How do I write a system of equations

Answers

Answer 1
So for a word problem I assume you must first define your variables. Ask yourself what is the question asking and how could the question be answered with what you know through relationships that the problem defines. For example if the problem says that the total of a few thing is a number put that in as one of your equations. Examine how relationships like if there is half the amount of variable A than variable B work and figure out how to write that as an equation that makes sense. To double check if you wrote your equations correctly double check the information given in the problem and mentally sound out the equation. Hope this helps and note there are as many equations as there are variables in your system.

Related Questions

A large helium balloon is tethered to the ground by two taut lines. One line is 100 ft. Long and makes an 80 degree angle with the ground. The second line makes a 40 degree angle with the ground. How long is the second line?

Answers

The second line is 153ft long.

We are making a figure out of the given statment. Where we have the Triangle ABC and other two Triangle ADB and ADC inside Triangle ABC. Here Angle ADC = 80 degress and Angle ACD = 40 egress.

According to given statement and figure,

In triangle ABO, AD= 100 ft

Hence, BD/AD = Cos80

or, BD = (100 * Cos80)

or, BD = 17.36 ft

Now, AB/AD = Sin80

or, AB = (100* Sin 80)

or, AB = 98.48

Now, In case of triangle ABC

AB/AC = Sin40

or, AC = AB/ Sin 40

or, AC = 98.48/ Sin40

or, AC = 153.2 ft (nearly equal to 153 ft)

The second line is 153ft long.

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A storm that moved through several states at a speed of 60 miles per hour affected 219 miles of land. What did that make the storm

Answers

The longest tornado ever recorded spanned 219 miles of land as it swept through many states at a pace of 60 miles per hour.

What are the importance of vector calculus?A tornado could cause a natural disaster to wreak havoc in significant geographic areas.A violent column of air between a thunderstorm and the earth is what is known as a tornado.In severe tornadoes, winds exceeding 200 miles per hour (h) are not uncommon.In conclusion, the longest tornado ever recorded affected 219 miles of land as it swept through many states at a speed of 60 miles per hour.Mathematically, a tornado is vector calculus with a fury. Severe storms are the result of the interaction of the two scalar forces of pressure and humidity with the vector field known as wind.

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Alana and Petra go to a ued book ale , where every book i the ame price. Alana buy 4 book and Petra buy 2 book. They run into their friend angu, who really love to read, and dicover that he ha bought 16 book. Angu received a $15 dicount, but he till pent $5 more than Alana and Petra combined. How much doe one book cot?

Answers

A book cost $2.00.

What are variables in maths?

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

What are the 2 basic types of variables?

Variables may be classified into two main categories: categorical and numeric. Each category is then classified in two subcategories: nominal or ordinal for categorical variables, discrete or continuous for numeric variables.

Given the no of books purchased by

Alana =4

Petra =2

Angus = 16

So, the total price of 4 books of Alana =$4

Total price for Petra = $2

Total price of Alana and Petra =4x+2x

=6x

Total price for Angus = 16x

But given Angus received a discount  of $15

So price post discount = 16x- 15

According to the question

16x-15 = 6x +5

Adding 15 both sides

16x +15-15 = 6x + 5+15

16x= 6x+20

Subtracting 6x both sides

16x - 6x = 6x - 6x + 20

10x = 20

i.e x=2

Cost of one book = $2

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How many times and how many ounces should I feed my goat if it is 7 pounds and I feed it 3 times a day

Answers

Since you're feeding it three times a day, you should feed your goat 0.74 ounces per feeding.

What is feeding?

The act of feeding involves giving a baby a mother's breast milk, either directly from the breast or by expressing (pump-out) the milk from the breast and giving it to the baby in a bottle.

Define Ounces and Pounding.

In the traditional method of measurement, a pound is used to measure weight. In the conventional system, ounces are smaller weight units that are defined in terms of pounds. 1 pound Equals 16 ounces.

Goats typically need around 2% to 4% of their body weight in feed per day. If your goat weighs 7 pounds, and you want to feed it 2% of its body weight per day, you would need to feed it 0.14 pounds of food per day, or 2.24 ounces per day. Since you're feeding it three times a day, you should feed it 0.74 ounces per feeding.

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Need help With answer

Answers

Answer:

Step-by-step explanation:

from the graph we konw the ∠ABD=∠DBC, because ∠DBC=20, so ∠ABD=20

The sum of the digits of a two-digit number is 7. When the digits are reversed, the number increases by 45. What is the original number?

original number: ⬜

Answers

The original number is 25.

We know that,

The sum of the original number is 7 --(i)

When reversed, the value of the number is increased by 45 --(ii)

Therefore, adding (i) and (ii), we get:

7 + 45 = 52

Also, 5 + 2 = 7

Since 52 is the reversed number,

Therefore, the original number is 25.

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A sequence is represented by the explicit formula

Answers

The value of a₂₆ in the  arithmetic sequence aₙ=  14 + 9n is 248.

The correct option is D.

What is an arithmetic sequence?

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

An arithmetic sequence,

aₙ=  14 + 9n

We have to find the value of a₂₆.

That means, n = 26.

Substitute the value of n = 26 to the sequence,

a₂₆ =  14 + 9(26)

a₂₆ =  14 + 234

a₂₆ =  248

Therefore, the value of a₂₆ is 248.

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Mario has 3/4 cups of chocolate chips needs 1/3 cup to make a batch of cookies how many batches can Mario make if he uses all of his chocolate chips

Answers

In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.

How to find the given equation?

First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).

[tex]3/4 cups * 1 = 3/4 cups\\[/tex]

Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:

[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]

Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:

[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]

Mario can make 2.25 batches of cookies using all of his chocolate chips.

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How do you find the domain and range of a function x 4?

Answers

The domain of x=4 is (−∞,∞) and range is {y|y=4} .

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

(−∞,∞)

{x|x ∈ R}

y=4

is a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

Set-Builder Notation:{y|y =4}.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

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15. A pool can hold 850 gallons. It now has 598 gallons of
water and is being filled at the rate shown. How many
more minutes, m, can water continue to flow into the
pool before it overflows? Write and solve an inequality.
Then graph the solutions.

Answers

850 >= 598+15.75m
252 >= 15.75m
16>=m
The pool can be filled for 16 minutes before it overflows

I want to know how to get the GCF and LCM of 8,24,48

Answers

Answer:

GCF = 8

LCM = 48

Step-by-step explanation:

What it means when a function and its inverse is the same?

Answers

Step-by-step explanation:

it means that the graph of the function above y=x must be the mirrored image of the graph under y=x.

it means that the function applied to itself gives x.

f(f(x)) = x

e.g.

f(x) = 5 - x

f(f(x)) = 5 - (5 - x) = 5 - 5 + x = x

so, this f(x) is its own inverse.

By some estimates, about 30% of all males have a particular defect related to their eyes. How would you assign random numbers to conduct a simulation based on this
statistic?

Answers

Answer:

related to their eyes. How would you assign random numbers to conduct a simulation based on this

Audrey walked 285 meters west and Billy walked 213 meters south from the same starting location. How far apart are Audrey and Billy?

Answers

Audrey and Billy are as far as 367 meters apart.

What is displacement of an object?

The displacement of an object is its distance covered or moved in a specific direction. Displacement is an example of vector quantity.

A vector quantity is generally any type of quantity which can be expressed in magnitude and direction. Some examples include: weight, displacement, acceleration, force, etc.

Since Audrey walked 285 meters west and Billy walked 213 meters south from the same starting location, then we can determined the distance far apart by applying the Pythagorean theorem.

So that,

/hyp/^2 = /opp/^2 + /adj/^2

Let their distance apart be represented by s,

s^2 = 231^2 + 285^2

      = 53561 + 81225

s  = (134586)^1/2

s = 366.86

Audrey and Billy are as far as 367 meters apart.

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Tyrese works each day and earns more money per hour the longer he works. Write a function to represent a starting pay of $20 with an increase each hour by 3%. Determine the range of the amount Tyrese makes each hour if he can only work a total of 8 hours.

Answers

The range of the amount Tyrese makes each hour if he can only work a total of 8 hours is 20 ≤ x ≤ 24.80

What is a range?

The range is the space between the highest and lowest numbers.

Given: Tyrese works every day and gets paid more per hour the more time he puts in. Create a function to represent a starting wage of $20 that rises by 3% each hour.

To find: Establish the range of Tyrese's hourly pay if he can only work a total of 8 hours.

The beginning wage is $20.

Suppose x hours are in a day.

A $20 salary is offered, with a 3% hourly raise.

e.g., increment = (3/100)*20*x = (3/5)x

A function's maximum possible earnings are

y = 20 + (3/5)x

He is only allowed to work a total of 8 hours, per our instructions.

Therefore, the most money she can make in 8 hours is

y = 20 + (3/5)*8

y = 20 + 4.8

y = 24*8

$20 is the first sum.

As a result, if Tyrese can only work a total of 8 hours every day, the range of his hourly wage is .

Therefore, the correct answer is option B) 20 ≤ x ≤ 24.80.

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I NEED HELP ASAP!!!!!!!!

Answers

Answer:

(- 1, 9 )

Step-by-step explanation:

6x - y = - 15 → (1)

x + 2y = 17 → (2)

multiplying (1) by 2 and adding to (2) will eliminate y

12x - 2y = - 30 → (3)

add (2) and (3) term by term to eliminate y

13x + 0 = - 13

13x = - 13 ( divide both sides by 13 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for y

substituting into (2)

- 1 + 2y = 17 ( add 1 to both sides )

2y = 18 ( divide both sides by 2 )

y = 9

solution is (- 1, 9 )

Shade the points in the plane whose x-coordinates are greater than their y-coordinates. Write the inequality that describes these points.

Answers

The inequality that describes these points is y ≤ -1/2(x) -3. The graph is given the attachment.

How to graph an inequality?

To graph a linear inequality in two variables (say, x and y), start with y on one side. Consider the related equation obtained by changing the inequality sign to an equality sign. This equation's graph is a straight line.

If the inequality is strict (< or >), draw a dashed line. If the inequality is not strict (≤ or ≥), draw a solid line.

Finally, choose one point that is not on either line ((0,0) is usually the easiest) and determine whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point. If they don't, shade the other half-plane.

Graph each of the system's inequalities in a similar way.

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ES = ___ units

Round your answer to the nearest tenth.

Answers

Answer:

15

Step-by-step explanation:

The table shows a bacterial population y after x days


days, X 0,1,2,3,4

Population,8,24,72,216,648


Write an exponential function that represents the population


Y=

Answers

The exponential function that represents the population is y = a*3^x.

What is exponential function?

The formula for exponential functions is y = ab^x, where b is the constant ratio and a  is the starting point. Observe that as the value of x increases by a constant amount, the value of y increases by a common ratio by looking at a table of ordered pairs. All exponential functions share this trait.

We have to find the exponential function for the given table.

Since,

Exponential function = ab^x

where,

a is the starting point

b is the common ratio.

Here,

Common ratio = 24/8 = 72/24 = 216/72 = 648/216 = 3

So, the function becomes,

Exponential function = y = a*3^x

Hence, the exponential function that represents the population is

y = a*3^x.

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Dalis' employer pays $2,150 in health insurance and $86
in life insurance per year. She also gets $3,520 in paid time
off per year. Her monthly gross pay is $4,370. What are
Dalis' total job benefits?

Answers

Answer: chiki

Step-by-step explanation:

The total number of books sold from 2010-2015 from
Amazon can be modeled by the function
3
2
f(x) = 40x + 8x + 14824x + 33000and the number of kinds
of books at Amazon from that same time period can be modeled
as g(x): =
10x + 22, where x is the number of years since
2010. What is the average number of each kind of book
Amazon sold?

Answers

Answer:

If you want to find out how many print copies the book is selling, just click the Paperback or Hardcover edition of the book on Amazon, scroll down to Product Details on that page, and find the Amazon Best Sellers Rank for the print edition.

Step-by-step explanation:

A company has two manufacturing plants with daily production levels of 5x +14 items and 3x - 5 items, respectively. The first plant produces how many more items daily than the second​ plant?

Answers

Answer:

21x

Step-by-step explanation:

5x+14=19x

3x-5=-2x

-2x-19x=21x

The ratio of the number of report cards Ms. Wickham folded to the number that Ms. Cho folded was 2:3. At the end of the day, Ms. Leiva and Mr. Gamory folded 300 report cards. Who folded more report cards and by how many

Answers

Ms. Wickham folded 200 report cards and Ms. Cho folded 300 report cards, giving Ms. Cho an average of 100 report cards.

Ms. Wickham and Ms. Cho together folded 500 report cards.

Ms. Wickham folded 200 report cards

(200/500 = 2/5)

Ms. Cho folded 300 report cards

(300/500 = 3/5)

Mr. Leiva and Mr. Gamory folded 300 report cards.

Ms. Cho folded more report cards than Ms. Wickham, by

100 (300 - 200 = 100).

Ms. Wickham and Ms. Cho together folded 500 report cards, with the ratio of Ms. Wickham's report cards to Ms. Cho's being 2:3. Ms. Wickham folded 200 report cards, while Ms. Cho folded 300. At the end of the day, Mr. Leiva and Mr. Gamory folded an average 300 report cards. This meant that Ms. Cho folded more report cards than Ms. Wickham, by 100. Therefore, Ms. Cho folded 400 report cards in total, while Ms. Wickham only folded 300.

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Your friend has read 6 more than twice as many pages as your
sister has read. Let 4
be the number of pages that your sister has
read. Write an expression for the number of pages that your friend
has read

Answers

Answer:

Expression: 2s + 6

# of Pages Friend Read: 14 pages

Step-by-step explanation:

Let's call the number of pages your sister has read, s, and the number of pages your friend has read, f. We will make our equation first. If your friend has read 6 more than twice as many pages as your sister has, your equation would look like this:

f = 2s + 6

That is your equation for how many pages your friend read, your expression would be just 2s + 6. Now, we will substitute in 4 for s, and we get:

f = 2 * 4 + 6

Multiplying gives:

f = 8 + 6 = 14

So your friend has read 14 pages.

Hope this helped!

Which triangles are congruent by ASA?
ABC and TUV
VTU and ABC
VTU and HGF
none of the above

Answers

Still in need of help ??
the answers VTU and ABC

Write a rule to calculate 1% of any number

Answers

If you are doing algebra the answer is most likely:

0.01 times x

0.01 is 1% and x is a variable that represents any number
0.01(x)

where x is the number

Solve for x: -24 = 6x

Answers

Answer:

x = -4

Step-by-step explanation:

Solve for x: -24 = 6x

-24 = 6x

x = -24 : 6

x = -4

---------------------

check

-24 = 6(-4)

-24 = -24

the answer is good

The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let
x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of
$500 and wanteho purchase as many DVDs as possible, which values of x and y could represent the number of new
release and classie movies bought?
O x= 8, y = 45
O x= 10, y = 22
O x = 16. Y = 22
Ox= 18, y=18
Mark this and return
Save and Exit
Next
Submit​

Answers

The Correct answer is option (C) x = 16. Y = 22 . number of new-release movies on DVD is 16 and the number of classic movies on DVD is 22 .

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Given,

To find the values of X and Y,

Let x = number of new releases

Let y = number of classics.

The equation to solve the question is ,

20x + 8y = 500

When x= 16 and y = 22

= 20x + 8y

= 20(16) + 8(22)

= 320 + 176

= 496

Therefore, the number of new-release movies on DVD is 16 and the number of classic movies on DVD is  x= 16, y = 22

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simply the following
a) 2(y-1)/3-3(y-2)/4=1
b) 3x=44/5=2x+6

Answers

The simplified value of x is 44 / 15 or 7 / 5 and value of y is -2

What is simplification?

Simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Given that, simply the following

a) 2(y-1)/3-3(y-2)/4=1

b) 3x=44/5=2x+6

1) 2(y-1) / 3 - 3(y-2) / 4 = 1

Multiplying by 12 to both sides,

8(y-1) - 9(y-2) = 12

8y-8 - 9y+18 = 12

-y + 10 = 12

y = -2

2) 3x = 44 / 5 = 2x+6

3x = 44 / 5

Multiplying by 5 to both sides,

15x = 44

x = 44 / 15

or,

44 / 5 = 2x + 6

Multiplying by 5 to both sides,

44 = 10x + 30

14 = 10x

x = 7 / 5

Hence, the simplified value of x is 44 / 15 or 7 / 5 and value of y is -2

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convert 11.011 to a base 10 number​

Answers

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

How to covert binary number to decimal number?

Once the bits of the binary number have been multiplied by the corresponding positional weights, the binary number can then be converted into its corresponding decimal number by adding the resulting products.

To convert a number in base 2 (binary), base 8 (octal) or base 16 (hexadecimal) to a base 10 (decimal) number, you can use the following method:

Write the number in base 2, 8, or 16 and the corresponding base 10 place values.

Multiply each digit by its corresponding place value and add the results.

For example, to convert the base 10 number 11.011 to a base 10 number:

Write the number and the corresponding base 10 place values: 11.011

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

As the number is already in base 10, it does not need to be converted. The value is 11.011

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which effect proves more conclusively that an object is charged, attraction to or rep;usion from antoher object What is the importance of participating in physical activities in your daily life? A fish swims at an altitude of -20. 2 meters. A bird flies at an altitude of 38. 1 meters. Which animal is closer to sea level? What is this simile comparing ? How do you find the difference between two different numbers? Help answer this pls if really appreciate it!! Also if you could explain a little Id appreciate it extra since Im a little lost. Thank you!!! Can one human be diagnosed with all of the following:BPD (Borderline Personality Disorder)DID (Dissociative Identity Disorder)PTSD (Post Traumatic Stress Disorder)AnorexiaOCD (Obsessive Compulsive Disorder)ADHD (Attention Deficit Hyperactivity Disorder)TrichotillomaniaGAD (Generalized Anxiety Disorder)Panic DisorderMDD (Major Depressive Disorder)Body DysmorphiaInsomnia 1/2% in decimalplease give me my answer Also I AM NOT ASKING for 1/2 in decimal I am asking for 1/2 percent in decimal 15 POINTS dont need to explain.a.)b.)c.) Which of the following will configure all the span elements with red (#FF0000) text color? a. span { color: #FF0000;} b. #span { color: #FF0000; } C. span { color:#FF0000; } d. Graph the solution to this inequality on the number line.-4x> 8.4-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 Because a monopolist must lower its price in order to sell another unit of output,a. marginal revenue is less than price.b. long-term economic profits will be zero.c. total revenue increases as price increases.d. average revenue is less than price. The mean of 4 5 6 7 8 Do you multiply grams to moles? What is an example of a progressive tax? An atom of carbon and an atom of element Z together have a mass of 6 amu less than doublethe mass of an atom of oxygen. If an atom of oxygen has a mass of 16 amu and the mass of anatom of carbon is 12 amu, what is the mass of an atom of element Z? SoA scientist collected a 37.50 g sample of acompound. Determine the % compositionof Cr in the compound if the sample ismade up of 19.01g O, Oxygen and 4.76 gC, Carbon, and the remainder is Cr,chromium. Type your answer to twodecimal places. Do not put the percentsign. Who stole the Elgin Marbles? The angle of elevation to the top of a Building in New York is found to be 4 degrees from the ground at adistance of 1.75 miles from the base of the building. Using this information, find the height of the building.Round to the nearest whole number.Your answer isSubmit Questionfeet. With industrialized food production, for every one unit of energy put on the table in the United States, how many units of nonrenewable fossil fuel energy are required to produce it