Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long. How long is the remaining piece of rope?

An equation which has an extraneous solution is: C. √x = -5.

In Mathematics, an extraneous solution can be defined as a type of solution (root) to a squared equation or transformed equation that isn't a direct solution (root) of the original equation.

This ultimately implies that, extraneous solutions are numerical values that are obtained when we solve equations that aren't solutions to the original equation as shown below:

Taking the fifth root of both sides of the equation, we have:

[tex]\sqrt[5]{x} = -2\\\\(\sqrt[5]{x})^5 = -2^5\\\\[/tex]

x = -32.

Taking the cubic root of both sides of the equation, we have:

∛(x + 1) = 10

[∛(x + 1)]³ = 10³

x + 1 = 1000

x = 1000 - 1

x = 999.

Taking the fourth root of both sides of the equation, we have:

[tex]\sqrt[4]{x-5} =3\\\\(\sqrt[4]{x-5})^4 =3^4[/tex]

x - 5 = 81

x = 81 + 5

x = 86.

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Step-by-step explanation:

-5x + 18 < -12

subtract 18 from both sides:

-5x + 18 - 18 < -12 - 18

-5x < -30

divide both sides by -5: [remember, when dividing by a negative number you must FLIP the sign direction]

(-5x)/-5 > (-30)/-5

x > 6

or

(6 , ∞)

Answer:

3/10

Step-by-step explanation:

4/5 - ½

The l.c.m of the Denominator is 10

=8-5/10

=3/10

The third quartile (upper quartile) of the data is 38

What is the Median?

The center value or middle value of a data set is the median.

What are the Upper Quartiles?

Upper quartile (Q3) is the center or middle data point of the second half of a data set.

The given data is 33, 25, 42, 25, 31, 37, 46, 29, 38

Order the data set given as:

25, 25, 29, 31, 33, 37, 38, 42, 46

Upper Quartile = 25, 25, 29, 31, 33, 37, 38, 42, 46 = 38

Therefore, the third quartile (upper quartile) of the data is 38

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Answer: andy drove  280 miles in 3 hours

Step-by-step explanation:  are you seriousseious right now?  

The required permutations are given as 168 letters will be formed.

Given that,
How many different 8-letter permutations can be formed from 6 identical h's and two identical t's is to be determined.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
A total number of combinations = 8!
The number of repetitions,  = 5!.2!
Permutation of letters = 8!/[5!.2!]

Thus, the required permutations are given as 168 letters will be formed.

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A loss of 8 points is the situation which is represented by integer -8.

A number system is defined as a system of writing to express numbers.

The situation that could be represented by -8 is option C, a loss of 8 points.

The negative sign indicates a decrease or loss in value.

A distance of 8 meters above sea level represents a positive number because the distance is above.

A rise in temperature of 8 degrees is also positive as it is increasing.

A gain of $8 is also represents the positive value.

-8 represents a loss of 8 points.

The negative sign denotes a decrease or loss in value.

Hence, a loss of 8 points is the situation which is represented by integer -8.

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Answer:

Rule SAS; side angle side

Step-by-step explanation:

Since they give that DM and CM are equal, and BM and AM are equal, you already have two sides. And since you have already marked vertical angles (correct because of intersection), you have 2 sides and 1 angle that are equal. This is enough to prove they are equal so it is the rule SAS or side, angle, side.

The measure of the obtuse angle is 128 degrees

From the question, we have the following statement that can be used in our computation:

Acute angle = 52  degrees

The measure of the obtuse angle is calculated as

Obtuse angle = 180 - Acute angle

Substitute the known values in the above equation So, we have the following equation

Obtuse angle = 180 - 52

Evaluate

Obtuse angle = 128

Hence, the angle is 128 degrees

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The maximum number of people Eddy can invite is 37.

The equation is simply used to show the relationship between the variables given.

In this case, it is going to cost him $150 to cater the party, plus $4 per person for drinks and he only has $300 to spend.

Let the number of persons be represented by p

The equation will be:

150 + (4 × p) = 300

150 + 4p = 300

Collect like terms

4p = 300 - 150

4p = 150

Divide

p = 150 / 4

p = 37.5

The maximum number is 37.

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The percentage change from 48 to 90 is 87.5%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, 48 to 90 represents a increase. The increase will be:

= 90 - 48

= 42

The percentage increase will be:

= Increase / Original number × 100

= 42 / 48 × 100

= 87.5%

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Answer:

300kg

Step-by-step explanation:

125/100=x/240

30000=100x

x=300

Step-by-step explanation:

[tex]- 4u + 3 + 6u =5 + 10u \\ ⇒ - 4u + 6u- 10u = 5 - 3 \\ ⇒ - 8u = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⇒u = - \frac{2}{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = - \frac{1}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

The width of the tent is twice the width of one side which is 10.5 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high and the sides of the tent make a 50° angle with the ground.

Here the opposite is the height with the reference angle of 50° and we have to determine the adjacent which is the width of the tent.

∴ tan50° = Height of the pole/width.

1.19 = 6.25/width.

width = 6.25/1.19.

width = 5.25 feet.

But the total width of the tent will be twice as we have obtained only one side width.

∴ Total width is (2×5.25) = 10.5 feet.

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The total number of small boxes is 2.1 and the large boxes is 6.3.

Given;

To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 150 nails in each small box and 400 in each large box. The contractor purchased 3 more tiny boxes than large boxes. Totaling 2850 nails.

To calculate the proportion of small and large boxes that were bought,

Let's assume the small boxes as 's' and the big boxes as '3s'.

∴ s(150) + 3s(400) = 2850

  150s + 1200s = 2850

  1350s = 2850

  s = 2850/1350

  s = 2.1

∴ 3s = 2.1 * 3

      = 6.3

Hence, the total number of small boxes is 2.1 and the number of large boxes is 6.3.

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Answer:

The number of small boxes purchased are 3 and the number of large boxes purchased are 6.

Step-by-step explanation:

Let the small boxes bought be x

Therefore the large boxes will be 2x

Total nails bought = 2850

Nails in x small boxes = 150x

Nails in 2x large boxes = 400. 2x = 800x

2850 = 150x + 800x

2850 = 950x

x= 2850/950 =  3

2x = 2x3= 6

The 12 terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

The formula to calculate the nth term of an Arithmetic Sequence is -

a(n) = a + (n - 1)d

a - first term of A.P.

d - Common difference of A.P.

n - position of term

We have -

a[1] = 3

a[12] = 25

Then, using the formula to calculate the nth term, we get -

a(n) = a + (n - 1)d

a[1] = 3

AND

a(12) = 3 + 11 x d

25 = 3 + 11d

22 = 11d

d = 2

So, the terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

Hence, the 12 terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

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Answer:

3:1

Step-by-step explanation:

bc the lcm is 3

Answer:

the ratio is 3/1

Answer:  a)  y - 4 = 2/3(x) - 2

b)  y - 4 = -3/2(x) -2

Step-by-step explanation:

equation of original line:  y = 2/3x -5

point on a line parallel to original line:  (3,4)

The slope of a line parallel to a given line has the same slope, so the equation of the parallel line (in point-slope form) is:

(y - y1) = 2/3(x - x1)

point (x1, y1) is (3, 4)

plug (3,4) into the equation:

y - 4 = 2/3(x - 3)

y - 4 = 2/3(x) - 2

rewrite in slope-intercept form:  y = 2/3(x) + 2

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line:  - 1/m

Therefore, the slope of the perpendicular line = -3/2

Equation for the perpendicular line is:

y - 4 = -3/2(x) -2

As per the given ratio, the number of boys in the school is 133.

Ratio:

Ratio refers the relationship between two things when it is expressed in numbers or amounts.

Given,

The ratio of girls to boys in the school is 3 to 1.

Here we need to find the number of boys in the school if the total number of students is 400.

Let x be the number of boys in the school.

So, the here we have the ratio from girls to boys and we have to convert it into boys into girls, then we get,

=> girls to boys ratio = 3:1

So, boys to girls ratio = 1:3

We know that the total number of students are 400

Therefore, the number of boys in the school is,

=> 1/3 x 400 = 133

So, the number of boys in the school is 133.

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Any piece of luggage must have a length, width, and height combined that is less than or equal to 150 cm. A traveler requests to take a package with the maximum permitted volume. if the length and width are to be equal, then the dimensions would be 48*96*72

Any piece of luggage must have a length, breadth, and height combined that is 216 cm or less.

L+W+H=216 (because we want the max volume, we may ignore the "less than part" and set them equal) (since we want the max volume, we can ignore the "less than part" and set them equal)

L = W if the length and width are equal.

Let's construct this new equation by swapping L for W.

Arrange H to the left so that H=216-2W when 2W+H = 216

Consequently, what is volume V=L*W*H=W=W2*(216-2W) =216W2-2W3 div./dW=432W-6W?

2\s432W-6W^2=0

72w-w2=0 divided by 6 on both sides.

W = 72 L H = 72 cm

L=2W is the only item that has altered.

Given that L+W+H=216 and that V=L*W*H=2W*W*(216-3W) =432W2-6W, 3W+H=216

864W-18W2 x 3 V prime

Set V prime to 0, solve it by dividing both sides by 18, and you'll get W = 48. dimensions will be

48, 96, and 72 cm in width ,lenght and height

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Answer:

7/5

Step-by-step explanation:

trust me

Answer:

[tex]b=\frac{-4i-2}{i}[/tex]

So the answer is...

A ) -2

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 12 on the left side and the dividend 6 on the right side like this:

 12 ⟌ 6    

Step 2:

The divisor (12) goes into the first digit of the dividend (6), 0 time(s). Therefore, put 0 on top:

      0    

 12 ⟌ 6    

Step 3:

Multiply the divisor by the result in the previous step (12 x 0 = 0) and write that answer below the dividend.

       0    

 1 2 ⟌ 6    

       0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (6 - 0 = 6) and write the answer below.

      0    

 12 ⟌ 6    

  - 0    

   6    

You are done.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 6 divided by 12 calculated using Long Division is:

0

6 Remainder

The time taken in minutes to fill a tank having a capacity or work of 1.5m³ is 1.2 minutes;

What are Time and Work?

According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.

The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.

W is the amount of work done.

N is the number of people.

D is the number of days or hours needed.

In the question, It is given that:

water flowing off a certain pipe is 75 liters per minute;

and;

the tank has a capacity of 1.5m³

First converting the Efficiency in liters per second,

So,

water flowing off a certain pipe is 75 liters per minute;

So, dividing it by 60 ;

Water flowing off the pipe = 1.25;

Now using the work-time relationship:

Efficiency × Time = work;

So,

1.25×Time = 1.5

⇒Time = 1.2

So, the time taken in minutes to fill a tank having a capacity of 1.5m³ is 1.2 minutes;

Hence,

the time taken in minutes to fill a tank having a capacity of 1.5m³ is 1.2 minutes;

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Natasha has left with 4.5 inches of oak boards.

What is a simplification?

The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining trade processes.

Here, we have

120 inches of oak boards

50.75 inches for shelves, 36 1/4 more inches of oak boards, and she didn’t use 401/2 inches for the top and 60.5 inches for the sides.

We have to find how many inches of oak boards Natasha has left.

We use here simplification, we get

= 120 + 36 1/4 - 50.75 - 40 1/2 - 60.5

= 4.5 inches

Hence, Natasha has left with 4.5 inches of oak boards.

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The balance of the account after 1 year and after 2 years  16400 and 16820 is respectively.

A bank account starts with a balance, P = $8000

rate of interest = 5%

compound interest for 1 year is :

[tex]CI = P(1 + R/100)^n[/tex]

CI = 8000(1 + 5/100)

CI = 8000(1 + 1/20)

CI = 8000(21/20) = 8400

A = CI + P = 8000 + 8400 = 16400

compound interest for 1 year is :

[tex]CI = P(1 + R/100)^{2n}[/tex]

CI = 8000(1 + 5/100)^2

CI = 8000(1 + 1/20)^2

CI = 8000(21/20)^2 = 8820

A = CI + P = 8000 + 8820 = 16820

The balance of the account after 1 year and after 2 years  16400 and 16820 is respectively.

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The required slope of the given line is 1 which is shown in the graph.

The slope of the line is represented as the rise of the line.

Slope m = (y₂ - y₁)/(x₂ -x₁  )

Grab two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

We take the two points (4, 10) and (9, 22)

Let

x₁ = 0, y₁ = 1

x₂ = 8, y₂ = 9

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula

m = (9 - 1) / (8 - 0)

m = (8)/(8)

m = 1

Thus, the required slope of the given line is 1 which is shown in the graph.

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Answer:

95%

Step-by-step explanation: