An absolute value is positive value of any value. So the abs value of -28 is 28. The abs value of 67 is 67. Makes sense?
If it were |27-3| for example, treat the inside of a abs as parenthesis, so you must complete PEMDAS inside of it to reduce the equation to |24|, unless you wanted it to become |27| - |3|.
For functions, this becomes slightly different and more difficult, especially when adding a variable such as x. Look below for a sample equation.
|2x-3|=1
This equation will actually have (and most others) 2 solutions for x. To find these, you’ll need to multiply the inside of the abs by -1 for one equation, and leave it as it is for the other!
2x-3=1 -(2x-3)=1
Now you have to solve BOTH equations to get your correct x-value answers.
For the first listed equation:
2x=4
x=2
For the second listed equation:
-2x+3=1
-2x=-2
x=-1
So you get the x-values -1 and 2 which both make the parent function true!
Answer:
see below
Step-by-step explanation:
slope intercept form: y=mx+b
you are given the slope, and can plug the points in to find b.
a) -3=2/3(6)+b --> b=-7
y=2/3x+7
b)10=-8(1/2)+b --> b=14
y=1/2x+13
c)4=-3(2)+b --> b=10
y=-3x+10
Answer:
(0 , 1)
Step-by-step explanation:
given y = f(x), then
y = f(x) + c is a vertical translation
• If c > 0 then vertical shift up of a units
• If c < 0 then vertical shift down of a units
here c = - 2, hence shift down of f(x) by 2 units
(0, 3) → (0, 3 - 2 ) = (0, 1)
The sample space for a particular event or number of events is simply anything that illustrates all possible outcomes of those events.
Tables can be used to display the sample space when you have two events happening, in this case, two spinners giving a number.
So, looking at the first white box (top-left corner), the number 1 that is written above it represents getting a number 1 on the spinner numbered 1 to 6 and the number of 1 written to the left of the white box represents getting a number 1 on the spinner numbered 1 to 3.
In the box, you would put 2 plus the extra points since you add the numbers on both spinners, and then add extra points because you got a double.
The numbers in each box, going along the rows (starting from top-left) are:
2 plus extra points;
3;
4;
5;
6;
7;
3;
4 plus extra points;
5;
6;
7;
8;
4;
5;
6 plus extra points;
7;
8;
9.
Notice, all possibilities of what the each of the spinners could land on and in what order are given, this is a sample space.
