MATHEMATICS MIDDLE SCHOOL

Using the given zero, find one other zero of f(x). Explain the process you used to find your solution.2 - 3i is a zero of f(x) = x4 - 4x3 + 14x2 - 4x + 13.
*Can someone show the work I have the answers

Answers

Answer 1
Answer:

The zeros of a function are the points where the function cross the x-axis.

One other zero of \mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13} is 2 + 3i.

The zero of \mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13} is given as:

\mathbf{Zero = 2 - 3i}

The above number is a complex number.

If a complex number a + bi is the zero of a function f(x), then the conjugate a - bi is also the zero of f(x).

This means that, one other zero of \mathbf{f(x) = x^4 - 4x^3 + 14x^2 - 4x + 13} is 2 + 3i.

Read more about zeros of functions at:

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Answer 2
Answer:

Answer:

One other zero is 2+3i

Step-by-step explanation:

If 2-3i is a zero and all the coefficients of the polynomial function is real, then the conjugate of 2-3i is also a zero.

The conjugate of (a+b) is (a-b).

The conjugate of (a-b) is (a+b).

The conjugate of (2-3i) is (2+3i) so 2+3i is also a zero.

Ok so we have two zeros 2-3i and 2+3i.

This means that (x-(2-3i)) and (x-(2+3i)) are factors of the given polynomial.

I'm going to find the product of these factors (x-(2-3i)) and (x-(2+3i)).

(x-(2-3i))(x-(2+3i))

Foil!

First: x(x)=x^2

Outer: x*-(2+3i)=-x(2+3i)

Inner:  -(2-3i)(x)=-x(2-3i)

Last:  (2-3i)(2+3i)=4-9i^2 (You can just do first and last when multiplying conjugates)

---------------------------------Add together:

x^2 + -x(2+3i) + -x(2-3i) + (4-9i^2)

Simplifying:

x^2-2x-3ix-2x+3ix+4+9  (since i^2=-1)

x^2-4x+13                     (since -3ix+3ix=0)

So x^2-4x+13 is a factor of the given polynomial.

I'm going to do long division to find another factor.

Hopefully we get a remainder of 0 because we are saying it is a factor of the given polynomial.

                x^2+1

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

x^2-4x+13|  x^4-4x^3+14x^2-4x+13                    

              -( x^4-4x^3+ 13x^2)

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

                                 x^2-4x+13

                               -(x^2-4x+13)

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

                                    0

So the other factor is x^2+1.

To find the zeros of x^2+1, you set x^2+1 to 0 and solve for x.

x^2+1=0

x^2=-1

x=\pm √(-1)

x=\pm i

So the zeros are i, -i , 2-3i , 2+3i

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There are 27 red or blue marbles in the bag. The number of red marbles is 5 less than 3 times of the blue marbles. How many red marbles are in the bag? How many blue marbles are in the bag?

Answers

Let

x--------> The number of red marbles

y--------> The number of blue marbles


we know that

x+y=27\n x=27-y

equation 1


x=3y-5

equation 2


equate equation 1 and equation 2

27-y=3y-5\n 3y+y=27+5\n 4y=32\n y=8

x=3*8-5\n x=19

therefore


the answer is

The number of red marbles is 19

The number of blue marbles is 8
27=3x-5+x
27+5=4x-5+5
4x=32
4x/4=32/4
x=8
There are 8 blue marbles and 19 red marbles.

5x divided by 6 = 20

Answers

We have such equation
(5x)/(6)=20          /*6 (multiply both sides by 6)
5x=20*6
5x=120           /:5   (divide both sides by 5)
x=24 - its the answer

The value of the variable "x" in expression "5x divided by 6 = 20" is 24.

To find the value of the variable "x" in the expression "5x divided by 6 = 20", we use algebraic-techniques.

To separate the variable "x," we multiply both sides of the equation by 6, the denominator of the fraction.

This cancels out the division on the left side, leaving us with 5x on the left side:

⇒ (5x divided by 6) × 6 = 20 × 6,

⇒ (5x/6) × 6 = 20 × 6,

Simplifying the equation:

⇒ 5x = 120

To solve for the variable "x," we divide both sides of equation "5x = 120" by 5:

⇒ (5x) / 5 = 120 / 5,

⇒ x = 24

Therefore, the required value of "x" is 24.

Learn more about Algebraic Expression here

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The given question is incomplete, the complete question is

Find the value of "x" in the expression "5x divided by 6 = 20".

1. Tom and his best friend Edward are seeking to join a gym. Tom saw on television that Platinum Gym was having a grand opening in a few months. Tom is considering a membership at Platinum Gym. Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month. Tom’s best friend Edward says he plans to join Super Fit because Super Fit only charges $10 a month but has a one-time registration fee of $150.(a) Write an expression to represent the membership cost of Platinum Gym for x months.(b) Write an expression to represent the membership cost of Super Fit for x months.
(c) If Tom decides to join Platinum Gym and Edward joins Super Fit, who would pay less during the first month of membership? Who would pay less after a year of membership? Show your work.
(d) Is there a membership period for which Tom and Edward would pay the same amount? If so, how long would this membership be and how much would it cost? Show your work.
(e) Which gym membership is a better deal? Explain why.

Answer:

Answers

A) let x=months let y=costy=mx+by= 20x+ 60Remember 20 is the variable which means in this case every month it cost 20$ and 60 is the constant which means you only pay it onceB) let x= Months let y= costy=10x + 150C) platinum gymy= 20x+60y=20(1)+60y=20+60y=80Superfity=10x+150y=10(1)+150y=10+150y=160Therefore Tom will pay less after the first monthD) y=y solve for xy=20x+60y=10x+15020x+60=10x+150-10x. -10x10x+ 60=150-60. -6010x=9010x/10=90/10X=99 monthsPick any equation and sub in xY=10x+150Y=10(9)+150Y=90+150Y=240240$Know that you only have to do one equation to find y but if you want to show both you canTherefore there is a period where Tom and Edward paid the same amount, after nine months they would both pay $240E) if they plan on going to the gym 9 months and less the best deal gym is platinum gym but if they want to go for more then 9 months then the best deal gym is super fit

What males the set of integers different from the set of whole number ?

Answers

integers include negatives and decimals
whole numbers only inlcude counting numbers and 0

integers:2/3, 0.33333333, 94.345345345345..., -99
whole:0,1,2,3,4,5,6,7,8,9....

Find the value of x. Then find the measure of Arc AN. Show work on a piece of paper.a) Value of x =

b) Arc AN =

Answers

Answer:

a. x = 36

b. ∠(AN) = 144°

Step-by-step explanation:

All the angle in the circle should add up to 360°.

x + x + 4x + 4x = 360

2x + 8x = 360

10x = 360

x = 36

∠(AN) = 4x

∠(AN) = 4(36)

∠(AN) = 144°

A group of mountain climbers begin an expedition with 250 pounds of food. They plan to eat a total of 12 pounds of food per day. Write and solve a linear equation to find the number of days their food will last,

Answers

The 250 pounds of food will last for 20.83 days.

What is an equation?

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

Initial quantity of food = 250 pounds,

Since, mountain climbers begin to eat 12 pounds per day,

Let the food will last for x days,

The equation can be written as,

12x = 250

x = 20.833

The food will last for 20.83 days.

To know more about Equation on:

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Use the equation y=mx+b where m is the slope (how much it increases each time) and b is the y intercept (starting point).

Your equation would be: y=12x+0 because they eat 12 pounds each day and they start out having eaten 0 pounds.

To solve the equation, plug in the total amount of food for y and use algebra to solve for x:
250=12x
(divide by 12)
(250/12)=x
X=20.833

Their food would last approximately 20 days. (Make sure you round if required)
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