The absolute value function |<em>x</em>| always returns a non-negative number. It takes any number <em>x</em> and returns <em>x</em> if it's already non-negative, or -<em>x</em> if it is negative in order to make it positive.
For the equation
-3 + 4 |2<em>x</em> - 5| = 14
rearrange terms to get
|2<em>x</em> - 5| = 17/4
Now,
• if 2<em>x</em> - 5 ≥ 0, then |2<em>x</em> - 5| = 2<em>x</em> - 5. Then
2<em>x</em> - 5 = 17/4
• and if instead 2<em>x</em> - 5 < 0, then |2<em>x</em> - 5| = -(2<em>x</em> - 5), so that
-(2<em>x</em> - 5) = 17/4, or
2<em>x</em> - 5 = -17/4
In the first case,
2<em>x</em> - 5 = 17/4
2<em>x</em> = 17/4 + 5 = 37/4
<em>x</em> = 37/8
In the second case,
2<em>x</em> - 5 = -17/4
2<em>x</em> = -17/4 + 5 = 3/4
<em>x</em> = 3/8
Answer:
D
Step-by-step explanation:
Probability of falling NOT in the shaded region is "area of white region" <em>divided by</em> "area of whole rectangle (big one)".
<u>Area of whole rectangle:</u>
Area of rectangle = length * width = 10 * 5 = 50
<u>Area of White Region:</u>
First, area of shaded region = length * width = 4 * 2 = 8
Now,
Area of white region = area of whole rectangle - area of shaded rectangle
Area of white region = 50 - 8 = 42
Hence, probability is 
0.84 = 84%
Answer choice D is right.
Z-m=z+bx
z-m-z=z+bx-z
-m=bx
bx=-m
bx/b=-m/b; b=0
x=-m/b; b=0
2(4x+5)>7x+20 perform indicated multiplication on left side
8x+10>7x+20 subtract 7x from both sides
x+10>20 subtract 10 from both sides
x>10
or in interval notation, x=(10, +oo)
If you cards are only 5,6,7, then the probability of getting even, then even would be zero.
The directions say that the card is not replaced. Therefore, once you pick the 6, there would be no more even cards.
