write the quotient as a power. a^21/a

Answers

Answer 1

the quotient as a power. a^21/a is a^20.

What is Power?

In mathematics, power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.

What is quotient?

The number we obtain when we divide one number by another is the quotient.

What is exponential function?

An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

Given that,

a^21/a

quotient as power = a^21/a

                             =  a^(21-1)

                             = a^20

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Related Questions

Evaluate Each expression show your work


1. Evaluate 3 + 4x if x = 5

Answers

Answer:

23

Step-by-step explanation:

3+4x

3+4(5)

3+20

23

Hopes this helps please mark brainliest

-16 > -4y solve for the inequality of y and simplify your answer as much as possible

Answers

The given inequality solved for y is y > 4

Solving linear inequalities

From the question, we are to solve the given linear inequality.

To solve an inequality, we will solve for the variable in the inequality.

The given inequality is

-16 > -4y

The variable in the inequality is y.

Now, we will solve for y

-16 > -4y

Divide both sides by -4

-16/-4 > -4y/-4

4 < y

Thus,
y > 4

Hence, the solution is y > 4

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find three consecutive integers such that 3 times the smallest is 18 more than the largest

Answers

The value of the three consecutive integers will be 10, 11, and 12.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Three consecutive integers are such that three times the smallest is 18 more than the largest.

Let the three consecutive number be x, x + 1, and x + 2. Then the equation will be:

3x = (x + 2) + 18

Simplify the equation, then the value of the variable x will be:

3x = x + 2 + 182x = 20x = 20 / 2x = 10

Then the value of the integers will be:

x + 1 = 10 + 1 = 11x + 2 = 10 + 2 = 12

The value of the three consecutive integers will be 10, 11, and 12

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Find the slope on the line going through the points (36, -21) and (-14, -21)

Answers

Answer:

0

Step-by-step explanation:

[tex]m=\frac{-21-(-21)}{-14-36}[/tex]

Answer: slope = 0  

Step-by-step explanation:

slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0

It's a horizontal line

3n=1/9 Find the value of n.​
PLEASE HELP

Answers

Answer: n=1/27=0.037

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*n-(1/9)=0

Simplify 1/9

3n -  1/9  = 0

Rewrite the whole as a fraction using  9  as the denominator :

          3n     3n • 9

    3n =  ——  =  ——————

          1        9  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3n • 9 - (1)     27n - 1

————————————  =  ———————

     9              9  

End of step 2  

27n - 1

 ———————  = 0

    9  

Start of step 3

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 27n-1

 ————— • 9 = 0 • 9

   9  

Now, on the left hand side, the  9  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  27n-1  = 0

Solving a Single Variable Equation:

3.2      Solve:    27n-1 = 0

Add  1  to both sides of the equation :

                     27n = 1

Divide both sides of the equation by 27:

                    n = 1/27 = 0.037

Which inequality correctly orders the numbers -2/5, -11/3 and -2.5?

Answers

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal ≤

Greater than and equal ≥

The inequality that correctly orders the numbers is

-3.67 < -2.5 < -0.4

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

-2/5 = -0.4

-11/3 = -3.67

-2.5

Now,

We see that,

-0.4 is greater than -2.5 and -2.5 is greater than -3.67.

This can be represented as an inequality:

-3.67 < -2.5 < -0.4

Thus,

The inequality that correctly orders the numbers is

-3.67 < -2.5 < -0.4

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What is the area of the figure at the right?

Answers

The area of the figure is 21. 25 m². Option D

How to determine the area

It is important to note that the figure is a kite.

The formula for calculating the area of a kite is expressed as;

A= pq/2

Where;

A is the area of the kitep is the diagonal of the kiteq is the diagonal of the kite

Using tangent identity

tan 45 = x/ 2. 5

1(2. 5) = x

x = 2. 5

p = 2. 5 + 2. 5 = 5

q = 2. 5 + 6 = 8. 5

Now, substitute the values into the formula

Area = 5(8. 5)/ 2

Area = 42. 5/ 2

divide the values

Area = 21. 25 m²

Hence, the value is 21. 25m²

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16. Points X, Y, and Z are collinear, and Y is
the midpoint of XZ. Find the value of b.

Answers

Answer:

b=11

Step-by-step explanation:

lets set up the equation. we know that both sides equal each other so the equation is

2b+7=3b-4 let's move the 2b to the other side so we get

7=b-4 now add the 4 to the other side

11=b

Answer:

B is 11

Step-by-step explanation:

Evaluate -7(x – 4y) when x = −4 and y = −6 a140 b52 c-28 d-140​

Answers

Answer: D

Step-by-step explanation:

-7(-4-(4)(-6))

-7(-4-(4)(-6))

=140

Quick help would be appreciated : )

Answers

The number of liters of fuel required for the vehicle to travel 1, 428 kilometers is 5. 67

What is inverse variation?

Inverse variation can be defined as the relationship between two variables, so that if the value of one of the variable increases the value of the other variable decreases.

Example: If a varies inversely as b

This can be represented as;

a ∝ 1/b

Then,

ab = k

Where k is the proportionality constant

From the information given, we have that;

The number of kilometers = xThe liters of fuel = y

x ∝ 1/ y

Then,

xy = k

Substitute the values

476 (17) = k

k = 8092

If x = 1428 and k = 8092

Let's determine the value of y

y = k/x

y = 8092/1428

y = 5. 67 liters

Hence, the value is 5. 67 liters

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Question For Middle School........
[tex]1.what \: is \: the \: value \: of \: pie \: (\pi)[/tex]​

Answers

answer: 3.14159 (pi*)
For middle school the value of pie is 3.14.

When $720 is divided in the ratio 3:5, the larger share is

Answers

Answer:

The larger share is $450.

Step-by-step explanation:

[tex]\frac{3}{5} =\frac{3x}{5x} \\\\3x-the smaller share\\5x-the larger share\\3x+5x=8x\\8x-money to split\\8x=720 /:8\\x=90\\5x=5*90=450[/tex]

Use three unit multipliers to convert 5280ft to meters

Answers

The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.

What is unit conversion?

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

As per the given,5280ft

It is known that 1 ft = 12 inches.

5280ft = 5280 x 12 inches

It is known that 1 inch = 2.54 cm

5280 x 12 inches = 5280 x 12 x 2.54 cm

It is known that 1 cm = 0.01 meter

5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter

⇒  1609.344 meters

Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".

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3. Martin finishes a swim race in 78.934 seconds. His teammate, Abby finishes the race in 83.978 seconds and their last teammate finishes the race in 84.765 seconds.

If the teammates were to have a combined time of less than 250 seconds to qualify to the next round, did they qualify or not? How do you know?


help me please i really need help!

Answers

You would add up the times each person got when the finished the race. Which equals out to 247.677 seconds, which Is lower than 250 making your answer yes they did qualify. We know this because we added up the times and it came out to lower than 250

how many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11? c) are divisible by both 7 and 11? d) are divisible by either 7 or 11? e) are divisible by exactly one of 7 and 11? f ) are divisible by neither 7 nor 11? g) have distinct digits? h) have distinct digits and are even?

Answers

The set of positive integers less than 1000 that are:

a)Divisible by 7 are 142

b)Divisible by 7 but not by 11 are 130

c)Divisible by both 7 and 11 are 12

d)Divisible by either 7 or 11 are 220

e)Divisible by exactly one of 7 and 11 are 220

f)Divisible by neither 7 nor 11 are 780

g)Having distinct digits are 576

f)Having distinct digits and even are 337

What is a positive integer?

A whole number that is greater than zero is known as positive integer

a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.

Total terms: 994, divided by 7, plus (n-1)

There are 142 total terms below 1000 that are divisible by 7.

b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.

The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.

c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.

There are 12 total integers below 1000 that can be divided by 77.

d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.

The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.

Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.

e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.

f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.

Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),

=> Unique digits from 1 to 100 equal 90.

=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),

=> Unique digits from 101 to 200 are: 100 to 28, 72.

=> Unique numbers between 201 and 1000 = 72 x 8 = 576.

h)Different digits and even values equal to 337

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Which equation represents a line which is perpendicular to the line y=7/6x-8

Answers

The equation of a line that is perpendicular to y = 7 / 6 x - 8 is y = -6 / 7 x + 8.

How to find the equation of a line?

The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form.

The lines that are perpendicular to each other will have the products of their slopes as negative 1.

Therefore, let express the equation in slope intercept form.

y = mx + b

where

m = slopeb = y-intercept

Therefore,

y = 7 / 6 x - 8

The slope of the equation is 7 / 6.

Therefore, let's find the equation of the line that is perpendicular to y = 7 / 6 x - 8.

m₁m₂ = -1

7 / 6 m₂ = -1

cross multiply

7m₂ = -6

m₂ = - 6 / 7

Hence, the equation of the line perpendicular to y = 7/6x - 8 should have the slope as - 6 / 7.

Hence, the equation can be y = -6 / 7 x + 8.

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A plumber has a 36-inch pipe that he has to cut into two
pieces so that one piece is 8 in. longer than the other. Find
the length of each piece.

Answers

A plumber has a 36-inch pipe that he needs to cut into two pieces, one 8 inches longer than the other. Each piece's length is x = 14, while the other piece's length is 22.

What is meant by length?The measurement or extent of something from end to end is defined as length. In other words, it is the larger of the two or the highest of three geometrical shapes or objects' dimensions. A rectangle, for example, has length and breadth dimensions.Centimeters, meters, kilometers, inches, feet, yards, and other standard units of length measurement are some examples.A segment's length or the dimensions of a room are examples of length measurements. Distance is the distance between two objects, such as two cities or two points. There will never be a negative value for length or distance.

Therefore,

let x = the first piece and x+14 is the second.

2x + 8 = 36

2x = 28

x = 14, the other piece is 22

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3. One batch of pancakes needs 1½ cups of pancake mix. One box has 9 cups of pancake mix.
How many batches of pancakes can be made with one box of pancake mix?

Answers

In linear equation, 27/2 pancakes are in the box .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a " of two variables," where x and y are the variables.

Number of b pancake mix  to be need  =  1½ cups

Number of box has pancake mix   = 9 cups

Therefore, in order to get the total number of  batches of pancakes  needed for the batches will be calculated thus

             =  1½  * 9

             = 3/2 * 9

             = 27/2

therefore 27/2 pancakes are in the box .

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what is the future amount of 12,000 invested for 5 years at 14% compounded monthly?

Answers

Answer:

$24,067.32

Step-by-step explanation:

If you look up a compound interest calculator and put in the data correctly you should get $24,067.32

Calculate the length of the unknown side of this right-angled triangle.
9 cm
8 cm

Answers

the length of the unknown side of the right angle triangle is 1 cm

Two parallel lines are cut by a transversal as shown below.
Suppose m2 = 46°. Find m5 and m 27.

Answers

Angle 5 and 7 = 132 degrees

Another thing you will need to know before you can perform a rotation is

direction of rotation

corresponding angles

corresponding sides

the angle measures

Answers

Direction of rotation


A triangle has an angle that measure 36.6° and a second angle that measures 59.3°. What is the
measure of the third angle?
2 pts

Answers

Answer: 82 is the answer

Step-by-step explanation: I just did this question and worked it out and it said it was right

Given the equation 6x + 18 = 72:

Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)

Part B: Solve the equation showing all work. (4 points)

Part C: Explain what the value of the variable represents. (2 points)

Answers

The short word problem that illustrates the given equation is seen below. The value of the variable is 9.

Expression of the algebraic equation into word problems:

Linear algebra equations are equations that can be expressed in word problems and these equations can be used to solve real-life scenarios. These algebraic equations are designed by the application of the desired set of variables with its arithmetic operations.

A.

In a food factory, Eighteen fried chickens are added to the six times the number of food plates is seventy-two. How much-fried chicken goes into each food plate?

B.

6x + 18 = 72

Subtract 18 from both sides;

6x + 18 - 18 = 72 - 18

6x = 54

Divide both sides by 6.

6x/6 = 54/6

x = 9

C.

The value of the variable is 9, and according to the example we used, it represents the number of chickens that goes into each plate of food.

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Which answer is correct?

(A)4x + y = 6

−2x + y = −5

(B)x + y = 8

2x − 9y = 4

(C)x − 4y = −6

−2x − y = 5

(D) −x + y = 9

9x + 2y = 4

Answers

The system of equations best represented by the graph are 4x + y = 6 and −2x + y = −5

How to determine the system of equations represented by the graph?

The solution of the equations plotted in the graph can be found by checking the point of intersection of the lines

By examining the given graph we can guess the x and y values of the point of intersection. We need to guess because we do not have a means of getting the exact value from the graph. I guess x = 1.9 and y = -1.4

In order to find the system of equations represented by the graph, we need to solve the equations given in the option and check which one gives us  x and y values close to what we guessed from the graph

By Solving 4x + y = 6 and −2x + y = −5:

4x + y = 6          (1)

−2x + y = −5      (2)

Using elimination, subtract (2) from (1), this gives:

6x = 11            

x = 11/6 = 1.83

Put x = 11/6 into (1):

4(11/6) + y = 6

y = 6 - 4(11/6)

y = 6 -44/6 = -4/3 = -1.33

Since these calculated values are very close to the guessed values

Therefore, 4x + y = 6 and −2x + y = −5 are the system of equations best

represented by the graph. So option A is the answer

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K(15) = ?
Please find what k(15) is of the following graph below

Answers

It’s 7 Bc if you add 8+7 it’s 15 Bc math

If 8^y =16^y+2what is the value of y?

O-8.
O-4.
O-2.
O-1.

Answers

Answer:

-8

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

The top of a 15-foot ladder is 3 feet farther up a wall than the foot of the ladder is from the bottom of the wall. How far up is the foot of the ladder from the bottom of the wall?


The answer is 9 but I don’t know how to get there.

Answers

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}[/tex]

let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.

Match the vocabulary word with the correct definition.


Base

Exponent

Scientific Notation

a.
The number that is going to be raised to a power.

b.
The number that tells you how many times you will multiply the base number.

c.
A way of writing VERY large or VERY small numbers so the numbers are easier to compare or calculate.

Answers

Answer:

Exponent: B

Base: A

Scientific Notation: C

Step-by-step explanation:

vocabulary

Answer:

Exponent and A

Base and B

Scientific Notation and C

Step-by-step explanation:

Because the Exponent is the number that is going to raise the Base and that Base is the number that you are going to multiply by.

for sample size n, the margin of error is 3. how many more samples do we need to make the margin of error 0.3?

Answers

We will need 100 more samples to make the margin error of 0.3 .

What are sample errors?When the statistical characteristics of a population are estimated from a subset, or sample, of that population, sampling errors are made in statistics. Statistics of the sample (commonly referred to as estimators), such as means and quartiles, usually diverge from those of the total population because the sample does not include all individuals of the population (known as parameters). The sampling error is defined as the discrepancy between the sample statistic and the population parameter. For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million persons in the country.

acc to our question-

Margin error is 3Margin error tobe 0.3 SAMPLE size ?0.3 =3/10Ratio =3/3/10=10n^2=10×10=100Samples in size of 100

Hence, We will need 100 more samples to make the margin error of 0.3 .

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