Mathematics College

1. According to the fundamental theorem of algebra, how many zeros does the function [tex]f(x) = 3x^6 - 7x^5 - 53x^3 - 43x - 34[/tex] have?

2. What are the zeros of [tex]f(x) = 6x^3 + 25x^2 - 24x + 5[/tex]

Answers

Answer 1

Answer:

See below for answers

Step-by-step explanation:

1) The Fundamental Theorem of Algebra states that in an nth-degree polynomial, there are n zeroes at most, including those that are complex. Therefore, there are 6 zeroes in the function since it's a 6th-degree polynomial.

2) Reduce the polynomial and use the Zero Product Property:

[tex]0=6x^3+25x^2-24x+5[/tex]

[tex]0=(6x^2-5x+1)(x+5)[/tex]

[tex]0=(3x-1)(2x-1)(x+5)[/tex]

[tex]x_1=\frac{1}{3},x_2=\frac{1}{2},x_3=-5[/tex]

Related Questions

At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)?

f (n) = 2.75 + 4.75 + f (n − 1), f (0) = 2.75
f (n) = 4.75 + f (n − 1), f (0) = 2.75
f (n) = 2.75 + 4.75n, n > 0
f (n) = (2.75 + 4.75)n, n > 0

Answers

The recursive equation for f(n) will be:

f(n) = 2.75 + 4.75n, n > 0

The cost of the shoe rental = $2.75

The cost of 1 game = $2.75

The cost if n games = 4.75n

The total cost of shoe rental and n games = Cost of the shoe rental + cost of n games

Let the total cost of shoe rental and n games be f(n)

f(n) = 2.75 + 4.75n

Since at least 1 game will be played,

the recursive equation for f(n) will be:

f(n) = 2.75 + 4.75n, n > 0

Learn more on recursive functions here: https://brainly.com/question/11316313

MARKING AS BRAINLIEST!!

Answers

Answer: They are inverses of each other

============================================================

Explanation:

We need to check two things:

f(g(x)) = xg(f(x)) = x

If both of those equations are true, then f and g are inverses of each other.

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

Part 1

[tex]f(x) = -3x-12\\\\f(g(x)) = -3( g(x) )-12\\\\f(g(x)) = -3\left( \frac{-12-x}{3} \right)-12\\\\f(g(x)) = 12+x-12\\\\f(g(x)) = x\\\\[/tex]

So far, so good. Now we need to check the other equation mentioned.

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

Part 2

[tex]g(x) = \frac{-12-x}{3}\\\\g(f(x)) = \frac{-12-( f(x) )}{3}\\\\g(f(x)) = \frac{-12-( -3x-12 )}{3}\\\\g(f(x)) = \frac{-12+3x+12}{3}\\\\g(f(x)) = \frac{3x}{3}\\\\g(f(x)) = x\\\\[/tex]

That works out as well. Both equations mentioned are true, which confirms the two original functions are inverses of one another.

Josh was issued a traffic ticket for speeding. The court cost
was $40 and he had to pay $10 for every mile per hour
over the speed limit. Determine how fast Josh was driving
if the speed limit was 65 mph and his fine was $110.

Answers

Answer:

72 mph

Step-by-step explanation:

i did this on achievemath3000 and 72 was the answer

6. (5 points) Graph using two intercepts; show your work in finding the intercepts. 6x - 3y = 18
х

Answers

Answer:

Divide both sides by 18. The new coefficients will be the reciprocals of the intercepts:

[tex]6x-3y=18 \rightarrow \frac6{18}x - \frac3{18}y = 1 \rightarrow \frac x3-\frac y6 =1[/tex] The two intercepts are then 3 and -6.

(I know, dividing by 3 both sides of the equations would have made the whole process way easier).

Alternatively, plug x = 0 to find the y intercept and y=0 to find the x intercept. Either way the graph will look something like the one I'm sketching on paint.

y=sech(tan‐¹x) find the derivative ​

Answers

Recall that

d/dx sech(x) = - sech(x) tanh(x)

d/dx tan⁻¹(x) = 1/(1 + x²)

Then by the chain rule,

dy/dx = - sech(x) tanh(x) / (1 + x²)

The line passes through point Q, located at (-1, 2), and point R, located at (1, -2). Which two points determine a line parallel to line Q R ?

Answers

Answer:

i need a picture to see sorry

-2.7f + 0.3f - 16 - 4=

Answers

Answer:

-2.4f or -8 1/3

Step-by-step explanation:

I am not sure what should be at the end of the equal sign but if it is to simplify it would be -2.4f-20

If you want to solve then you get -2.4f=20 so f=-20/2.4 which equal to -8 1/3

(-4x^3-x^2+3)-(x^3-2x^2-7x+2)

Answers

[tex](-4x^3-x^2+3)-(x^3-2x^2-7x+2)\\\\=-4x^3 -x^2 +3 - x^3 + 2x^2 + 7x -2 \\\\= -5x^3 +x^2 +7x +1 \\\\=-5x^3 -5x^2 +6x^2 +6x+ x+1\\\\=-5x^2(x+1) +6x(x+1) + (x+1)\\\\=(x+1)(-5x^2 +6x +1)\\\\=-(x+1)(5x^2 -6x -1)[/tex]

7 grade math hellp mee

Answers

ANSWER: 40°
EXPLANATION: 180-140=40°

first winter event question: wort 50 points and best explenation wins brainliest

whats 50 x 23 = ? Explain your awenser

Answers

Answer:

1150

Step-by-step explanation:

50x 23=150 +100=1150

Solve for x.

5(x−4)2=4x+14


x = 9

x = 8

x=−6

x=−16

Answers

Answer:

9 is the answer.

Step-by-step explanation:

5(x − 4)2 = 4x + 14

=> 10x - 40 = 4x + 14

=> 6x = 54

=> x = 9

Therefore, 9 is the answer.

Hoped this helped.

The value of the x after solving the equation 5 (x - 4) 2 = 4x + 14 is x = 9.

What are Linear Equations?

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given linear equation,

5 (x - 4) 2 = 4x + 14

5 × 2 (x - 4) = 4x + 14

10 (x - 4) = 4x + 14

By distributive property, p (q + r) = p q + p r

10x - (10 × 4) = 4x + 14

10x - 40 = 4x + 14

10x - 4x = 14 + 40

6x = 54

x = 54 / 6

x = 9

Hence the value of x is 9.

To learn more about Linear Equations, click on the link given below :

https://brainly.com/question/11897796

#SPJ2

If f(x)=|x−5|+2, find f(3).

Answers

Answer:

4

Step-by-step explanation:

Substitute 3 for x and solve.

|3 - 5| + 2

=|-2| + 2

= 2 + 2 = 4

Which expression is equivalent to squareroot 100?
A10
B10^2
C50
D50^2

Answers

The answer is A. The square root of 100 is ten because ten times ten is 100.

Answer:

10^2=100

because all u would do is put down 10 two times and then u just multiply those 2 numbers

Step-by-step explanation:

Here is the list of numbers.

5
11
16
24
29

From the list, write down a multiple of 3.

Plz write down the answer.

Answers

Answer:

From the list the multiple of 3 is 24

Two cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find P(X = 1).

Answers

Answer:

0.14479638

Step-by-step explanation:

Because 2 cards out of 52 are drawn without replacement, hypergeometric probability distribution should be used. Hence,

Combination of drawing 1 ace of 4 total aces C(4,1)

Combination of drawing 1 non-ace of 48 total non aces C(48,1)

Combination of drawing 2 cards of total 52 cards C(52.2)

C(4,1) = 4, C(48,1) = 48, C(52,2) = 1326

4*48/1326 = 0.14479638

If a trailer carries 625 gags of cocoa. How many bags will 265 trailers carry?

Answers

Answer:

165,625 bags of cocoa.

Step-by-step explanation:

One trailer = 625 bags of cocoa, and if you have 265 trailers it means you will have to multiply 625 by 265.

88π
Rational or irrational
Good answer i mark brainlest

Answers

Answer:

Irrational

Step-by-step explanation:

The number is irrational because when you convert it to decimal form, you get 276.4601... a repeating decimal that goes on and on.

Answer:

Irrational

Step-by-step explanation:

π is irrational and 88 is rational number.

The product of the two is irrational.

If Janet earned e extra credit points. Mona earned 32 fewer extra credit points than Janet.

What is the expression that shows how many extra credit points Mona earned?

How many terms are in the expression?

Answers

e-32 is equal to the number of points Mona earned. There are two terms in this expression.

How many solutions does this system have?

y = 2/3x + 3

2x - 3y = -9


A. one solution

B. two solutions

C. no solutions

D. infinitely many solutions

Answers

Answer:

the answer is A .

Step-by-step explanation:

-2x+y=3 ----> 2x - y = -3

6x=9-3y

6x + 3y = 9

divide by 3 ,

2x + y = 3

Since the slopes are different, they will intersect.

So ONE solution.

Help me pls thank you so much

Answers

Answer: the second one

Step-by-step explanation:

An electronic company refurbishes game systems The table shows the profit made for the number of game systems sold. How much profit will be made for 35 game systems?

Answers

Answer: Give me the table and ill answer..

Step-by-step explanation:

A unique source of water pollution contributing to water quality problems in the Ganges River is: A. raw sewage. B. disease-causing organisms. C. zebra mussels. D. PCBs. E. ash from human cremations.

Answers

Is this a multiple choice answer? If not, the answer is E. Ash from human cremations

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 77 kilograms. A delivery of 6 large boxes and 2 small boxes has a total weight of 104 kilograms. How much does each type of box weigh?

Answers

I don’t know the awnser but have a great day and never give up :)

Find each key feature of the function shown in the graph. Write the range and domain in interval notation, and assume all values are integers. What's the domain and range for this graph ?

Answers

The domain of the graph is  [tex]-8<x\leq 9.5[/tex] while the range of the graph is [tex]-4\leq x<4[/tex].

The domain of the graph is input values of "x" for which the function exists while the range is the output values "y" for which the function exists.

For the graph, the domain will be the values of the graph along the x-axis.

Domain = [tex]-8<x\leq 9.5[/tex] (Note that -8 is not included)

For the range, the interval is given as: [tex]-4\leq x<4[/tex]. Note that the value of 4 is not included since it is opened.

Learn more on domain and range here: https://brainly.com/question/1942755

A runner ran 1 4/5 miles on Monday and 6 3/10 on Tuesday. How many times her Monday's distance was her Tuesday's distance? Please help me I need an answer that makes sense

Answers

He ran more than enough that’s all extra talk

Judith bought a rowboat priced at 671.65.shipping anf handling cost and additional 20% of the prices What was the total cost of the rowboat,including shipping and handilng?

Answers

Answer:

805.98

Step-by-step explanation:

671.65x.20=134.33

134.33+671.65=805.98

I need help with this badly. It's geometry and angles.

Answers

Answer:

∠ C = 118°

Step-by-step explanation:

DE = DF , then Δ DEF is isosceles with base angles congruent , then

∠ DEF = ∠ DFE = [tex]\frac{180-56}{2}[/tex] = [tex]\frac{124}{2}[/tex] = 62°

∠ DFE and ∠ DFB are adjacent angles on a straight line and sum to 180° , so

∠ DFB = 180° - 62° = 118°

BCDF is a parallelogram ( opposite sides are parallel )

The opposite angles of a parallelogram are congruent , then

∠ C = ∠ DFB = 118°

Ok done. Thank to me :>

Identify the slope and the y- intercept, as a point (0,b), from the equation.

Y=2/5x-11


Slope -

Y-intercept -

Answers

Step-by-step explanation:

Given line:

y = 2/5x - 11

Compare this with the slope-intercept form:

y = mx + b

The slope is:

m = 2/5

Y-intercept is:

b = - 11

As a point on the line it has coordinates (0, - 11)

Answer:

Hope this helps!

Step-by-step explanation:

The slope is:

m = 2/5

Y-intercept is:

b = - 11

The coordinates on the line are: (0, - 11)

(2a+15ab)-(7a+6b-10ab)

Answers

Answer:

Step-by-step explanation:

-5a - 6b + 25ab

add like terms

I don’t understand this question can you please help me ?.

Answers

Answer:

Girl: YES = 12 ; NO = 38

Boy: YES = 29 ; NO = 21

Total: YES = 41 ; NO = 59

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Girl yes=12;no=38 boy yes=29 no=59 and Yes=41 and no =59
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