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Amanda [17]
3 years ago
8

A polynomial function has a root of –5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7

. If the function has a negative leading coefficient and is of even degree, which statement about the graph is true? The graph of the function is positive on (-infinite, –5). The graph of the function is negative on (–5, 3). The graph of the function is positive on (-infinite, 1). The graph of the function is negative on (3, infinite).
Mathematics
1 answer:
Citrus2011 [14]3 years ago
4 0

The root of -5 with multiplicity 3 implies that the polynomial is a multiple of

(x+5)^3

Similarly, the two other roots imply that the polynomial is a multiply of

(x-1)^2(x-3)^7

So, the minimal polynomial which satisfies your requests on the roots is

(x+5)^3(x-1)^2(x-3)^7

which would be a polynomial of degree 12. This polynomial would be:

  • positive in (-\infty, -5)
  • negative in (-5, -3)
  • positive in (3, \infty)

Since we want a negative leading term, the signs will be opposite: your polynomial is

  • negative in (-\infty, -5)
  • positive in (-5, -3)
  • negative in (3, \infty)

So, the only true statement is the last one.

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krok68 [10]
<h3>#29</h3>

<u>Find the value of x:</u>

  • 7x - 2 = 55 + 4x (as corresponding angles)
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  • x = 19

<u>Find the value of y:</u>

  • y = 7x - 2 (as alternate exterior angles)
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<h3>#30</h3>

<u>Find the value of x:</u>

  • 14x - 34 = 9x + 1 (as alternate interior angles)
  • 14x - 9x = 1 + 34
  • 5x = 35
  • x = 7

<u>Find the value of y:</u>

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4 0
3 years ago
Please help me i need someone to help me through this whole thinggggg ill mark u as brainlist ​
bekas [8.4K]

Answer:

(36,25)

Step-by-step explanation:

We want to find where the two lines intersect

We know the x value is about 1/2 way between 30 and 40 and the y value is close to 25

The closest value is (36,25)

4 0
3 years ago
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An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are norma
Komok [63]

Using the normal distribution, it is found that 0.0329 = 3.29% of the population are considered to be potential leaders.

In a <em>normal distribution</em> with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

  • The mean is of 550, hence \mu = 550.
  • The standard deviation is of 125, hence \sigma = 125.

The proportion of the population considered to be potential leaders is <u>1 subtracted by the p-value of Z when X = 780</u>, hence:

Z = \frac{X - \mu}{\sigma}

Z = \frac{780 - 550}{125}

Z = 1.84

Z = 1.84 has a p-value of 0.9671.

1 - 0.9671 = 0.0329

0.0329 = 3.29% of the population are considered to be potential leaders.

To learn more about the normal distribution, you can take a look at brainly.com/question/24663213

8 0
3 years ago
How to find the legs of a right triangle with only the hypotenuse?
GuDViN [60]

Let x = legs of right triangle.

The set up would be:

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Understand?

8 0
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Which expression is equivalent to 4.35 - 5.5?
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Answer:  4.35 - 5.5 = -1.15 ≈ - (23÷20)

Step-by-step explanation:  

4.35 - 5.5= -1.15

The equivalent equation to 4.35 - 5.5 will be,

-1.15 ≈ - (23÷20)

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