When you isolate the variable,the goal is to get the variable

Answer:

Since AC is perfectly equal to BD, 4x-60=30-x. If you solve for x, x=18. Then plug 18 into BD=30-x. Therefore, BD=12.

The difference between four times a number and one can be expressed as 4x - 1, where "x" represents the number. This expression involves multiplying the number by 4 and then subtracting 1.

The difference between four times a number and one can be succinctly expressed as the result of multiplying that number by four and then subtracting one from the product. In mathematical notation, this difference can be represented as:

4x - 1

Here, "x" represents the unknown number, and we are performing two operations: multiplying it by 4 and subtracting 1 from the result. Let's break this down further:

Four times a number: When you multiply a number by 4, you are essentially scaling it up by a factor of 4. For example, if the number is 5, then four times that number would be 4 * 5 = 20.

Subtracting one: After obtaining the result of four times the number, we subtract 1 from it. In our example, if the number is 5, then after four times the number (20), subtracting 1 results in 19.

So, the difference between four times a number and one is the value obtained after performing these two steps. It's a simple arithmetic expression that can be calculated for any given value of "x."

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Nancy and Matilda will meet in 3 hours.

Step-by-step explanation:

Given,

Distance to cover = 60 miles

Speed of Matilda = 12 miles per hour

Speed of Nancy = 8 miles per hour

Combined speed of Nancy and Matilda = 8+12 = 20 miles per hour

Let,

x be the time taken by them

Distance = Speed * Time

[tex]60=20*x\\60=20x\\20x=60[/tex]

Dividing both sides by 20

[tex]\frac{20x}{20}=\frac{60}{20}\\x=3[/tex]

Nancy and Matilda will meet in 3 hours.

Keywords: distance, speed

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In 3 hours Nancy and Matilda meet.

Given

Nancy and Matilda are 60 miles apart, cycling towards each other on the same road.

Matilda rides 12 miles per hour and Nancy rides 8 miles per hour.

Speed is defined as the ratio of distance and time.

The time will take to meet Nancy and Matilda is given by;

[tex]\rm \dfrac{12}{8}=\dfrac{x}{60}\\\\8 \times x=60\times 12\\\\8x=720\\\\x = \dfrac{720}{8}\\\\x=90[/tex]

Therefore.

The time taken to meet them is;

[tex]\dfrac{12}{8}+\dfrac{90}{60}\\\\1.5+1.5= 3[/tex]

Hence, in 3 hours will they meet.

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Answer:

The amount of a check issued for an 08/11 invoice, would depend on when the invoice is paid.  

If it's paid within 13 days, there's a 3% discount . which will be calculated as

648.50 x 3% = $19.455 discount

If it's paid within 11 - 15 days, there's a 2% discount.

648.50 x 2% = $12.97 discount

If it's paid within 16 - 30 days, there is no discount

If it's paid after 30 days, 5% APR is added to the bill

The check would be for the invoice amount of $648.50 plus a late fee of $2.67, totaling $651.17. The late fee is applied since the payment was made 3 days after the 30-day period from the invoice date and calculated using a daily rate derived from the 5% APR.

The invoice has specific payment terms: 3/10, 2/15, N30. These are discounts offered for early payment. The first part '3/10' means that the payer gets a 3% discount if they pay within 10 days. The second part '2/15' offers a 2% discount if the payer pays within 15 days. 'N30' means that the full amount due needs to be paid within 30 days from invoice date. Additionally, there is a 5% APR (annual percentage rate) charge for late payments.

The invoice was issued on 08/11, and the payment was made on 09/13, which is 33 days after the invoice date. Therefore, there aren't any discounts for the payment because it's not within the 10 or 15 days period. However, it's slightly over the 30 days, so there will be a late fee applied. The late fee is commonly calculated based on a daily rate. The daily rate is the APR divided by 365 (5%/365=0.0137%). Multiply the daily rate by the number of late days (33-30=3) and the invoice amount ($648.50).

So the late fee is 648.50*0.0137%*3=$2.67. The amount of the check would be the original invoice amount $648.50 plus late fee $2.67,  so the total is $651.17.

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[tex]\frac{79}{10}[/tex], which is a complex fraction, can be written as a mixed number resulting in [tex]7\frac{9}{10}[/tex].

A mixed number is a combination of a whole number, a numerator and a denominator.

The numerator is always less than the denominator in a mixed number because it has been converted from a complex fraction to its current status as a mixed number.

Mixed numbers are complex fractions, like [tex]\frac{79}{10}[/tex].  Before the conversion, complex fractions are fractions where the numerator is greater than the denominator.

Thus [tex]\frac{79}{10}[/tex] written as a mixed number is [tex]7\frac{9}{10}[/tex].

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Answer:

10

Step-by-step explanation:

if you take 8 and divide it by 4 you get 2 meaning that each fifth is 2 pounds. if there are 5/5 that means there are 10 pounds

Answer:

12y and 6bc

Step-by-step explanation:

multiply by 2

The product of [tex]6y[/tex] and [tex]3bc[/tex] after doubling would be as follows:

[tex]36bcy[/tex]

Variable

Product of [tex]6y,3bc=18bcy[/tex]

Double the product of [tex]6y,3bc=2(18bcy)[/tex]

                                                [tex]=\textbf{36bcy}[/tex]

Thus, it is the correct answer.

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Answer:

B) 1

Step-by-step explanation:

Answer:1

Step-by-step explanation:

Answer:   x-4, 2x-8, 8x-32

Step-by-step explanation:

First, let's move combine like terms:

-5y + 8y = 6 + 2 -12.

3y = -4.

y = -4/3

Answer:

x = -3 + 2y

Step-by-step explanation:

I'm not sure if that's correct, sorry, dear~!

Answer:

112 candies

Step-by-step explanation:

Start from the end.

Joe gave 25% of the remaining candies to his sister and has 21 candies left. Then

[tex]21 \ candies - 75\%\\ \\x \ candies - 25\%[/tex]

Write a proportion:

[tex]\dfrac{21}{x}=\dfrac{75}{25}\\ \\75x=21\cdot 25\\ \\x=\dfrac{21}{3}=7[/tex]

Joe gave 7 candies to his sister, so before this he had 21 + 7 = 28 candies.

He gave 4/6 of what he had left to his brother when he went home, so 2/6 of all his candies left ot him. Hence,

[tex]28\ candies - \dfrac{2}{6}\\ \\x\ candies - \dfrac{4}{6}[/tex]

Write a proportion:

[tex]\dfrac{28}{x}=\dfrac{\frac{2}{6}}{\frac{4}{6}}\\ \\\dfrac{28}{x}=\dfrac{1}{2}\\ \\x=28\cdot 2=56[/tex]

Joe gave 56 candies to his brother, so Joe had 28 + 56 = 84 candies when he went home.

Joe gave 1/4 of his total candies to his classmates, so 3/4 of his candies left to him. So,

[tex]x\ candies - \dfrac{1}{4}\\ \\84\ candies - \dfrac{3}{4}[/tex]

Write a proportion:

[tex]\dfrac{x}{84}=\dfrac{\frac{1}{4}}{\frac{3}{4}}\\ \\\dfrac{x}{84}=\dfrac{1}{3}\\ \\3x=84\\ \\x=28[/tex]

Therefore, initially, Joe had 28 + 84 = 112 candies.

Answer:

C i think..

Step-by-step explanation:

Answer:

Step-by-step explanation:

30/5=6

Final answer:

Benjamin rides his scooter for a total of 6 miles over a period of 10 days, by multiplying the daily distance of 3/5 mile by 10 days.

Explanation:

To calculate the distance Benjamin rides his scooter over 10 days, we multiply the daily distance by the number of days. Benjamin rides 3/5 of a mile each day.

Distance per day = 3/5 mile
Number of days = 10 days

The total distance is:

3/5 mile/day × 10 days = 6 miles

Therefore, the correct answer is  Benjamin will have traveled a total of 6 miles over the course of 10 days.

Answer:

1) The polynomial [tex]8x^3+1[/tex] represents a sum of cubes

2) The polynomial [tex]49x^2-25[/tex] represents a difference of squares

Step-by-step explanation:

1) To find the polynomials represents a sum of cubes :

[tex]8x^3+1[/tex] represents a sum of cubes

For [tex]8x^3+1[/tex]

[tex]=2^3x^3+1^3[/tex]

[tex]=(2x)^3+1^3[/tex]

Therefore [tex]8x^3+1=(2x)^3+1^3[/tex]

Therefore [tex]8x^3+1[/tex] represents a sum of cubes

2)To find the polynomials represents a difference of squares :

[tex]49x^2-25[/tex] represents a difference of squares

For [tex]49x^2-25[/tex]

[tex]=7^2x^2-5^2[/tex]

[tex]=(7x)^2-5^2[/tex]

Therefore [tex]49x^2-25=(7x)^2-5^2[/tex]

Therefore [tex]49x^2-25[/tex] represents a difference of squares

23-n > 33

- <--- that's a greater than or equal to sign

Answer:

23-n > 33

Step-by-step explanation:

Answer:

15.666666666667=15.67 to the nearest hundredth or to two decimal places.

Step-by-step explanation:

We want to round 15.66666666667 to the nearest hundredth or to two decimal places.

We count two numbers after the decimal place to get:

15.66|6666666667

The next digit is 6

Since 6>5, we round up.

This means we add 1 to the number the hundredth place to get

15.67

Answer:

1) D

2) A, D, F

3) 3.5 mph

4) equation in explanation $15

Step-by-step explanation:

4) equation: 27.50-12.50

Answer:

20

Step-by-step explanation:

Average =

sum of scores/number of score

= 14 + 17 + 22 + 27 / 4

= 80/4

= 20

a) North Carolina has 4,910,119 more people than South Carolina

b) the population of North Carolina is 2.06 times larger than that of South Carolina

Step-by-step explanation:

a)

Here the question is asking "how much larger is the population of North Carolina than South Carolina". This means that we have to compare the absolute value of the population of North Carolina with the population of South Caroline.

We have:

NC = 9,535,483 is the population of North Carolina

SC = 4,625,364 is the population of South Carolina

In order two compare the two, we have to calculated the difference between NC and SC. Plugging into a calculator, we get:

[tex]NC-SC=9,535,483-4,625,34=4,910,119[/tex]

So, North Carolina has 4,910,119 more people than South Carolina.

b)

In this question, we are asked "how many times larger is North Carolina’s population than South Carolina’s population". This is equivalent to ask what is the ratio between the population of North Carolina to that of South Carolina.

As we said before, we have:

NC = 9,535,483 is the population of North Carolina

SC = 4,625,364 is the population of South Carolina

And by calculating the ratio, we find:

[tex]\frac{NC}{SC}=\frac{9,535,483}{4,625,364}=2.06[/tex]

So, the population of North Carolina is 2.06 times larger than that of South Carolina.

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Answer: the population of North Carolina is 2.06 times larger than that of South Carolina.

Answer:

New average = 85.9.

Step-by-step explanation:

Yes, the new class average can be calculated.

The New total of the scores = 37*86 + 76 + 81 + 97

= 3436.

The new total of examinations sat = 37 + 3 = 40.

Therefore the new class average =  3436 / 40

= 85.9

Answer:

1) the set of all points in a plane that are at a given distance from a given point in the plane

2)a chord of a circle that contains the center of the circle

3)circles that have equal radii

4)two or more circles that lie in the same plane an have the same center

5)a segment joining the center of a circle to a point of the circle

Answer:

D

Step-by-step explanation:

x - 6 = - 3 + 8

x = 5 + 6

x = 11

3w - 8w = 35

- 5w = 35

5w = - 35

w = - 35 : 5

w = - 7

3(3x - 3) = 10x

9x - 9 = 10x

- 9 = 10x - 9x

x = - 9

Answer:

1. x = 11,

2. w = -7,

3. x = -5

4. x = -5

5. x = -9

Step-by-step explanation:

1. x-6 = -3+8

x - 6 = 8 -3

x - 6 = 5

Adding 6 to both sides:

x - 6 + 6 = 5 + 6

x = 11

2. 3w - 8w = 35

3w - 8w = 35

-5w  = 35

Divide both sides by -5

-5w/-5 = 35/-5

w = -7

3. - 4 x - 4 x = 44 - 4

- 4 x - 4 x = 44 - 4

-8x = 40

Divide both sides by -8

-8x/-8 = 40/-8

x = -5

4. 5 -8 = 3x +2 - 2x

Collecting like terms and rearranging equation

3x - 2x = 5 - 8 - 2

x = 5 - 10

x = -5

5. 3(3x - 3) = 10x

3(3x - 3) = 10x

Expanding and removing parenthesis

9x - 9 = 10x

Collecting like terms and rearranging equation

10x - 9x = -9

x = -9

Answer: Estimate means a close guess.

For example, when estimating with decimals, we would round them to the nearest whole number to estimate the answer.

Example: 3.6 + 1.2

1.2 is closest to 1

3.6 is closes to 4

4 + 1 = 5

A good estimate is 5

3.6 + 1.2 = 4.8

4.8 is very close to 5, so 5 is a very good estimate.

Final answer:

Estimating a math problem involves making an educated approximation of a quantity using prior knowledge and reasoning. It applies to various fields and helps to rule out unrealistic numbers, as well as develop important problem-solving skills.

Explanation:

To estimate a math problem means to find a rough approximation or a ballpark figure of the quantity in question, rather than calculating the exact number. Estimations are based on sound reasoning, prior experience, and a strong grasp of the relevant variables and physical principles. The process is not a wild guess but a calculated approximation that can be derived from formulas where the input quantities are known to a limited precision.

For example, to estimate the mean rent for a two-bedroom apartment in a town, you might calculate the average of several listed rents. Or, in physics, to estimate how large a current will be in a circuit when it is turned on, you would apply the relevant principles and any known quantities to arrive at an approximate value. The goal of estimation is to get within a reasonable range of accuracy without needing a precise computation.

The skills of estimation are vital in many fields, including physics, and they help in ruling out unrealistic results. Practicing these skills, getting familiar with units, and understanding relationships between variables all contribute to making better estimates. Moreover, after arriving at an estimate, it's important to do a sanity check to make sure the result seems reasonable within the context of what is known.

Answer:

[tex]\left[\begin{array}{cc}0&2\\3&3\\6&4\\9&5\end{array}\right][/tex]

Step-by-step explanation:

+2 means that when c is at 0 w is at 2.

1/3c means that c moves up 3 at a time.

Answer:

Total population = 200

Step-by-step explanation:

recaptured tagged/recaptured total ≈ tagged/total population

The best estimate for the total population of Robin's is 200.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

Number of robins which are tagged = 20

Let x be the total population of robins.

Her catches some other robins.

Number of robins that he catched = 120

Number of robins he catched also is tagged = 12

We can write the expression as,

20 / x = 12 / 120

Cross multiplying, we get,

12x = 120 × 20

12x = 2400

x = 2400 / 12

x = 200

Hence the number of robins is 200.

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Answer:

You'll need 18 cups of chicken broth!

Step-by-step explanation:

You are using a ratio of 1/4 cup (lentils) to 2 cup (broth). Therefore, you need to find the relationship between lentil and broth.

Therefore, 18 cups are needed :D

To make a soup with 2 1/4 cups of dried lentils, you would need 9 cups of chicken broth.

To find the number of cups of chicken broth needed, we need to multiply the given number of cups of dried lentils (2 1/4 cups) by the ratio of chicken broth to dried lentils. The ratio is 2 cups of chicken broth per 1/4 cup of dried lentils. So, for 2 1/4 cups of dried lentils, we would need:

2 1/4 cups × (2 cups/1/4 cup) = 9 cups of chicken broth

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Step-by-step explanation:

9x2= 3 • 3 • x2

6x= 3 • 2 • x

12x= 2 • 2 • 3 • x

8= 2 • 2 • 2

Answer:

84

Step-by-step explanation:

Using PEMDAS: (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

7*(3+9)

7*(12)

84

Answer:

83

Step-by-step explanation: