reciprocal</u><u> </u><u>(</u><u>opposite</u><u>)</u><u> </u><u>of</u><u> </u><u>8</u><u>.</u><u>1</u><u>/</u><u>1</u><u>,</u><u> </u><u>then</u><u> </u><u>multiply</u><u>:</u>
7/24.3 is your simplified answer.
Answer:
the minimum value of y is -324
Step-by-step explanation:
Add the square of half the g coefficient:
g^2 -2g +1 = y +324
(g -1)^2 -324 = y
This is "vertex form" indicating the vertex is (1, -324). The leading coefficient is positive, so the parabola opens upward. The vertex is the minimum.
Minimum y-value is -324.
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Answer:
-2, and 3
Step-by-step explanation:
-x² +x +6 = 0 is the same as
x²-x-6=0
but, x² -Sx+P=0
think what 2 numbers have the sum =1 and product = -6 that will be -2 and 3 witchh are your zeros
or you can use the graph or quadratic formula to solve
3x^2 + 3y^2 + 12x − 6y − 21 = 0 => x^2 + y^2 + 4x - 2y - 7 = 0 => x^2 + 4x + 4 + y^2 - 2y + 1 = 12 => (x + 2)^2 + (y - 1)^2 = 12 => centre is (-2, 1)
5x^2 + 5y^2 − 10x + 40y − 75 = 0 => x^2 + y^2 - 2x + 8y - 15 = 0 => x^2 - 2x + 1 + y^2 + 8y + 16 = 32 => (x - 1)^2 + (y + 4)^2 = 32 => centre is (1, -4)
5x^2 + 5y^2 − 30x + 20y − 10 = 0 => x^2 + y^2 - 6x + 4y - 2 = 0 => x^2 - 6x + 9 + y^2 + 4y + 4 = 15 => (x - 3)^2 + (y + 2)^2 = 15 => centre is (3, -2)
4x^2 + 4y^2 + 16x − 8y − 308 = 0 => x^2 + y^2 + 4x - 2y - 77 = 0 => x^2 + 4x + 4 + y^2 - 2y + 1 = 82 => (x + 2)^2 + (y - 1)^2 = 82 => centre is (-2, 1)
x^2 + y^2 − 12x − 8y − 100 = 0 => x^2 - 12x + 36 + y^2 - 8y + 16 = 152 => (x - 6)^2 + (y - 4)^2 = 152 => centre is (6, 4)
2x^2 + 2y^2 − 8x + 12y − 40 = 0 => x^2 + y^2 - 4x + 6y - 20 = 0 => x^2 - 4x + 4 + y^2 + 6y + 9 = 33 => (x - 2)^2 + (y + 3)^2 = 33 => centre is (2, -3)
4x^2 + 4y^2 − 16x + 24y − 28 = 0 => x^2 + y^2 - 4x + 6y - 7 = 0 => x^2 - 4x + 4 + y^2 + 6y + 9 = 20 => (x - 2)^2 + (y + 3)^2 = 20 => centre is (2, -3)
3x^2 + 3y^2 − 18x + 12y − 81 = 0 => x^2 + y^2 - 6x + 4y - 27 = 0 => x^2 - 6x + 9 + y^2 + 4y + 4 = 40 => (x - 3)^2 + (y + 2)^2 = 40 => centre is (3, -2)
x^2 + y^2 − 2x + 8y − 13 = 0 => x^2 - 2x + 1 + y^2 + 8y + 16 = 30 => (x - 1)^2 + (y + 4)^2 = 30 => centre = (1, -4)
x^2 + y^2 + 24x + 30y + 17 = 0
=> x^2 + 24x + 144 + y^2 + 30y + 225 = 352 => (x + 12)^2 + (y + 15)^2 = 352 => center is (-12, -15)
Therefore, 3x^2 + 3y^2 + 12x − 6y − 21 = 0 and 4x^2 + 4y^2 + 16x − 8y − 308 = 0 are concentric.
5x^2 + 5y^2 − 10x + 40y − 75 = 0 and x^2 + y^2 − 2x + 8y − 13 = 0 are concentric.
5x^2 + 5y^2 − 30x + 20y − 10 = 0 and 3x^2 + 3y^2 − 18x + 12y − 81 = 0 are concentric.
2x^2 + 2y^2 − 8x + 12y − 40 = 0 and 4x^2 + 4y^2 − 16x + 24y − 28 = 0 are concentric.