Answer:
1/2 (1 half)
Step-by-step explanation:
any number less than 4 is "1,2, and 3" and a standard die has 6 numbers. so if you have 3 out of 6 is equivalent to 1/2
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
<u>Step 1: Define</u>
<u /><u />
<u />
<u>Step 2: Solve for </u><em><u>y</u></em>
- Cross-multiply:
- Multiply:
- Isolate <em>y</em>:
- Rewrite:
<u>Step 3: Check</u>
<em>Plug in y to verify it's a solution.</em>
- Substitute:
- Divide:
Here, we see that 3.125 does indeed equal 3.125. ∴ y = 1.44 is a solution of the equation.
The equation y = -x^2+6x+5 is really the equation y = -1x^2+6x+5. It is in the form y = ax^2 + bx + c where
a = -1
b = 6
c = 5
We will use 'a' and 'b' in the formula below
h = -b/(2a)
h = -6/(2*(-1))
h = -6/(-2)
h = 3
The h refers to the x coordinate of the vertex. Since we know the x coordinate of the vertex (is 3), we can use it to find the y coordinate of the vertex
Simply plug x = 3 into the original equation
y = -x^2 + 6x + 5
y = -(3)^2 + 6(3) + 5
y = -(9) + 6(3) + 5
y = -9+18+5
y = 14
This is the k value, so k = 14.
In summary so far, we have a = -1, h = 3 and k = 14. Plug all this into the vertex form below
y = a(x-h)^2 + k
y = -1(x-3)^2 + 14
y = -(x-3)^2 + 14
Therefore the vertex form equation is y = -(x-3)^2 + 14
So when x = 3, the paired y value is y = 14. The point (x,y) = (3,14) is a point on the parabola. This point is either the highest or lowest point.
How can we figure out if it's the highest or lowest point? By looking at the value of 'a'. Notice how a = -1 and this is less than zero. In other words, a < 0
Since a < 0, this means the parabola opens downward forming a "frown" so to speak. That's one way to remember it: negative 'a' leads to sad face.
Anyways, this parabola opening downward means that the vertex is the highest point.
So (3,14) is the vertex
The maximum is y = 14.
Answer:
The correct answer is x < 2 or x > -2. The graph would be a line between -2 and 2 with an open circle on both.
Step-by-step explanation:
To solve, first solve the equation for the absolute value portion of the equation.
2|x| + 1 < 5
2|x| < 4
|x| < 2
Now since there is an absolute value around it, we have to complete it for the positive and negative versions.
x < 2 OR x > -2