Answer:
4). (x + 2)^2 + (y - 1)^2 = 25.
Step-by-step explanation:
x^2 + y^2 + 4x - 2y - 20 = 0
x^2 + 4x + y^2 - 2y = 20
Completing the square on the x and y terms:
(x + 2)^2 - 4 + (y - 1)^2 - 1 = 20
(x + 2)^2 + (y - 1)^2 = 20 + 4 + 1
(x + 2)^2 + (y - 1)^2 = 25.
Answer:
2 inches
Step-by-step explanation:
x= smallest
3x=largest
2x=medium
x+3x+2x=12
6x=12
x=2
so smallest is 2
largest is 6 (3x)
medium is 4 (2x)
2+6+4=12
If there are real roots to be found for this polynomial, the Rational Root Theorem and synthetic division are the best way to find them. I teach from a book that uses c and d for the possible roots of the polynomial. C is our constant, 2, and d is the leading coefficient, 1. The factors of 2 are +/- 1 and +/-2. The factors for 1 are +/-1 only. Meaning, in all, there are 4 possibilities as roots for this polynomial. But there are only 3 total (because our polynomial is a third degree), so we have to find the first one, at least, from our possibilities above. Let's try x = -1, factor form (x + 1). If there is no remainder when we do the synthetic division, then -1 is a root. Put -1 outside the "box" and the coefficients from the polynomial inside: -1 (1 2 -1 -2). Bring down the first coefficient of 1 and multiply it by the -1 outside to get -1. Put that -1 up under the 2 and add to get 1. Multiply 1 times the -1 to get -1 and put that -1 up under the -1 and add to get -2. -1 times -2 is 2, and -2 + 2 = 0. So we have our first root of (x+1). The numbers we get when we do the addition along the way are the coefficients of our new polynomial, the depressed polynomial (NOT a sad one cuz it hates math, but a new polynomial that is one degree less than that of which we started!). The new polynomial is

. That can also be factored to find the remaining 2 roots. Use standard factoring to find that the other 2 solutions are (x+2) and (x-1). Our solutions then are x = -2, -1, 1, choice B from above.
Yes...thats what u want to do. you want to get the x terms on one side and everything else on the other side.
8x = 7x + 3....so we will subtract 7x from both sides
8x - 7x = 7x - 7x + 3....simplify
1x, or just x = 3 (because ur 7x's cancelled each other out)
so ur answer is : x = 3
and u can check ur answer by subbing it back into the original equation.
8x = 7x + 3
8(3) = 7(3) + 3
24 = 21 + 3
24 = 24 (correct)
There are 8 layers in the crate!
Our volume is 576 units, or cereal boxes. 576 = 12 × 6 × UNKNOWN.
We can find our unknown number by dividing:
576 ÷ 12 ÷ 6 = 8 layers!
I hope this explained it!