why is 6 divided by zero, zero and zero divided by six is undefined?

Answers

Answer 1

Answer:

See below.

Step-by-step explanation:

The reason a number divided by zero is undefined is as follows.

Every operation, addition, multiplication, subtraction, and division, is carried out between two numbers and must have a single correct answer.

For example 1 + 5 = 6. The only correct answer to 1 + 5 is 6. There is no other correct answer to that addition. The same is true of any multiplication, subtraction, or division. Another example: 8/2 = 4. No other correct solution exists to the division of 8 by 2 other than 4.

Division is defined in terms of multiplication.

The definition of dividing a number by another number is:

a divided by b equals c if and only if b * c = a.

For example, 10/5 = 2 if and only if 5 * 2 = 10. 5 * 2 does equal 10, so it is correct that 10/5 = 2.

Now let's try dividing by zero and see the problem that arises.

Let's try to divide 8 by 0.

8/0 =

Since we are not used to dividing by zero, we don't really know what the answer should be, but we can try different answers.

Let's say 8/0 = 8

Then by the definition of multiplication, we need 0 * 8 to equal 8, but we know that 0 * 8 = 0, so the answer of 8/0 cannot be 8. Let's try a different answer.

8/0 = 0, then we need 0 * 0 to equal 8, but 0 * 0 = 0, not 8, so 0 also does not work.

We can generalize and try

8/0 = k, but then that requires 0 * k to equal 8. Since multiplication by 0 always has a result of 0, there is no number k that will multiply by 0 and give 8. This means that a number divided by 0 cannot give a result.

Now let's try one more thing.

What about 0 divided by 0.

Let 0/0 = 1. Then 0 * 1 = 0. It seems to work, but here there is a different problem. We could also say that 0/0 = 2 since 0 * 2 = 0; 0/0 = 3 since 0 * 3 = 0, etc. and now 0/0 can equal every number. The result of a division must be a unique answer, not all numbers.

When we try to divide a non-zero number by 0, no number works in the definition of division, so dividing a non-zero number by 0 is undefined. When we try to divide 0 by 0, every number works. Since there is no unique solution, 0/0 is also undefined. Therefore, division by zero is undefined.

Now the last part of your question.

What about 0 divided by 6?

0/6 = 0 if and only if 6 * 0 = 0. Well, 0 * 6 does equal zero. There is no other number that you can use as the quotient of 0/6 and have the corresponding multiplication equal zero, so 0/6 is indeed 0, and that operation is defined.

0 divided by any number other than zero is a defined division and equals 0.

Conclusion:

(any number)/0 is undefined

0/(any number other than zero) is defined and equals zero

Related Questions

A power company calculates a person's monthly bill from the number of kilowatt-hours (kWh), x, used.
The function b(x) = {
0.15x
0.10 (x – 400) + 60,
2 < 400
2 > 400
determines
the bill.

Answers

The function illustrates that the bill for someone who uses 600 kilowatt will be $80.

How to illustrate the function?

It should be noted that a function simply means an expression that defines the relationship between a variable and another variable. In this case, one can infer that functions are essential in the formulation of relationship between the variables that are given.

Based on the information given, it should be noted that it was stated that the power company calculates a person's monthly bill from the number of kilowatt-hours.

The bill for someone who uses 600 kilowatt will be:

= 0.1(x - 400) + 60

= 0.1(600 - 400) + 60

= 0.1(200) + 60

= 20 + 60

= 80

In conclusion, the bill will be $80.

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simplify these fractions
xy-xz/y-z

Answers

Answer:

[tex]\frac{xy-xz}{y-z} = x[/tex]

Step-by-step explanation:

Hello!

We can simplify the fraction by factoring and canceling out common factors.

Simplify[tex]\frac{xy-xz}{y-z}[/tex][tex]\frac{x(y - z)}{y-z}[/tex][tex]\frac{x(\not y\not-\not z)}{\not y \not- \not z}[/tex][tex]x[/tex]

We are left with x as the final simplified form.

Which of the following characteristics describe the graph of an exponential function?

Answers

Answer:

A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION

(

)

An exponential function with the form

(

)

≠

, has these characteristics:

one-to-one function

horizontal asymptote:

domain:

(

−

∞

)

range:

(

∞

)

x-intercept: none

y-intercept:

(

)

increasing if

decreasing if

Step-by-step explanation:

hope it helps you

Question Find the area of a trapezoid whose height is 9 ft and w hose bases are 13.4 ft and 8.6 ft.

Answers

Answer: Use this calculator to easily calculate the area of a trapezoid given its base s and height. The formula for the area of a trapezoid is (base 1 + base 2) / 2 x height,

Step-by-step explanation:

The cubic foot is a unit of volume used in the imperial and U.S. customary measurement systems.

The cubic foot can be used to describe a volume of a given material, or the capacity of a container to hold such a material.

Please help me with this i need big help in this

Answers

The value of the angle TSU is.97°. Therefore, none of the given options are correct.

How to calculate the angle?

From the information given, the value of UZ will be:

= YZ - YU

= 63 - 26

= 37°

UZ = TZ = 37°

Therefore, the value of TSU will be:

= 23° + (37° × 2)

° 23° + 74°

= 97°

In conclusion, the correct option is E.

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f(x) = √2x
g(x) = √8x
Find (f g)(x). Assume x ≥ 0.
OA. (f g)(x) = 4x
OB. (f g)(x) = 8x
O C. (f g)(x) = 4√√x
OD. (f.g)(x) = √/10x

Answers

Answer:

Step-by-step explanation:

hello :

f(x) = √(2x)

g(x) = √(8x)

(f g)(x) = f(x)×g(x) =√(2x)×√(8x) = √(16x²) =4/x/

x ≥ 0: /x/ = x (f g)(x) = 4x......(answer : A)

A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. How many different license plates are possible? (Exact steps shown for credit)

Answers

A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. So, there are 17576000 license plates can be made.

Given that, license plates consists of 3 letters followed by 3 digits.

Let the numbers on license plates be N

Let the letters on license plates be L

So, the license plate consisting of 3 letters and 3 digits will be LLLNNN.

Letters can be anything from A to Z.

There are 26 letter combinations for the first letter. That is applicable for the following 2 letters.

So, the combination for letters = 26×26×26 = 17576

Numbers can be anything from 0 to 9.

There are 10 combinations for each place.

So, the combination for numbers = 10×10×10 = 1000

Now, the combination for letters and numbers= 17576×1000

= 17576000

Therefore, 17576000 license plates can be made.

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|6 - (-1.3) + 2| + |4 - (2.8 - 3)|

Answers

Answer:

13.5

Step-by-step explanation:

( WILL GIVE BRAINLIEST ) a dog trainer compared the mean numbers of lessons for two groups of dogs which statement is true about the data?

Answers

Answer:

Answer number 1

......................

4
Select the correct answer from each drop-down menu.
AABC is similar to ADEF. The ratio of the perimeter of AABC to the perimeter of ADEF is 1:10. T
The length of the longest side of AABC is
2
4
16
30
units. The ratio of the area of AABC to the are.

Answers

The ratio of the area of ∆ABC to the area of ∆DEF is; 1:100.

What is the ratio of the area of ∆ABC to the area of ∆DEF?

Since, a major criterion for similarity and congruence of triangles is that the ratio of corresponding sides are equal.

On this note, since the task content suggest that the ratio of the perimeters is; 1:10, it follows from conventional mathematics that the ratio of their areas is given as; 1²:10²; 1:100.

Answers

The person which is more vulnerable to identity theft include:

The elderlyCollege studentsChildren

What is Identity theft?

This involves using someone's personal information to commit fraud and other forms of crime.

The set of people mentioned above are usually naive and innocent thereby making them more vulnerable to identity theft.

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A motorboat travels 132 km in 4 hours going upstream. It travels 196 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Answers

Answer:

Step-by-step explanation:

x = speed of the boat

y = speed of the current

x + y = 162/3 = 54 mph

x - y = 132/3 = 44 mph

Add the two equations to get

2x = 98

x = 49 mph

y = 54 - x = 54 - 49 = 5 mph or something

9. For Investment Plan A to C, solve for the future value at the end of the term based on the
information provided.
Investment Plan Principal
A
$7,500
B
$53,000
C
$19,000
Interest Rate
8% compounded quarterly
6% compounded monthly
5.75% compounded semi-annually
Term
3 years
4
years and 3 months
6 years and 6 months

Answers

The future value of Investment A is 9511.81

The future value of Investment B is 68,351.02

The future value of Investment C is29.067.07.

What are the future values?

When an amount earns a compound interest, it means that both the amount invested and the interest rate already accrued increases in value at the next compounding date. For example, if interest is compounded quarterly, both the amount invested and the interest accrued increases every quarter.

The formula for calculating future value:

FV = P (1 + r)^nm

FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years

Investment A = 7500 x [(1 + (0.08/4)]^(4 x 3) = 9511.81

Investment B = 53,000 x [(1 + (0.06/12)]^[(4 x 12) + 3) = 68,351.02

Investment C = 19,000 x [(1 + (0.0575/2)]^{6 x 2) + 6/2) = 29.067.07

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What is the price of a two year bond with a 9% annual coupon and a yield to maturity of 8%? 101.78 105.25 102.53 97.51

Answers

The bond price 101.78

What is the price of a bond?

A bond price is the present value of its future cash flows discounted at the yield to maturity which is the appropriate discount rate.

Specifically, the bond price is the present value of annual coupons for 2 two years and the face value discounted at the 8% yield to maturity.

We can determine the bond price using the present value formula of a single cash flow for all cash flows.

PV=FV/(1+r)^N

FV=future cash flow(annual coupons for 2 years and face value)

annual coupon=face value*coupon rate

face value=100

coupon rate=9%

annual coupon=100*9%

annual coupon=9

r=discount rate=8%

N=year of cash flows, 1 for year 1 and 2 for year 2

bond price=9/(1+8%)^1+9/(1+8%)^2+100/(1+8%)^2

bond price= 101.78

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PLEASE PLEASE PLEASE answer this question!!! FROM KHAN ACADAMY PRE ALGEBRA

Answers

Answer:

Step-by-step explanation:

Hope this helps:)

Answer:

B & D

Step-by-step explanation:

A The variable "x" is canceled does not apply

B One solution

C does not apply

D One solution

Hope this helps

The following data show the height, in inches, of 11 different plants in a garden:

9

4

10

9

5

2

22

10

3

3

5

After removing the outlier, what does the mean absolute deviation of this data set represent?
On average, the height of a plant varies 2.8 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 5 inches.
On average, the height of a plant varies 2.8 inches from the mean of 5 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

Answers

On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

What does the mean absolute deviation represent?

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.

Mean absolute deviation = (1/n) x ∑ l x - m(x) l

Mean without the outlier : (9 + 4 + 10 + 9 + 5+ 2 + 10 + 3 + 3+ 5) / 10 = 6

(1/10) x ∑ l (9 - 6) + (4 - 6) + (10 - 6) + (9 - 6) + (5 - 6) + (2 - 6) + (10 - 6) + (3 - 6) + (3 - 6) + ( 5 - 6) = 3.2

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A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.

1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.
2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.

Answers

Mark's method is correct, because even though it is impossible to deliver mail to 1.2 houses in minute, it represents the unit rate of houses per minute .

Is Mark's method correct?

The first step is to determine the unit rate of houses per minute. This can be done by dividing 36 houses by 30 minutes.

36/30 = 1.2 houses per minute

The second step is to multiply 1.2 by 7.5: 1.2 x 7.5 = 9 houses

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50 points!!! answer this quickly with an explanation

Answers

Answer:

x = 24°

Step-by-step explanation:

If two parallel lines are being intersected by the same line, the opposite inside angles are congruent. This means that ∠EFH should be equal to ∠JHF. However, we cannot set these angles equal because we do not know the value of ∠JHG.

Line IG is intersected by line HJ. This means the value of ∠JHG is 24° (180° - 156° = 24°). Know that we know this value, we can set up an equation to find "x".

∠EFH = 2x

∠JHG = 24°

∠GHF = x

∠EFH = ∠JHF <----- Opposite interior angles are equal

∠EFH = ∠JHG + ∠GHF <----- Break ∠JHF into 2 angles

2x = 24 + x <----- Insert values

x = 24 <----- Subtract x from both sides

Select all of the following that are quadratic equations.
5x-1=3x+8
5 x- 3 = 0
x²-2x = 4x+1
2x²+12 x = 0
x³-6x² + 8 = 0
9x²+6x-3=0

Answers

The quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

Given six equations as under:

5x-1=3x+85 x- 3 = 0x²-2x = 4x+12x²+12 x = 0x³-6x² + 8 = 09x²+6x-3=0

We are required to find the quadratic equations among the above equations.

Quadratic equations are those equations in which the highest power of the variable present in the equation is 2.

It is in form of [tex]ax^{2} +bx+c=0[/tex].

In our options quadratic equations are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

5x-1=3x+8: It is not a quadratic equation as the highest power is 1.

5 x- 3 = 0:It is also a linear equation not quadratic equation.

x³-6x² + 8 = 0:It is a cubic equation not a quadratic equation.

Hence the quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

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Evaluate functions from their graph Problem g(3) =
See attached for the correct answer!

The notation g (3), left parenthesis, 3 refers to the output of the function when the input is x=. If the point (3, b) is on the graph, then g (3) =b.

We should look for the point on the graph whose x- coordinate is 3 is the point )3, 4).
The point on the graph whose x-coordinate is 3 is the point (3,4).

Therefore, g (3) = 4

Answers

The value of g(3) is g(3) = 4

How to evaluate the function?

The function value is given as:

g(x)

The notation g(3) implies that:

We determine the value of g(x) when x = 3

From the graph, the function has a point at (3,4)

This means that:

When x = 3, g(x) = 4

i.e. g(3) = 4

Hence, the value of g(3) is g(3) = 4

Answers

Answer:

2635

Step-by-step explanation:

the first two stand for 1000

2000

is the first part

the second numeral stands for 100

there are 6 of them

600

is the second part

the third numeral stands for 10 and there are 3 of them

thus

is the third part

there are 5 lines so the last part is 5

so your answer is 2635

This table reflects the result of a survey conducted in a town to find out the number of cars of a particular color.

Which of the following ranges would be appropriate to use in order to represent the numerical data on the vertical axis of a Bar Graph?

A. 10 to 20
B. 20 to 100
C. 0 to 50
D. 0 to 30

Answers

the range that would be the most appropriate to represent the numerical data on the vertical axis is B. 20 to 100.

what range would be most appropriate?

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approximately to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

Consider the graph of f(x) given below.

A curve labeled f of x declines through the points (negative 4, 7), (negative 3, 6), (negative 2, 5), (0, 3), (2, 1), (3, 0), (4, negative 1), (5, negative 2), (6, negative 3) and (7, negative 4) on the x y coordinate plane.

The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)?

A.
g(x) = f(x + 2)
B.
g(x) = f(x - 5)
C.
g(x) = f(x) - 2
D.
g(x) = f(x) - 5

Answers

The functions could represent g(x) is B. [tex]g(x) = f(x - 5)[/tex]

How can the function be determined?

Using the general equation [tex]g(x) =f(x)+ b[/tex]

The g(x) has intercept of y=-2,

Then the y-intercept of f(x) is at y=3

If we find the difference between both y-intercepts, we have

( -2 -3) = -5

Then b=-5

Hence, [tex]g(x) = f(x - 5)[/tex] is correct.

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If f(x) = x and g(x) = 2, what is (fog)(x)?

Answers

Step-by-step explanation:

=fog(x)

−2x=0

x(x−2)=0

x=0,2

Explain how to determine if Carlos’s allowance is directly proportional to the number of chores he completes.

A 2-column table with 3 rows. Column 1 is labeled number of chores with entries 10, 13, 15. Column 2 is labeled Allowance with entries 75 dollars, 97 dollars and 50 cents, 112 dollars and 50 cents.

Answers

Using a proportional relationship, it is found that Carlos earns an allowance of $7.5 for each chore that he completes.

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the constant is:

k = 75/10 = 97.5/13 = 112.5/15 = 7.5.

Hence Carlos earns an allowance of $7.5 for each chore that he completes.

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Determine the output voltage of the op-amp circuit shown below:

Answers

The output voltage of the op-amp circuit shown is -5v.

What is voltage?

It should be noted that voltage is the electric potential difference between two points l.

In this case, the output voltage will be:

= -5 × i

where I = 1.

Voltage = -5 × 1

= -5v

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Which of the following functions best describes this graph?

Answers

Answer:

Step-by-step explanation:

We can use process of elimination

D is incorrect because the roots are 3 and -4 and there are no negative roots visible

B is wrong because the roots -3 and -6 are both negative

You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6

For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate

( 13/7 ) ^2
[answer in fraction form]

Answers

Answer:

[tex]\frac{169}{49}[/tex]

Step-by-step explanation:

Square the top and bottom numbers in the fraction

13^2 = 169

7^2 = 49

169/49

Amy made a circle graph of the U.S. population for 2000. This is the data that she used and the graph that she made.

Answers

The true statement is (b). No, because males and females should add up to 100% of the population.

How to determine the true statement?

The complete question is added at the end of this solution.

From the complete question, we have the following percentages

Male = 26%Female = 27%

When the above percentages are added, we have

Total = 26% + 27%

Evaluate the sum

Total = 53%

The above shows that the display of the circle graph is accurate.

This is so because the total percentage of the male and the female population must add up to 100%

Hence, the true statement is (b). No, because males and females should add up to 100% of the population.

Answers

The given coordinates to polar forms are:

[tex]\sqrt{5}[/tex]1.107

How to find the polar form

In order to calculate it to polar forms we would have

We have these equations

r² = x² + y²

tanθ = y/x

From here we would have

r² = (-1)² + (-2)

r² = 1 + 4

r = √5

We have tanθ = -2 / -1

= we have θ = tan⁻¹(2)

= 1.107

why is 6 divided by zero, zero and zero divided by six is undefined?​

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why is 6 divided by zero, zero and zero divided by six is undefined?