Let x be the first odd number.
Second odd number will be x+2
Proof:
If 3 (was) the first odd number, 3+2 would be the next which is 5.
So,
(x) (x+2) = 99
xsquare + 2x = 99
xsquare +2x - 99 = 0
xsquare +11x - 9x -99 = 0
x(x +11) -9(x + 11) = 0
(x+11) (x-9) = 0
So the two odd numbers were 9 and 11
Given that a polynomial function P(x) has rational coefficients.
Two roots are already given which are i and 7+8i,
Now we have to find two additional roots of P(x)=0
Given roots i and 7+8i are complex roots and we know that complex roots always occur in conjugate pairs so that means conjugate of given roots will also be the roots.
conjugate of a+bi is given by a-bi
So using that logic, conjugate of i is i
also conjugate of 7+8i is 7-8i
Hence final answer for the remaining roots are (-i) and (7-8i).
Answer: The first one is not a function the second is a function the third one is not one and the fourth one is
Step-by-step explanation:
The equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D
<h3>How to determine the equation</h3>
Let the number of rows be x
Number of cars in each row = x - 6 = 56
Number of rows for parking lot = 2x
Then,
Number of cars for new parking lot = 2x ( x - 6 = 56)
Expand the expression,
2 ( x - 6 = 56)
2x² - 12x = 112
Thus, the equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D
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Answer:
A function f(x) is said to be periodic, if there exists a positive real number T such that f(x+T) = f(x).
You can also just say: A periodic function is one that repeats itself in regular intervals.
Step-by-step explanation:
The smallest value of T is called the period of the function.
Note: If the value of T is independent of x then f(x) is periodic, and if T is dependent, then f(x) is non-periodic.
For example, here's the graph of sin x. [REFER TO PICTURE BELOW]
Sin x is a periodic function with period 2π because sin(x+2π)=sinx
Other examples of periodic functions are all trigonometric ratios, fractional x (Denoted by {x} which has period 1) and others.
In order to determine the period of the determined graph however, just know that the period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π. To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve.
Hopefully this helped a bit.
