Odd functions are those that satisfy the condition
f(-x)=-f(x)
For example, check if x^3 is odd =>
f(x)=x^3
f(-x) = (-x)^3
-f(x)=-x^3
Since (-x)^3=-x^3, we see that f(x)=x^3 is an odd function.
In fact, polynomials which contain odd-powered terms only are odd. (constant is even)
As an exercise, you can verify that sin(x) is odd, cos(x) is even.
On graphs, odd functions are those that resemble a 180 degree rotation.
Check with graphs of above examples.
So we identify the first graph (f(x)=-x^3) is odd (we can identify a 180 degree rotation)
Odd functions have a property that the sum of individually odd functions is
also odd. For example, x+x^3-6x^5 is odd, so is x+sin(x).
For the next graph, f(x)=|x+2| is not odd (nor even) because if we rotate one part of the graph, it does not coincide with another part of the graph, so it is not odd.
For the last graph, f(x)=3cos(x), it is not odd, again because if we rotate about the origin by 180 degrees, we get a different graph. However, it is an even function because it is symmetrical about the y-axis.
Answer:
The statement is true.
Step-by-step explanation:
Let us assume that x is the required number.
Now, given that the number minus 3 is at most 12.
Hence, x - 3 ≤ 12
⇒ x ≤ 15 ......... (1)
And also given that 1 more than 2 times the number is at least 25.
Hence, 2x + 1 ≥ 25
⇒ 2x ≥ 24
⇒ x ≥ 12 .......... (2)
Therefore, from equations (1) and (2) we get the number must be greater than or equal to 12 or less than or equal to 15.
So, the statement is true. (Answer)
Answer:
-7/6
Step-by-step explanation:
The slope formula can be used with any pair of points.
m = (y2 -y1)/(x2 -x1)
m = (1 -8)/(-2 -(-8)) = -7/6
The slope of the line is -7/6.
Answer:
Answer: x=65
Step-by-step explanation:
Since they're vertical angles both sides are equal to 145 degrees
So, 145-15= 130 to get rid of the constant
Then, 130/2=65
To check you work add up all of your solutions to get 145
2*65=130 & 130+15=145
Therefore, x=65
The probability of rolling an even number on the first dice is 1/2(3/6)
The probability of rolling an even number on the first dice is also 1/2 (3/6)
So the probability of getting two even numbers on both dice is 1/2*1/2=1/4
