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3 years ago

According to the fundamental theorem of algebra, how many zeros does the function f(x) = 15x17 + 41x12 + 13x3 − 10 have?

Mathematics

2 answers:

nlexa [21]3 years ago

8 0

The answer you are looking for is 17

liberstina [14]3 years ago

3 0

The fundamental theorem of algebra states that a polynomial of degree has exactly n roots (including complex and multiple).
The degree of a polynomial is the highest (non-negative) exponent of the polynomial, in this case is 17 from the term 15x^17.

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A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial off

Zolol [24]

Answer:

(a) There are 32,760 different ways to appoint the officers.

(b) 3003 different ways can the committee be appointed.

(c) Probability of getting the five youngest of the qualified candidates is 0.00033.

Step-by-step explanation:

We are given that a corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members.

There are 15 qualified candidates, and officers can also serve on the committee.

(a) The number of officers are 4, i.e; A president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO).

There are 15 qualified candidates.

To find the number of ways to appoint the officers, we will use permutation because here the order of selecting the officer's matters.

So, the number of ways to appoint the officers = $^{15}\text{P}_4$

= $\frac{15!}{(15-4)!}$ { $\because ^{n}\text{P}_r = \frac{n!}{(n-r)!}$ }

= $\frac{15!}{11!}$ = 32,760 ways

(b) The number of committee numbers to appoint include five members.

There are 15 qualified candidates.

To find the number of ways in which the committee can be appointed, we will use combination because here the order of selecting the members doesn't matter.

So, the number of ways to appoint the committee = $^{15}\text{C}_5$

= $\frac{15!}{5! \times (15-5)!}$ { $\because ^{n}\text{C}_r = \frac{n!}{r! \times (n-r)!}$ }

= $\frac{15!}{5! \times 10!}$ = 3003 ways

(c) The probability of randomly selecting the committee members and getting the five youngest of the qualified candidates is given by;

Number of ways of selecting the committee = 3003

Selecting the five youngest of the qualified candidates = 1

So, the required probability = $\frac{1}{3003}$

= <u>0.00033</u>

4 0

3 years ago

How many even numbers are between 11 and 30

Debora [2.8K]

Answer:

9 even numbers are between 11 and 30.

Step-by-step explanation:

12, 14, 16, 18, 20, 22, 24, 26, 28

8 0

3 years ago

EASY QUESTION 20 POINTS& BRAINLIEST

xenn [34]

Answer:

See explanation below, and see attached photo for graphs

Step-by-step explanation:

To graph 3x + y = 6, find the x and y intercepts.

We get the x intercept when y = 0, so plug in 0 for y and solve...

3x + 0 = 6

3x = 6

x = 2, so the x intercept is at (2, 0)

We get the y intercept when x = 0, so plug in 0 for x and solve...

3(0) + y = 6

y = 6, so the y intercept is at (0, 6)

Plot those two points and draw a line through them

To graph -3x - 4y = 12, find the x and y intercepts.

We get the x intercept when y = 0, so plug in 0 for y and solve...

-3x - 4(0) = 12

-3x = 12

x = -4, so the x intercept is at (-4, 0)

We get the y intercept when x = 0, so plug in 0 for x and solve...

-3(0) - 4y = 12

-4y = 12

y = -3, so the y intercept is at (0, -3)

Plot those two points and draw a line through them

6 0

4 years ago

DB is a diameter of circle C. KAis a tangent line to circle C at point A.

Arte-miy333 [17]

Answer:

BAD is 67°

ABC is 90°

Step-by-step explanation:

ABC is 90 due to the diameter rule in circle theorem

If you need any other help alert me

5 0

3 years ago

Honey and Money are twin brothers. Mother wants to equally divide a rectangular shaped cake of 5cm wide and 6cm long. Find the l

tatuchka [14]

Answer:

Length of rectangular cake = 5 cm

Breadth of rectangular cake = 6 cm

Area of rectangle = 5 cm × 6 cm =30 cm²

If cake is equally distributed between Honey and Money, then areas of two parts should be equal.

So, Amount of cake that Honey and money got $\frac{30}{2}=15$

Share of each (Honey and Money)=15 cm²

So, if the third cake if it was cut diagonally ,the cake must have some height.

Let the height of cake be H.

So, Height of third cake $=\sqrt{L^2+B^2+H^2}\\\\=\sqrt{5^2+6^2+H^2}\\\\=\sqrt{61+H^2}$

If , H=0 that is height is negligible having 0 thickness,

Then the Length of third cake, which is divided into two parts=√61=7.81 cm

5 0

3 years ago