Answer:
- zeros are {-2, 3, 7} as verified by graphing
- end behavior: f(x) tends toward infinity with the same sign as x
Step-by-step explanation:
A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.
<h3>Zeros</h3>
The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.
<h3>End behavior</h3>
The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.
- x → -∞; f(x) → -∞
- x → ∞; f(x) → ∞
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<em>Additional comment</em>
The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.
We know the x^2 coefficient is the opposite of the sum of the zeros:
-(7 +(-2) +3) = -8 . . . . x^2 coefficient
And we know the constant is the opposite of the product of the zeros:
-(7)(-2)(3) = 42 . . . . . constant
These checks lend further confidence that the zeros are those given.
(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)
Answer:
Step-by-step explanation:
When we collect a large data we may find a single entry repeated. In these cases we prepare frequency distribution with x = the item in one column and f = the no of times it repeats i.e. frequency in other column.
Similarly for class intervals also, we write as frequency to the right side of interval column which gives no of items which fall within the class.
This process ensures compact presenting of data.
Hence we have
a)The number of observations that fall in a class
answer: Frequency
b) The relative frequency of a class multiplied by 100
answer: Percentage. Because when we express probability as a percentage we get total 100
c) The ratio of the frequency of a class to the total number of observations
answer: Relative frequency
(Relative frequency also known as probability is frequency/total entries)
Answer:
V = StartFraction 7 times 6 over 2 EndFraction times 8
Step-by-step explanation:
Volume of a triangular prism is expressed as V = Base area × Height
Base area = area of the triangle = 1/2 × base × height
If the triangular base has a base of 7 inches and height of 6 inches.
The height of the prism is 8 inches.
Base area = 1/2 × 7 × 6
Base area = (7×6)/2
Height = 8
V = (7×6)/2 × 8
The right option is V = StartFraction 7 times 6 over 2 EndFraction times 8
Answer:
9
Step-by-step explanation:
k, n - integers
2k+1 - an odd integer
2n+1 - another odd integer
The product of them:
(2k + 1)(2n + 1) =
= 4kn + 2k + 2n + 1 =
= 2(2kn + k + n) + 1
The product of integers (2kn) is integer
and the sum of them (2kn+k+n) also is integer
So (2k + 1)(2n + 1) = 2(2kn + k + n) + 1 is an odd integer
