All categories

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

You might be interested in

A television sports commentator wants to estimate the proportion of citizens who "follow professional football." Complete parts

masha68 [24]

Answer:

626 and 654

Step-by-step explanation:

Given that a television sports commentator wants to estimate the proportion of citizens who "follow professional football."

Part I:

p = 0.48

$q=1-p = 0.52\\se = \sqrt{\frac{pq}{n} } \\\frac{0.4996}{\sqrt{n} } =$

Margin of error = $2.045*\frac{0.4996}{\sqrt{n} }626$

Sample size should be >626

Part II:

If unknown we take p = 0.5 because maximum std error for this

Here everything would be the same except insted of 0.48 we use 0.5

Margin of error = $2.045*\sqrt{\frac{0.5}{\sqrt{n} } } 654$

-------------------------

a and b are too close because 0.46 proportion is close to part b proporti0n 0.5

4 0

2 years ago

Approximately what is the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertica

Lera25 [3.4K]

Answer:

212m

Step-by-step explanation:

The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.

Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;

Since we have the angle theta = 45° and opposite = 150m

According to SOH;

Sin theta = opposite/hypotenuse.

Sin45° = 150/hyp

hyp = 150/sin45°

hyp = 150/(1/√2)

hyp = 150×√2

hyp = 150√2 m

hyp = 212.13m

Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m

8 0

2 years ago

6 tractors take 10days to collect the harvest. How long would it take 18 tractors to do the same amount of work?

Nutka1998 [239]

This is a question of proportionality. However, it is not direct proportionality as it is expected that as the number of tractors increases, the work is finished faster as opposed to fewer number of tractors. This is referred to as inverse proportionality.

Therefore;
6 tractors ----- 10 days
18 tractors --- x days

Then,
x = (6*10)/18 = 10/3 days = 3 days, and 8 hours.

This means that 18 tractors will take 3 days and 8 hours to collect the same harvest.

6 0

2 years ago

Daniel deposited $500 into a savings account and after 8 years, his investment is worth $807.07. The equation A = d(1.005)12t mo

shtirl [24]

Answer:

Step-by-step explanation:

The equation A = d(1.005)^12t modelling the value of Daniel’s investment shows a monthly compounded interest. This means that the interest is compounded 12 times in a year.

We can confirm by inputting the given values

t = 8 years

d = 509

Therefore,

A = 500(1.005)12 × 8

A = 500(1.005)^96

A = $807.07

Therefore, the true statements are

Increases

Exponential

Never Decrease

5 0

2 years ago

Corinne and Aretha are having a 26-mile race. Corinne gave Aretha a head start by letting her begin 3.5 miles in front of the st

Ronch [10]

From the table, the speed of Corinne is given by

$speed=slope= \frac{2.5-1.25}{20-10} = \frac{1.25}{10} =0.125 \ miles / minute$

From the graph, the speed of Aretha is given by

$speed=slope= \frac{5.5-4.5}{20-10} = \frac{1}{10} =0.1 \ miles / minute$

The distance from the starting point of Corinne at any time t is given by D = 0.125t while the distance from the starting point of Aretha at any time t is given by D = 3.5 + 0.1t

Let t be the number of minutes after the start of the race when Corinne catchs Aretha, then

0.125t = 3.5 + 0.1t
0.025t = 3.5
t = 3.5 / 0.025 = 140

Therefore, the number of <span>minutes after the start of the race that Corinne will catch Aretha</span> is 140 minutes.

6 0

2 years ago

Read 2 more answers