Which of the following tables of values is correct for the equation y equals 2 vertical bar 2 vertical bar minus 1?
A.
x y left parenthesis x comma y right parenthesis
negative 2 3 left parenthesis negative 2 comma 3 right parenthesis
negative 1 1 left parenthesis negative 1 comma 1 right parenthesis
0 negative 1 left parenthesis 0 comma negative 1 right parenthesis
1 1 (1,1)
2 3 (2,3)
B.
x y left parenthesis x comma y right parenthesis
negative 2 4 left parenthesis negative 2 comma 4 right parenthesis
negative 1 2 left parenthesis negative 1 comma 2 right parenthesis
0 0 (0,0)
1 2 (1,2)
2 4 (2,4)
C.
x y left parenthesis x comma y right parenthesis
negative 2 negative 5 left parenthesis negative 2 comma negative 5 right parenthesis
negative 1 negative 3
left parenthesis negative 1 comma negative 3 right parenthesis
0 negative 1 left parenthesis 0 comma negative 1 right parenthesis
1 1 (1,1)
2 3 (2,3)
D.
x y left parenthesis x comma y right parenthesis
negative 2 negative 4 left parenthesis negative 2 comma negative 4 right parenthesis
negative 1 negative 2
left parenthesis negative 1 comma negative 2 right parenthesis
0 0 (0,0)
1 2 (1,2)
2 4 (2,4)
A.
The equation y = 2|2|-1 can be simplified to y = 3, because the absolute value of 2 is 2 and the absolute value of 2 is also 2, so 2|2| is the same as 2(2), which equals 4. Subtracting 1 from 4 gives us 3.
Therefore, for all values of x, y is equal to 3. The correct table of values is:
x y (x,y)
negative 2 3 (-2,3)
negative 1 3 (-1,3)
0 3 (0,3)
1 3 (1,3)
2 3 (2,3)
Simplify. left parenthesis negative 24 x cubed plus 18 x plus 6 right parenthesis divided by left parenthesis 6 x plus 3 right parenthesis
A. negative 4 x squared plus 2 x minus 2
B. 4 x squared minus 2 x plus 2
C. 4 x squared plus 2 x minus 2
D. negative 4 x squared plus 2 x plus 2
C.
First, factor out 6 from the numerator:
-24x³ + 18x + 6 = 6(-4x³ + 3x + 1)
Then factor out 3 from the denominator:
6x + 3 = 3(2x + 1)
Now we can cancel out the common factor of 3:
(-4x³ + 3x + 1)/(2x + 1)
To simplify this further, we can use synthetic division or long division:
-2 | -4 0 3 1
|______ 8 -16 26
-4 8 -13 27
Therefore,
-4x³ + 3x + 1 = (-2x - 4)(2x² + 4x - 13) + 27
So the final simplified expression is:
(-24x³ + 18x + 6)/(6x + 3) = -4x² + 2x - 2 + 27/(2x + 1)
Which simplifies to:
-4x² + 2x - 2 + (27/2)(1/(x + 1/2))
This is equivalent to answer choice C: 4x² + 2x - 2.
Simplify. start fraction x over 4 x plus x squared end fraction
A. one-fourth
B. start fraction 1 over 4 plus x end fraction; where x not equals negative 4 comma 0
C. start fraction 1 over 4 plus x end fraction; where x not equals negative 4
D. start fraction 1 over 4 x end fraction; where x not equals 0
B.
We can start by factoring out x from the numerator:
x/(4x + x²) = x/(x(4 + x))
Then we can cancel out the common factor of x:
x/(x(4 + x)) = 1/(4 + x)
This simplifies to answer choice B:
1/(4 + x); where x is not equal to -4 or 0.
Simplify. negative 12 times x to the fourth power over the quantity x to the fourth power plus 8 times x to the fifth power
A. negative 12 over the quantity 1 plus 8 times x, where x does not equal negative one eighth
B. negative 12 over the quantity 1 plus 8 times x, where x does not equal negative one eighth, 0
C. negative 12 over 9 times x, where x does not equal 0
D. negative 12 over 9
A.
We can factor out x to the fourth power in the denominator:
-12x⁴/(x⁴ + 8x⁵) = -12x⁴/x⁴(1 + 8x)
We can then cancel out the common factor of x⁴:
-12x⁴/x⁴(1 + 8x) = -12/(1 + 8x)
This simplifies to answer choice A:
-12/(1 + 8x), where x is not equal to -1/8.
Simplify. The quantity x minus 2 over the quantity x squared plus 4 times x minus 12
A. 1 over the quantity x plus 6, where x does not equal negative 6
B. 1 over the quantity x plus 6, where x does not equal negative 6, 2
C. 1 over the quantity x plus 2, where x does not equal negative 2
D. x plus 2
A.
We can start by factoring the denominator:
x² + 4x - 12 = (x + 6)(x - 2)
Then we can simplify the fraction:
(x - 2)/(x² + 4x - 12) = (x - 2)/[(x + 6)(x - 2)] = 1/(x + 6); where x is not equal to -6.
This simplifies to answer choice A:
1/(x + 6), where x is not equal to -6.
Simplify. The quotient 7 over 2 times a times the quotient 5 over a squared
A. 35 over 2 times a squared, where a does not equal 0
B. 35 over 2 times a squared
C. 12 over 2 times a cubed, where a does not equal 0
D. 35 over 2 times a cubed, where a does not equal 0