answer ASAP pls with as as much detail in how to complete it as possible :))

Answer ASAP Pls With As As Much Detail In How To Complete It As Possible :))

Answers

Answer 1
answer:
19.8
step by step:
ok so we know that a holds 18 oz. thats a 100%. B would be 110%, since it holds 10% more. Now all we have to do is multiply 110% by the 18 oz and then divide it by 100%. (rule of thirds) when we do that, the answer we get is b= oz 19.8
if you could give me brainliest that would be appreciated:))
hope i could help!

Related Questions

I'm 2x-3y=-13

4x+2y= -2

Solve ỉn substitute method,Elimination method and Graphical Method

Answers

The value of x and y are -3 and 3 respectively as shown in the graph

What is an equation?

An equation is an expression that shows how numbers and variables using mathematical operators.

Given the equation:

2x - 3y = -13      (1)

Also:

4x + 2y = -2    (2)

From equation 2:

4x + 2y = -2

2y = -4x - 2

y = -2x - 1

substitute y = -2x - 1 in equation 1:

2x - 3(-2x - 1) = -13

2x + 6x + 3 = -13

8x = -16

x = -2

Put x = -2 in eqn 2:

4(-2) + 2y = -2

-8 + 2y = -2

2y = 6

y = 3

The value of x and y are -3 and 3 respectively

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100 Points! Algebra question. Find each value if f(x)=5/x+2and g(x)=-2x+3. Only looking for an answer to question A. Please show as much work as possible. Photo attached. Thank you!

Answers

Therefore, the value of f(m-2) is 5/(m-2) + 2, and the value of function g(1/2) is 2.

What is function?

In mathematics, a function is a rule or correspondence between two sets, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function is often represented by a formula, equation, or graph.

Here,

1. To find f(m-2), we substitute (m-2) for x in the expression for f(x):

f(m-2) = 5/(m-2) + 2

So the value of f(m-2) is 5/(m-2) + 2.

2. To find g(1/2), we substitute 1/2 for x in the expression for g(x):

g(1/2) = -2(1/2) + 3

So the value of g(1/2) is -1 + 3, which simplifies to 2.

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Use the Internet to briefly define each of the following terms and explain how they are examples of annuities.

a) RRSP

Answers

A registered investment account, or RRSP, enables you to put money aside for retirement while delaying taxes on investment gains.

What is annuities?

An annuity is a financial product that provides regular payments over a specified period of time in exchange for a lump sum of money. It's often used as a retirement income source and comes in different types such as fixed, variable, immediate, and deferred annuities. It's important to understand the terms, fees, and charges before purchasing an annuity.

What is the full form of RRSP?

Registered Retirement Savings Plan is the full form of RRSP.

In Canada, both workers and independent contractors can save and invest during their retirement through Registered Retirement Savings Plans (RRSP).

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Suppose the odds for a bet are 11: 1. Your friend tells you that he thinks the odds are too generous. Select all of the odds that are less generous.

Select all that apply.
4:1
6:1
19:1
18:1

Answers

In the ratio, the odds that are less generous is C) 19:1 and D)18:1.

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Here odds for bets are 11:1.

That means if for every $1  you bets, you may wins $11.

There are [tex]\frac{1}{1+11}=\frac{1}{12}=8.33\%[/tex] chance of this happens.

If the friends thinks odds are too generous , then the odds that less than generous are,

=> for 4:1 then [tex]\frac{1}{1+4}=\frac{1}{5}= 20\%[/tex]

=> For 6:1 then [tex]\frac{1}{6+1}=\frac{1}{7}= 14\%[/tex]

=> For 19:1 then [tex]\frac{1}{19+1}=\frac{1}{20}=5\%[/tex]

=> For 18:1 then [tex]\frac{1}{18+1}=\frac{1}{19}=5.2\%[/tex]

Hence the odds that are less generous is C) 19:1 and D)18:1.

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During a sale the regular price of a pair of running shoes is reduced by 20%. If the sales price is $64 what is the regular price of the running shoes

Answers

The regular price of the running shoes is $80.

Let's denote the regular price of the running shoes as P. We know that during the sale, the price is reduced by 20%, which means the sales price is 80% (100% - 20%) of the regular price.

Given that the sales price is $64, we can set up the equation:

0.8P = $64

To find the regular price P, we divide both sides of the equation by 0.8:

P = $64 / 0.8

P = $80

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James four year old brother is trying to arrange black and yellow blocks in rows. He has 56 yellow blocks and 120 black blocks. He wants to arrange them in rows so that there are either only yellow or only black blocks in each row. He also wants to arrange them so that each row has the same number of blocks. What is the least number of rows he can make?

Answers

Answer: 5

Step-by-step explanation:

the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color.

How to solve the question?

To find the least number of rows, we need to determine the greatest common divisor (GCD) of 56 and 120, since each row must have the same number of blocks. We can use the Euclidean algorithm to find the GCD:

120 = 2 x 56 + 8

56 = 7 x 8 + 0

Therefore, the GCD of 56 and 120 is 8. This means that each row must have 8 blocks, and there will be a total of (56+120) = 176 blocks to be arranged.

Since each row can have either only yellow or only black blocks, we need to determine which color will have the greater number of rows. To do this, we can divide the total number of blocks by the number of blocks in each row:

Yellow blocks:

Number of rows = 56 ÷ 8 = 7 rows

Black blocks:

Number of rows = 120 ÷ 8 = 15 rows

Since there are more black blocks, we will use 15 rows of black blocks. Each row will have 8 blocks, so there will be a total of (15 x 8) = 120 black blocks.

We can then use the remaining 56 yellow blocks to create rows of only yellow blocks. Each row will have 8 blocks, so there will be a total of (56 ÷ 8) = 7 yellow rows.

Therefore, the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color

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Mrs. Evans wants to buy enough dog food to feed her dog for 90 days. Her dog eats 4 ounces of dog food twice a day. How many pounds of dog food should she buy?

Answers

The quantity of pounds of dog food that Mrs. Evans should buy that would be enough for her dog = 720 ounces.

How to calculate the quantity of pounds of dog food needed?

The total number of days the food is required to last = 90 days.

The quantity of dog food in ounce the dog eat per day = 4 × 2 = 8 ounces.

Therefore the quantity of pounds that will be enough for the dog for the whole 90 days would be = ?

That is;

1 day = 8 ounces

90 days = X

Make X the subject of formula;

X = 90× 8

= 720 ounces

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4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B

Answers

Answer: Vertical angles are formed by the intersection of two lines and are always equal in measure. Therefore, to find the angle that is vertical to angle ∠DEB, we need to look for another angle that has the same measure as ∠DEB.

Unfortunately, we do not know the measure of angle ∠DEB, so we cannot determine which angle is vertical to it based on the given information.

Therefore, the correct answer is: None of the angles can be determined as vertical to angle ∠DEB without additional information.

Step-by-step explanation:

Find the missing side
Please help

Answers

Answer:

Step-by-step explanation:

64 - 16= 48

[tex]\sqrt{48}[/tex]

[tex]\sqrt{3*16}[/tex]

4[tex]\sqrt{3}[/tex]

1- Assume X is a Normal random variable with mean 20 and variance 25. Find the following:
(a) P (X < 15)
(b) P (X > 30)
(c) P (18 ≤ X ≤ 25)
2. Assume ∼(0,1). Find the following:
(a) a such that P (X < a) = 0.95
(b) b such that P (X ≤ b) = 0.05
(c) c such that P (X > c) = 0.8485

Answers

1) The value of given random variable having mean 20 and variance 25 is (a) 0.1587, (b) 0.0228 and (c) 0.5328.

2) The z-score corresponding to a probability of a) 0.95 is 1.645, b) 0.05 is -1.645 and c) 0.1515 is -1.04.

What about mean?

The mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.

According to question:

1) (a) We can standardize the random variable X using the formula z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. Therefore,

z = (15 - 20) / 5 = -1

Using a standard normal distribution table or calculator, we can find P(Z < -1) = 0.1587.

(b) Similarly, we have

z = (30 - 20) / 5 = 2

Using the standard normal distribution table or calculator, we can find P(Z > 2) = 0.0228.

(c) To find P(18 ≤ X ≤ 25), we can again standardize the random variable:

z1 = (18 - 20) / 5 = -0.4

z2 = (25 - 20) / 5 = 1

Then we can use the standard normal distribution table or calculator to find P(-0.4 ≤ Z ≤ 1) = 0.5328.

2) (a) Since we are given that X is a standard normal random variable, we can use the standard normal distribution table or calculator to find the value of a such that P(X < a) = 0.95. From the table, we find that the z-score corresponding to a probability of 0.95 is 1.645. Therefore,

a = μ + σ * z = 0 + 1 * 1.645 = 1.645

(b) Similarly, we can find the value of b such that P(X ≤ b) = 0.05 using the standard normal distribution table or calculator. From the table, we find that the z-score corresponding to a probability of 0.05 is -1.645. Therefore,

b = μ + σ * z = 0 + 1 * (-1.645) = -1.645

(c) We want to find the value of c such that P(X > c) = 0.8485. Since the normal distribution is symmetric about the mean, we know that P(X > c) = 1 - P(X < c), so we can find the value of c such that P(X < c) = 1 - 0.8485 = 0.1515. From the standard normal distribution table, we find that the z-score corresponding to a probability of 0.1515 is -1.04. Therefore,

c = μ + σ * z = 0 + 1 * (-1.04) = -1.04.

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The null and alternate hypotheses are:

H0: μd = 0
H1: μd ≠ 0

The following paired observations show the number of traffic citations given for speeding by Officer Dhondt and Officer Meredith of the South Carolina Highway Patrol for the last 5 months.

Number of Citations Issued
May/June/July/August/September
Officer Dhondt: 30, 22, 25, 19, 26
Officer Meredith: 26, 19, 20, 15, 19

At the .05 significance level, is there a difference in the mean number of citations given by the two officers?

a. What is the p-value?

Answers

The value of  p-value is (a)   0.0025. (b). The decision regarding the null hypothesis is to  Reject the H0 (c.) Yes there is a difference in the mean given by the two offices.

How to solve the statistics using the data?

Recall that The p-value or probability value is a number, calculated from a statistical test, that describes how likely your results would have occurred if the null hypothesis were true.

The first thing is to find the difference between the set of data

30 - 26 = 4

22 - 19 = 3

25 - 20 = 5

19 - 15 = 4

26 - 19 = 7

The find the average of the set of scores

24.4 , 19.8, 1.52

Hypothesis formulation

H0: µ1 = µ2

Ha: µ1 ≤ µ2

Decide the test statistic and the level of significance:

alpha = 0.05

df = 5 - 1 = 4

The upper critical value at the level of significance = 2.7764

And the lower critical value at the level of significance = -2.7764

The decision rule

Reject H0 if |t| > 2.7764

Test statistics calculating

bar x1 - bar x2 =

24.4 - 19.8 = 4.6

standard error = s / √n

= 0.6798

t statistic = 4.6 / 0.6798

= 6.767

The decision would be given that 6.7670 > 2.7764, we would have to reject the null hypothesis and accept the alternate hypothesis.

The p value is given as 0.0025. This is the probability of rejecting the true H0

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Two sides of a right triangle have lengths of 2 centimeters and 6 centimeters. The third side is not the hypotenuse. How long is the third side?

Answers

Answer: 12

Step-by-step explanation: 2 x 6 = 12 = the third side

Correct answer gets brainliest!!!!

Answers

Option B

One dimensional objects

Answer:

B. One-dimensional objects

A line segment can "grow" from one-dimensional objects. A line segment is a one-dimensional figure that has two endpoints and connects them with a straight path. One-dimensional objects include lines and curves, and a line segment can be a part of a longer line or curve.

Three-dimensional objects (A) are made up of length, width, and height and cannot "grow" into a line segment, but a line segment can be a part of a three-dimensional object, such as an edge or a diagonal.

Zero-dimensional objects (C) are points, which do not have any length, width, or height. A line segment cannot "grow" from a point, but a point can be one of the endpoints of a line segment.

Find the area
Round to nearest tenth

Answers

The area of the triangle is 87.6 cm².

How to find the area of a triangle?

The area of the triangle can be found as follows:

Therefore,

area of a triangle = 1 / 2 bh

where

b = base of the triangleh = height of the triangle

Therefore,

b = 17 cm

h = 10.3 cm

Hence,

area of a triangle = 1 / 2 × 17 × 10.3

area of a triangle = 1 / 2 × 175.1

area of a triangle = 87.55

area of a triangle = 87.6 cm²

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In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?

Answers

25% percent of the females in Math town have brown eyes. To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes

what is percent  ?

A percent is a way of expressing a number as a fraction of 100. The symbol for percent is %, which means "per hundred".

In the given question,

Let's assume that there are 100 people in Math town.

60% of them are males, so there are 60 males and 40 females.

Out of the 60 males, 30% have brown eyes, so there are 18 males with brown eyes.

28% of the entire population have brown eyes, so there are 28 people with brown eyes.

To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes:

28 - 18 = 10

So, there are 10 females with brown eyes.

Out of the 40 females in Math town, what percentage have brown eyes?

10 brown-eyed females out of 40 females is:

10/40 = 0.25 or 25%

Therefore, 25% of the females in Math town have brown eyes.

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A business owner applies for a credit card to cover $15,000 in emergency expenses. The credit card charges 17.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?

$21,443.51
$21,495.64
$17,934.68
$17,956.46

Answers

Answer:

  (b)  $21,495.64

Step-by-step explanation:

You want to know the value of $15,000 after it has earned continuously compounded interest at 17.99% for 2 years.

Compound continuously

The value of an account earning interest at annual rate r compounded continuously is ...

  A = P·e^(rt)

where P is the initial account value, and t is the number of years.

Application

In this problem, we have P=15000, r=0.1799, and t=2, so the amount due will be ...

  A = $15,000·e^(0.1799·2) ≈ $21,495.64 . . . choice B

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Simplify (m2n)3. .... that is M to the 2nd power times n in parenthesis to the 3rd power

Answers

(m^2*n)^3=m^6n^3
For more questions like this, use Symbolab, it’s free, easy to use, and shows the steps.

Arc Length Formula
What is the formula representing the arc length
S generated by a radius r that rotates
5 1/2 revolutions?
S=?

Answers

The arc length generated by a radius r is S = 11πr

what is  formula for arc length?

The formula for arc length is given by:

S = θr

where θ is the central angle in radians and r is the radius of the circle.

For a full revolution, a radius r revolves around the center of the circle at an angle of 2 radians. Therefore, the central angle for 5 1/2 revolutions would be:

θ = (5 1/2) * 2π radians

θ = 11π radians

So, the arc length generated by a radius r rotating 5 1/2 revolutions is:

S = θr

S = 11πr

Note that if the radius is not given, then the arc length cannot be determined.

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Schuyler purchases 0.4 pound of
almonds that cost $9.95 per pound.
She also purchases 0.6 pound of
walnuts that cost $14.95 per pound. If
she gives the cashier $20, how much
change will she receive?

Answers

By adding the formed equations, Schuyler will receive $7.05 in change.

What is addition?

Addition is a basic arithmetic operation in mathematics that involves combining two or more numbers to form a sum.

To find the total cost of the almonds and walnuts, we need to calculate the cost of each separately and then add them together.

The cost of 0.4 pound of almonds is:

0.4 x $9.95 = $3.98

The cost of 0.6 pound of walnuts is:

0.6 x $14.95 = $8.97

The total cost of the almonds and walnuts is:

$3.98 + $8.97 = $12.95

Schuyler gives the cashier $20, so the amount of change she will receive is:

$20 - $12.95 = $7.05

Therefore, Schuyler will receive $7.05 in change.

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3/4 + x = 2. What is the value of x?

Answers

3/4 + x = 2
Subtract 3/4 to both sides to get x by itself:
x = 2 - 3/4
Calculate:
x = 5/4
***explanation to 2 - 3/4 = 5/4:
To subtract fractions, we must get a common denominator. 2 can also be written as 2/1 or 4/2, or 8/4. So we will do 8/4 - 3/4. When adding/subtracting fractions, only calculate the numerator and keep the denominator. So 8 - 3 = 5. 8/4 - 3/4 = 5/4

So the value of x is 5/4 or 1 1/4 or 1.25.

Hope this helped!

A particle moving in the horizontal direction has its position given by x(t). Find the expression for the velocity.

Ignore the pencil writing and red pen, just answer the printed answer.

Answers

The expression for the velocity is v(t) = 30m/s

Expression for the Velocity calculation

(a) x(t) = 30t

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 30t, we have:

v(t) = d/dt (30t)

= 30

So the expression for velocity is v(t) = 30 m/s.

(b) x(t) = 7sin(30)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 7sin(30), we have:

v(t) = d/dt (7sin(30))

= 7cos(30) * d/dt (30t)

= 3.5cos(30)

So the expression for velocity is v(t) = 3.5cos(30) m/s.

(c) x(t) = ecos(701)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = ecos(701), we have:

v(t) = d/dt (ecos(701))

= -e sin(701) * d/dt (701t)

= -701e sin(701t)

So the expression for velocity is v(t) = -701e sin(701t) m/s.

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if L(x) =sinx-cosx, then dxy=?​ A. cosx+sinx B. cosx-sinx C. sin²x+cosx D. none​

Answers

Answer: To find d(L(x))/dx, we need to differentiate L(x) with respect to x using the derivative rules.

d(L(x))/dx = d/dx (sinx - cosx)

= cosx + sinx

Therefore, the correct answer is option A, cosx+sinx.

Step-by-step explanation:

18 7/8 + __ = 20 1/5
what is the blank?

Answers

Answer:

x = [tex]\frac{53}{40}[/tex]

Step-by-step explanation:

18 7/8 + __ = 20 1/5

18 7/8 = 151/8

20 1/5 = 101/5

[tex]\frac{151}{8}[/tex] + x = [tex]\frac{101}{5}[/tex]

x = [tex]\frac{101}{5}[/tex] - [tex]\frac{151}{8}[/tex]

x = [tex]\frac{53}{40}[/tex]

So, the answer is [tex]\frac{53}{40}[/tex]

PLS HELP I WILL RATE!!
Consider the graph of the function f(x)= 1n x Which is a feature of function g if g(x)=-f(x-4)

Answers

A feature of function gif g(x) = f(x-4) is D. horizontal asymptote of y = 4

What is the asymptote about

A horizontal asymptote is a straight line on a graph that a function approaches but never touches as the independent variable (usually denoted as x) increases or decreases without bound. In other words, the function gets closer and closer to the horizontal line as x becomes very large or very small, but it never actually touches or crosses it.

A function can have at most two horizontal asymptotes - one on the left side of the graph and one on the right side. The horizontal asymptotes of a function are determined by the highest degree of the polynomial in the numerator and the denominator of the function.

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Given the piecewise function below, evaluate the function as indicated

Answers

The evaluation of the functions using piecewise function gives:

f(-9) =  8

f(0) =  2

f(6) =  7

f(-6) =  4

f(3) =  4.5

f(9) = -6

How to evaluate the functions using piecewise function?

To evaluate the functions using piecewise function, we have to the condition they satisfy. That is:

For f(-9), x = -9. Thus, x≤ -6. So use f(x) = (-4/3)x - 4 to evaluate f(-9). That is:

f(-9) =  (-4/3)*(-9) - 4

f(-9) =  8

For f(0), x = 0. Thus, -6 x ≤ 6. So  use f(x) = (5/6)x + 2 to evaluate f(0). That is:

f(0) = (5/6)*0 + 2

f(0) =  2

For f(6), x = 6. Thus, -6 x ≤ 6. So use f(x) = (5/6)x + 2 to evaluate f(6). That is:

f(6) = (5/6)*6 + 2

f(6) =  7

For f(-6), f(x) = (-4/3)x - 4:

f(-6) = (-4/3)*(-6) - 4

f(-6) =  4

For f(3), f(x) = (5/6)x + 2:

f(3) = (5/6)*3 + 2

f(3) =  4.5

For f(9), x = 9. Thus, x > 6. Use f(x) = -2x + 12:

f(9) = -2*9 + 12

f(9) = -6

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Which equation is correct for the circle shown on the graph?

(x+3)²+ (y-6)² = 4

(x-3)² + (y+6)² = 4

(x+3)² + (y-6)² = 2

(x-3)² + (y-6)² = 4

Answers

I think I would be a do u need the reason why

Option 2 is the correct answer, that is, the equation of the given circle is (x+3)² + (y - 6)² = 4 with center at (-3,6) and radius 2.

What is a distance formula?

The distance formula is a mathematical formula used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem as:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

where  (x₁, y₁) and (x₂, y₂) are the x and y coordinates of the said two points. This formula works for any two points in a two-dimensional space with a Cartesian coordinate system.

To answer this we need to know the equation of a circle.

Let (a,b) be the center of a circle with radius r, then the equation of the circle can be written as:

(x - a)² + (y - b)² = r²

We see that from the given graph center of the circle is the point (-3,6) and radius will be 2.

We can now substitute these information in the circle equation,

(x - -3)² + (y - 6)² = 2²

(x+3)² + (y - 6)² = 4

That is the equation of the given circle is (x+3)² + (y - 6)² = 4.

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A bicycle training wheel has a radius of 3 inches. The bicycle wheel has a radius of 10 inches. Approximately how much smaller, in square inches and rounded to the nearest hundredth, is the area of the training wheel than the area of the regular wheel?

Answers

The training wheel has an area approximately 286.34 square inches smaller than the regular wheel.

The area of a circle is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since we have the radii of both wheels, we can use this formula to find their respective areas.

The area of the training wheel is A₁ = π(3)² = 9π square inches.

The area of the regular wheel is A₂ = π(10)² = 100π square inches.

To find the difference in their areas, we can subtract A₁ from A₂:

A₂ - A₁ = 100π - 9π = 91π

So the difference in their areas is 91π square inches. To round to the nearest hundredth, we can use the approximation π ≈ 3.14:

91π ≈ 286.34 square inches

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Determine the rate of change of the function given by the table.

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Answers

Answer:

Step-by-step explanation:

1

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12

Answers

Answer:

To determine the classification of a triangle based on its side lengths, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the shorter sides) is equal to the square of the length of the hypotenuse (the longest side).

For this particular triangle with side lengths 6 cm, 10 cm, and 12 cm, we can apply the Pythagorean theorem to determine whether the triangle is acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is equal to 90 degrees).

Using the Pythagorean theorem, we find:

6^2 + 10^2 = 136

12^2 = 144

Since 136 is less than 144, we know that 6 cm, 10 cm, and 12 cm are the side lengths of a triangle that is obtuse (one angle is greater than 90 degrees), because the longest side (the hypotenuse) is greater than the sum of the squares of the lengths of the other two sides.

Therefore, the correct answer is: obtuse, because 6^2 + 10^2 < 12^2.

100 Points! Write a polynomial function of least degree with integral coefficients that have the given zeros of -1,1,i√6. Photo attached. Please show as much work as possible. Thank you!

Answers

The required polynomial  [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex].

What is a polynomial ?

A polynomial is a mathematical expression that consists of variables and coefficients, combined by addition, subtraction, and multiplication, but not division by a variable.

To write a polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex], we need to include their conjugates as well. This is because complex roots always come in conjugate pairs.

The conjugate of  [tex]i\sqrt{6[/tex] is  [tex]-i\sqrt{6[/tex], so our polynomial function will have the following zeros: -1, 1,  [tex]i\sqrt{6[/tex], and  [tex]-i\sqrt{6[/tex].

To find the polynomial function, we can use the fact that the product of the factors of a polynomial is equal to the polynomial itself. So, we can start by multiplying out the factors:

[tex](x+1)(x-1)(x-i\sqrt6)(x+i\sqrt6)[/tex]

Expanding this out gives:

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

Multiplying these two expressions gives:

[tex]x^4+5x^2-6[/tex]

So the polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex] is [tex]f(x) = x^4+5x^2-6[/tex]

To verify that this polynomial has the desired zeros, we can factor it using the difference of squares:

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

And the quadratic factor has no real roots, so it must be the factorization [tex](x-i\sqrt6)(x+i\sqrt6)[/tex].

Therefore, [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex], as required.

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