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2 years ago

Which statements are true about the graphs of all nth degree polynomials?

Mathematics

2 answers:

vova2212 [387]2 years ago

6 0

The statements are true about the graphs of all nth degree polynomials are B and D.

B. It goes up and down at most a total of n times.

D. The number of x-intercepts is at most n.

vagabundo [1.1K]2 years ago

5 0

<h2>Answer:</h2>

The statement that is true about the graphs of all nth degree polynomials is:

B.) It goes up and down at most a total of n times.

D.) The number of x-intercepts is at most n.

<h2>Step-by-step explanation:</h2>

We know that the number of times the graph goes up and down depends on the number of distinct zeros of a polynomial and as we know that a polynomial of nth degree may have repetitive zero.

Hence, the graph of nth degree polynomial goes up and down at most a total of n times.

Also, the number of x-intercept is the x-value of the point where the function is zero i.e. it depends on the number of zeros of polynomial.

Hence, The number of x-intercepts is at most n.

Also, the end behavior of graph depends on degree as well as sign of the leading coefficient.

Hence, correct options are:

Option B and option: D

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Find the average speed of a plane that leaves Bristol at 14.00 and lands in Rome at 17.15.The distance is 1200 miles

horrorfan [7]

It is very important to go through all the details that have been provided in the question. These information's will come in very handy while getting to the solution for the answer. Now let us concentrate on the problem in hand.
Distance between Bristol and Rome that the plane covers = 1200 miles
Starting time of the plane from Bristol = 14:00 hrs
Landing time of the plane in Rome = 17:15 hrs
Then
Total time taken by the plane to travel from Bristol to Rome = 17:15 - 14:00 hours
= 3 .15 hours
So
The average speed of the plane = 1200/3.15 miles per hour
= 380.95 miles per hour
From the above deduction we can conclude that the average speed of the plane traveling from Bristol to Rome is 380.95 miles per hour.

6 0

2 years ago

Kirima is building a wall for her snow fort. She first makes a firm base out of snow, and then piles uniformly sized blocks of s

MrMuchimi

Answer:

The correct option is;

0.4 represents the height of each block

Step-by-step explanation:

The information given are;

Kirima first builds a firm base of a given height

Kirima is building her wall using uniformly sized bricks

the height of the wall she is building depends on the number of blocks stacked to form the wall

Therefore, variable that depends on other variable, which is the dependent variable, y, is the height of the wall

The independent, which determines the value of the dependent variable is the number of blocks added, x

The gradient of the equation is the height of each block = 0.4

The y-intercept is the starting value, which is the firm base of dimension, 0.6

Therefore, 0.4 represents the height of each block.

7 0

2 years ago

For the data that are shown on the graph below, which best describes within which range of x-values extrapolation occurs? On a g

aalyn [17]

Given:

On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22).

To find:

The range of x-values extrapolation occurs.

Solution:

Consider the below figure attached with this question.

From the graph or given points it is clear that the x-values are 0, 1, 3, 4, 6.

It means the x-values are from 0 to 6.

So, the range of the x-values is $x\geq 0$ or $x\leq 6$ .

The required compound inequality for the range of x-values is $0\leq x\leq 6$ .

Therefore, the correct option is D.

7 0

2 years ago

For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7

Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k$

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean $210x^6y^4$

We can deduce that this term will be located somewhere in the middle. So I will calculate $k= 5; k=6 \text{ and } k =7$ .

For $k=5$

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$