The area of a rectangle is given by the function A(x) = 2x3 + 6x2 + 5x + 15. If the length is defined by x + 3, what is the width of the rectangle?

2x3 + 6x2 + 4x + 12
2x3 + 6x2 + 6x + 18
2x2 + 6x + 5
2x2 + 5

A man that is 6 feet tall cast a shadow that is 15 feet if a child Cassa shadow that is 10 feet long then the child is 4 feet tall.

To find the height of the child, we can use the concept of similar triangles. The man's height and shadow form one

triangle, and the child's height and shadow form another.

Step 1: Identify the given information.

Man's height = 6 feet

Man's shadow = 15 feet

Child's shadow = 10 feet

Step 2: Set up a proportion using the given information.

Man's height/Man's shadow = Child's height/Child's shadow

6/15 = Child's height/10

Step 3: Solve for Child's height.

To do this, cross-multiply:

6 × 10 = 15 × Child's height

60 = 15 × Child's height

Step 4: Divide both sides by 15 to find the Child's height.

Child's height = 60 / 15

Child's height = 4 feet

So, the child is 4 feet tall.

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The predicted population of the city in the year 2030 is 5,780 person.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

Years = 2030 - 2010 = 20 years.

By substituting given parameters, we have the following:

[tex]P(t) = I(1 + r)^t\\\\P(t) = 3200(1 + 3/100)^{20}\\\\P(t) = 3200(1 + 0.03)^{20}[/tex]

P(t) = 5,779.56 ≈ 5,780 person.

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Answer:

No you would not use all your money, you would have 9 bananas with $0.10 left.

Step-by-step explanation:

t = m(x)

substitute

3.25 = .35(x)

inverse operations (divide by .35 on both sides)

3.25/.35 = (x)

9(rounded to the nearest whole number) = x

9 is the number of bananas. Now we need to find the change.

9 * .35 = 3.15

3.25 - 3.15 = .10

You will have 9 bananas with 10 cents left.

Answer:

Like terms

Step-by-step explanation:

Are the terms that contain same variables, same exponents of variables and same coefficients.

HOPE THIS HELPS

We have to calculate the number of combinations of 3 laser printers that can be selected from the 30 shipped. In this case, the number of possible combinations is 4060.

The combination can be calculated using the formula

ⁿCr = n! / r! (n-r)!

Where n is the total number of items and r is the number of items chosen. In this case, n is 30 and r is 3.

³⁰C₃= 30! / (3! * (30-3)!) ⇒ 30! / (6 * 24)

⇒ 30 * 29 * 28 / 6

⇒ 4,060

Therefore, the answer is 4060 possible combinations of 3 laser printers that can be selected from the 30 shipped.

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The system of inequalities "2x – y > 1 and x – 2y < –1." are graphically shown below in the image section.

Inequalities in mathematics describe the connection between two non-equal values. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, a number of inequality comparisons are made to determine whether one value is greater than or less than another. The various inequality symbols, their meanings, and methods for solving them will all be covered in this article using examples of both one- and two-variable linear inequalities. We'll also discuss the algebraic inequalities that are commonly used.

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—------ CORRECT QUESTION FORMAT IS GIVEN BELOW - - - - - -

(Q). Solve the following system of inequalities graphically: 2x – y > 1 and x – 2y < –1.

a) The distance of P from the base of the building is 168.0 m.

b) The height of the building is 43.8 m.

c) The length of the flagstaff is 25.8 m.

The given information is used to solve the three parts of the problem. First, to calculate the distance of P from the base of the building, the tangent of the angle of elevation of the top of the flagstaff, 32°, is used. The tangent of 32° is 0.6, and this is equal to the ratio of the height of the building and the distance from P to the base of the building. This gives the equation 0.6 = 43.8/x, where x is the distance of P from the base of the building. Solving for x gives x = 168.0 m.

Second, to calculate the height of the building, the tangent of the angle of elevation of the bottom of the flagstaff, 29°, is used. The tangent of 29° is 0.546, and this is equal to the ratio of the height of the building and the distance from P to the base of the building. This gives the equation 0.546 = h/168.0, where h is the height of the building. Solving for h gives h = 43.8 m.

Third, to calculate the length of the flagstaff, the tangent of the angle of elevation of the top of the flagstaff, 38°, is used. The tangent of 38° is 0.717, and this is equal to the ratio of the length of the flagstaff and the distance from Q to the base of the building. This gives the equation 0.717 = x/93.0, where x is the length of the flagstaff. Solving for x gives x = 25.8 m.

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Answer:

$51

Step-by-step explanation:

You convery the percentage into a decimal, by dividing it by a hundred.

15÷100= 0.15

then you multiply the decimal and the price.

60×0.15= 9.

The question said it got cheaper so we have to subtract 9 from the original price.

60-9=51.

First, we need to find the coordinates of each vertex of triangle ABC. Let's assume that A is located at (a,b), B is located at (c,d), and C is located at (e,f). Since we know the measures of the angles, we can also determine the slopes of the lines connecting the vertices:

The slope of line AB is (d-b)/(c-a), which is equal to tan(55°).

The slope of line BC is (f-d)/(e-c), which is equal to tan(80°).

The slope of line AC is (f-b)/(e-a), which is equal to tan(55°-45°) = tan(10°).

Using these slopes, we can find the equations of the three lines and solve for the coordinates of the vertices:

Line AB: y-b = tan(55°)(x-a)

Line BC: y-d = tan(80°)(x-c)

Line AC: y-b = tan(10°)(x-a)

Solving these equations simultaneously, we get:

A = (b + (c-a)tan(55°), b + (c-a)tan(55°-45°))

B = (c + (f-d)/tan(80°), d + (f-d))

C = (e + (b-f)/tan(10°), f + (e-a)tan(10°))

Next, we need to apply the rotation and reflection to these vertices to find the corresponding vertices of triangle XYZ. The rotation by 90° counterclockwise about the origin transforms a point (x,y) into (-y,x), while the reflection across the line y=x transforms a point (x,y) into (y,x). So:

Vertex A of ABC is mapped to vertex X of XYZ: (a,b) → (-b,a) → (a,-b)

Vertex B of ABC is mapped to vertex Y of XYZ: (c,d) → (-d,c) → (c,d)

Vertex C of ABC is mapped to vertex Z of XYZ: (e,f) → (-f,e) → (e,f)

Now we need to find the measure of angle Y. Since we don't know the exact coordinates of the vertices of XYZ, we'll use the fact that the rotation by 90° counterclockwise about the origin preserves angles and the reflection across the line y=x changes the orientation of angles but not their measure. Therefore:

m∠Y = m∠ZOX, where O is the origin

m∠ZOX = 90° - m∠XOZ

m∠XOZ = m∠COA = 55° + 45° = 100°

Therefore, m∠Y = 90° - 100° = -10°, but since angles can't have negative measures, we add 360° to get m∠Y = 350°.

So the measure of angle Y in triangle XYZ is 350°.

Question 1

1/1

Triangle ABC

maps to triangle XYZ

by a rotation of 90∘

counterclockwise about the origin followed by a reflection across the line y=x.

In triangle ABC,

m∠A=45∘,

m∠B=55∘,

and m∠C=80∘.

What is the measure of ∠Y?

Enter your answer as the correct value, like this: 42

55 is the answer I'm not joking try it lol

Answer:

The correct answer is:

x = 0°, 30°, 150°, 180°

This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.

Step-by-step explanation:

The frequency of a sound wave is the number of cycles it completes in a given amount of time. In this case, we can find the frequency of each sound wave by looking at the period of the functions.

The function y = 2sin2x has a period of π (since 2sin(2x) has a period of π/2, which is then compressed horizontally by a factor of 2). The function y = sinx has a period of 2π.

If the frequencies are the same, then the two functions must complete an equal number of cycles in the interval [0°, 360°), which is the same as the interval [0, 2π) in radians.

Let's first look at the function y = sin x. It completes one cycle in the interval [0, 2π), so we can say that it completes n cycles in the same interval, where n is an integer.

Now let's look at the function y = 2sin2x. It completes two cycles in the interval [0, π), so it completes four cycles in the interval [0, 2π). Therefore, we can say that it completes m cycles in the interval [0, 2π), where m is an integer.

For the frequencies to be the same, we need to find values of n and m such that:

n = m

Solving for n and m, we get:

n = m = 2

So both functions complete two cycles in the interval [0, 2π). We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:

2sin2x = sin x

2sin2x - sin x = 0

sin x (2sin x - 1) = 0

sin x = 0 or 2sin x - 1 = 0

sin x = 0 when x is an integer multiple of π.

2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.

Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.

The correct answer is:

x = 0°, 30°, 150°, 180°

This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.

The company caught approximately 1,461,880 fish over the first 13 years. We can calculate it in the following manner.

Since the number of fish caught by the company decreases by 4% each year, the number of fish caught in the second year will be 96% of the first year, and the number of fish caught in the third year will be 96% of the second year, and so on.

To find the total number of fish caught by the company over the first 13 years, we can use the following formula:

Total fish caught

[tex]= 130,000 + 0.96130,000 + 0.96^{2130,000} + ... + 0.96^{12*130,000}[/tex]

Using the formula for the sum of a geometric series, we can simplify this to:

Total fish caught = 130,000 * (1 - 0.96¹³)/(1 - 0.96)

Plugging in the values and solving for the total fish caught, we get:

Total fish caught = 130,000 * (1 - 0.96¹³)/(1 - 0.96) = 1,461,880

Therefore, the company caught approximately 1,461,880 fish over the first 13 years.

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Answer:

59

Step-by-step explanation:

60 + 61 + m<4 = 180

m<4 = 59°

Concept: "Logos" has greatly affected Western philosophy and a variety of scientific disciplines. Acknowledgement: the interaction between logical reasoning and empirical observation as well as the influence of language and discourse worldview.

For the concept:

Topic: The significance of the Greek philosophical idea of "Logos" in contemporary scientific disciplines.

Greek philosophy's basic idea of "Logos" has had numerous interpretations throughout history. The word "logos" is most commonly used to refer to reasoned discourse and language. It is frequently linked to human conversation and reasoning as well as the cosmic or divine principle that creates and sustains the universe.

The significance of "Logos" can be observed in its impact on contemporary scientific disciplines, including, but not limited to, biology, psychology, and technology. For instance, the word "biology" is derived from the Greek terms "bios" (life) and "logos" (word or reason), illustrating the notion that the study of life necessitates both practical observation and logical analysis.

Parallel to this, the scientific discipline of psychology, which examines how the human mind and behaviour function, gets its name from the Greek words "psyche," which means "soul," and "logos," which means "reason." This illustrates the notion that both empirical research and theoretical analysis are necessary for the study of the mind and behaviour.

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Translation: The first schools of classical philosophy founded by the Greek word "logos" are widely understood as the apex of Western rationalist culture. In actuality, he is the one who gave the titles of numerous branches of science, including philology, psychology, technology, and biology. The idea of "logos" does not have such an abstract meaning because it involves both internal and exterior mental and physical actions, as well as the mental idea and word pronunciation. Topic: Main Idea:

The probability that shares of Acme and Best will both increase in value over the next month is 0.2 (20%). This is calculated by multiplying the individual probabilities of each stock increasing in value (50% x 40%)

1. Calculate the individual probability of Acme increasing in value: 50%

2. Calculate the individual probability of Best increasing in value: 40%

3. Multiply the two individual probabilities together to calculate the probability that both stocks will increase in value: 50% x 40% = 0.2 (20%)

The probability that shares of Acme and Best will both increase in value over the next month is 0.2 (20%). This is calculated by multiplying the individual probabilities of each stock increasing in value (50% x 40%)

The complete question is :

The probability that shares of acme will increase in value over the next month is 50% and the probability that shares of acme and shares of best will both increase in value over the next month is 40%.What is the probability that shares of Acme and shares of Best will both increase in value over the next month?

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The answer is option B: 54,000,000/mL. The sperm concentration is 0.54 million per cubic centimeter, or 54 million per milliliter.

To calculate the sperm concentration using a Neubauer counting chamber, we can use the following formula:

Sperm concentration = (number of sperm counted ÷ number of counting squares) ÷ dilution factor

In this case, we have:

Number of sperm counted = 54

Number of counting squares = 5

Dilution factor = 1:20

First, we need to calculate the total volume of the diluted sperm sample that was loaded onto the counting chamber. To do this, we can use the following formula:

Total volume = volume of loaded sample ÷ dilution factor

Since the dilution factor is 1:20, this means that the volume of loaded sample is 1/20th of the total volume. The total volume depends on the depth of the chamber and is usually 0.1 mL (or 100 μL) for a standard Neubauer counting chamber. Therefore:

Total volume = 0.1 mL ÷ 20 = 0.005 mL

Next, we can calculate the sperm concentration using the formula above:

Sperm concentration = (54 ÷ 5) ÷ 1/20

Sperm concentration = 54 ÷ 5 × 20

Sperm concentration = 54 ÷ 100

Sperm concentration = 0.54 million/cc

Therefore, the answer is option B: 54,000,000/mL. The sperm concentration is 0.54 million per cubic centimeter, or 54 million per milliliter.

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Your question is incomplete, but probably the complete question is :

Using a 1:20 dilution and the 5 RBC counting squares of the Neubauer counting chamber, an average of 54 sperm is counted. The sperm concentration is:

A. 54,000/cc

B. 54,000,000/mL

C. 108,000/cc

D. 108,000,000/mL

After answering the provided question, we can conclude that As a result, equation the wrapper must have been dropped around 4.875 seconds ago.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

a) Set f(x) to 450 and solve for x to find the amount of time since dropping the wrapper when it is 450 feet in the air:

-16x² - 2x + 600 = 450

b)

-16x² - 2x + 150 = 0

[tex]x = (-(-2) + \sqrt((-2)^2 - 4(-16)(150))) / (2(-16))\\x = (2 + \sqrt(4 + 9600)) / (-32)\\x = (2 + \sqrt(9604)) / (-32)\\x = (2 + 98) / (-32)\\x = -3.125\\ or\\ x = 4.875\\[/tex]

c) Because time cannot be negative and the candy wrapper cannot have been at a height of 450 feet before it was dropped, the solution that makes the most sense in the context of the circumstance is x = 4.875. As a result, the wrapper must have been dropped around 4.875 seconds ago.

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Answer:

length times with equals to base times height

Step-by-step explanation:

length times with times height equals to 3400

Answer:The most accurate inference from this boxplot is that: The visiting team had more variability in the number of shots taken.

Step-by-step explanation:

The box and whiskers plot is a way of presenting data that gives 5 major information about the distributionFrom the whiskers of the plot, one can read- The minimum value - The maximum value Then, from the boxplot, one can read- The Median, represented by the middle line of the boxplot.- The first Quartile or 25th percentile, represented by the lower end of the boxplot.- The third quartile or 75th percentile, represented by the upper end of the boxplot.Other variables that can be obtained from these five data points include- The range of the distribution (maximum value minus minimum value)- The interquartile range (a measure of variation, which is the difference between the third and first quartile of the distribution)For the two boxplots that the coach madeHome teamWhiskers range from 16 to 32Minimum value = 16maximum value = 32the box ranges from 20 to 23. A line divides the box at 22.First quartile = 20Third quartile = 23Median = 22IQR = 23 - 20 = 3For the visiting teamWhiskers range from 14 to 32Minimum value = 14maximum value = 32the box ranges from 16 to 24. A line divides the box at 18.First quartile = 16Third quartile = 24Median = 18IQR = 24 - 16 = 8Since the median only represents the midpoint of the distribution, one cannot conclude with certainty that home team took more shots than the visiting team, information on the mean would confirm that. A less controversial and evident inference is that the visiting team had more variability in their shots as their distribution has a higher Interquartile Range (IQR of 8 > 3) which is a direct measure of variation for distributions.

Hope this Helps!!!

Answer:y = (1/2)x + 4

Step-by-step explanation:

The equation of the line that passes through the points (-6, 1) and (6, 7) can be found using the slope-intercept form of a line. The slope m is calculated as (y2 - y1)/(x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. Plugging in the values for these points gives us a slope of m = (7-1)/(6-(-6)) = 1/2.

Now that we have the slope, we can use point-slope form to find the equation of the line: y - y1 = m(x - x1). Substituting one of our points and our calculated slope into this equation gives us y - 1 = (1/2)(x + 6). Simplifying this expression gives us y = (1/2)x + 4, which is the equation of our line in slope-intercept form.

So, an equation for this line is y = (1/2)x + 4.

Answer:

y = [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (6, 7 )

m = [tex]\frac{7-1}{6-(-6)}[/tex] = [tex]\frac{6}{6+6}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 7 )

7 = [tex]\frac{1}{2}[/tex] (6) + c = 3 + c ( subtract 3 from both sides )

4 = c

y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Answer:

Step-by-step explanation:

They should be used carefully because they can potentially increase fuel consumption and engine damage.

The space or length separating two points or objects is measured as distance. It is used to define the distance between objects in space or their relative position in space, and it is a fundamental idea in mathematics and physics. The distance formula, which is based on the Pythagorean theorem, is typically used in mathematics to calculate distance. In a two-dimensional coordinate system, the distance between two locations is calculated as the square root of the sum of the squares of the disparities between their x and y coordinates.

given

While travelling at slower speeds, ascending hills, or travelling down or up steep inclines, lower gears are often employed. When driving, you might want to shift into a lower gear in the following circumstances:

Driving on ice or snow Using a lower gear can provide you more traction and help you keep control of the car when driving in slick conditions.

Driving on windy roads: Using a lower gear while driving on winding roads might help you keep a steady speed and prevent the car from accelerating too quickly.

In general, when the engine needs to work harder than usual, using lower ratios might provide you greater power and control.

They should be used carefully because they can potentially increase fuel consumption and engine damage.

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The undefined terms in this axiom set are "line" and "point." These terms are not defined within the axioms themselves and are assumed to be understood.

The axiomatic system is consistent. The axioms do not contradict each other, and it is possible to construct a model of the system that satisfies all the axioms.

For example, we can imagine a Euclidean plane where each line is a set of three non-collinear points, and each point is contained by exactly two lines. Two distinct lines in this plane intersect at exactly one point, satisfying all the axioms.

The specific property of this axiomatic system is that it defines a Euclidean plane, which is a specific type of geometry characterized by the three axioms given.

The axioms capture some of the fundamental properties of Euclidean geometry, such as the existence of points and lines, the intersection of lines, and the relationship between points and lines.

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The correct option is (a), i.e. The mean would increase.

What is mean?

Mean is a measure of central tendency that is commonly used in statistics and mathematics. The mean of a set of numbers is calculated by adding up all the numbers in the set and dividing the sum by the total number of values in the set.

The mean of the number of air conditioner units sold by the 10 sales representatives last year can be calculated by adding up all the sales and then dividing by the total number of representatives, which is 10:

Mean = (6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36) / 10

= 169 / 10

= 16.9

So the mean number of air conditioner units sold per representative is 15.9.

If the representative who sold the lowest number of units left the department and his sales are cancelled out, the new sum of sales will be:

6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36 - 6 = 163

This is because we subtract the sales of the representative who left (which is 6 units in this case). The new mean can then be calculated by dividing this sum by the new total number of representatives, which is 9:

New mean = 163 / 9

= 18.11

So the new mean number of air conditioner units sold per representative is 18.11, which is higher than the original mean of 16.9. This is because removing the lowest value (which is smaller than the mean) increases the overall average.

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In a class, there are 18 girls and 14 boys. If the teacher selects two students at random to attend a party with the principal, the probability that the two students are the same sex is 0.49.

Therefore, the total number of students = 18 + 14 = 32

This can be calculated by using the combination formula: ⁿC₂ = n! / ((n - r)! r!).

Here, n = 32 (total number of students), and r = 2 (number of students that we have to select).

ⁿC₂ = 32C₂ ⇒ 32! / ((32 - 2)! 2!) ⇒ (32 × 31) / (2 × 1) ⇒ 496

The number of ways of selecting two girls = ¹⁸C₂ ⇒ 153

The number of ways of selecting two boys = 14C₂ ⇒ 91

Total number of ways of selecting two students of the same sex = 153 + 91 = 244

Probability of selecting two students of the same sex = (Number of ways of selecting two students of the same sex) / (Total number of ways of selecting two students)

⇒ 244 / 496 ⇒ 0.49

Therefore, the probability that the two students are the same sex is 0.49.

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Answer:

how web is it you feel like a a a a a a a a a make

Step-by-step explanation:

hf and I have been working on the topic on the topic on the topic on the topic on the topic ona the topic on the topic on the topic on the topic on the

To meet the​ recommendation, the ramp needs to have a horizontal distance of at least 16 feet. The ramp has a horizontal distance of 17.9 feet.

If the ramp has a horizontal distance of 17.9 feet, it meets the recommended minimum distance of 16 feet for a ramp with a maximum slope of 1:12, as per the ADA Accessibility Guidelines.

It's important to note that the slope of the ramp should also be taken into consideration to ensure that it is safe and easy to use for individuals with disabilities. If the ramp's slope is too steep or too shallow, it may not meet accessibility standards and could pose a hazard to users.

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using what we know about whole number division can be helpful when dividing with fractions. We can use the inverse operation of multiplication, simplify fractions, and use estimation to check our work and ensure that our division is accurate.

When dividing with fractions, one can use what they know about whole number division to check their work. This is because the rules of division remain the same for both whole numbers and fractions. One important rule is that division is the inverse operation of multiplication. In other words, when we divide, we are essentially finding how many times one number (the divisor) fits into another number (the dividend).

To check our work when dividing with fractions, we can use the same approach. We can multiply the quotient (the result of our division) by the divisor to see if we get back the dividend. If we do, then we know that our division was correct. For example, if we divide 3/4 by 1/2 and get a quotient of 3/2, we can check our work by multiplying 3/2 by 1/2.

Another important rule is that we can simplify fractions before dividing them to make the process easier. This means that we can divide both the numerator and the denominator by a common factor to get an equivalent fraction with smaller numbers. For example, if we want to divide 6/8 by 2/3, we can simplify 6/8 to 3/4 and 2/3 to 8/12. Then we can divide 3/4 by 8/12, which is much easier.

Finally, we can also use estimation to check our work when dividing with fractions. Estimation involves rounding the fractions to the nearest whole number or using benchmarks, such as 1/2 or 1, to get an approximate answer. This can help us quickly check if our quotient is reasonable or if we made an error in our division.

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Answer: 4x√5

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

196

Step-by-step explanation: