Need help with Algebra.....?

Question

Identify the standard form of the equation that correctly represents each problem. (Since some solutions will be complex, you should not solve them.)

Matching:
1) The square of a number is less than the number. Find the number.

2) The product of two consecutive integers is 6. Find the numbers.

3) The area and perimeter of a rectangle are numerically equal. Find the dimensions if the length is three more than the width.
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a. x^2 + x + 6 = 0
b. x^2 + x - 6 = 0
c. x^2 - x - 6 = 0
d. x^2 - x + 6 = 0

Thanks for your help. =)

Answer 1

"the number" is X, so how do we get the six and the X alone on the other side of the equal sign to see how the square is related? the signs flip as you move them over, +6 becomes -6. so, in b., changing the signs and putting them on the other side gives x^2=6-X. (the number X less 6).

product means multiply, integers are just numbers. knowing that the squaring function just means that two integers (numbers) are multiplied by itself we must be looking at the squaring function on one side and the six on the other (=6). What to do with the X alone? the problem must end us 6= (-) something squared, a positive integer, minus X. answer a. gives us 6= -3^2 -3? it works.

ok, i've gotta go now, good luck on the last one!

Answer 2

I think you left something out in problem 1.
It should read The square of a number is 6 less than the number.

[1]D
[2]B
[3]C
~~
[1] x² = x - 6
[2] x(x+1) = 6
[3] (x+3)(x) = 2[x + (x+3)]

Answer 3

1) x² < x
0 < x < 1

2) x(x+1) = 6
x² + x - 6 = 0
(x - 3)(x + 2) = 6
x = 3 or -2
Answer: {2,3} or {-3,-2}

3) a = l * w
p = 2l + 2w
l * w = 2l + 2w
l = w + 3
w(w + 3) = 2(w + 3) + 2w
w² + 3w = 2w + 6 + 2w
w² - w - 6 = 0
(w - 3)(w + 2) = 0
w = 3 or -2
Since we don't measure lengths in negative values, w = 3 and l = 6

a = 18, p = 18

Q.E.D.

Answer 4

1) x^2 0
2) x(x+1) = 6
x^2+x-6 = 0

3) x=width
x+3 = length
A = x(x+3)
P = 4x+6
x^2+3x = 4x+6
x^2-x-6 = 0

Answer 5

For increasing cubic binomials the familiar formula is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D

Answer 6

okay, well i'm pretty sure 2 is c:
x^2 - x - 6 = 0
+ 6 +6
x^2 - x = 6? Idk

are we s'posed to match 1,2,3 w/ a,b,c,d?

.............i'll be back!