Write an equation with a variable on both sides of the equal sign that has indefinitely many solutions. Solve the equation and explain why it has an infinite number of solutions

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

Many answers 3x + 2 = 2x + x + 2

combine like terms

3x + 2 = 3x + 2  Subtract 3x from both sides

2 = 2

This means that there are infinite solutions.  Any number that I replace x with will make a true statement.

Lett's say x = 5

3x + 2 = 2x + x + 2

3(5) + 2 = 2(5) + 5 + 2

15 + 2 =  10 + 5 + 2

17 = 17

What if we try 10?

3x + 2 = 2x + x + 2

3(10) + 2 = 2(10) + 10 + 2

30 + 2 = 20 + 10 + 2

32 = 32

When I combine the like terms the left side looks just like the right side.

3x + 2 =  2x + x + 2

3x + 2 = 3x + 2.  Any number that I put in for x will work.

Answer 2
5x + 3 - 4x = 3 + x

Combine like terms on both sides of the equation.
5x + 3 - 4x = 3 + x What to do: (5x + 4x =1x or just x)
x + 3 = 3 + x

Isolate the x term by subtracting x from both sides
x + 3 = 3 + x
-x - x
————————
3=3

Since 3 does, in fact, equal 3, it implies there are an infinite number of solutions to this equation. The solution can be written as indefinite solutions or all real numbers.

Related Questions

Please help me ( and please use the letter so easy for mr to find it, Thank you ^^ )On which number line do the points represent negative five and one over two and +2? (4 points)

a
Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 5th and 6th tick marks to the left of 0. A point labeled T is placed between the 3rd and 4th tick marks to the left of 0.

b
Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 3rd and 4th tick marks to the right of 0. A point labeled T is placed between the 5th and 6th tick marks to the right of 0.

c
Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 2nd tick mark to the left of 0. A point labeled T is placed between the 5th and 6th tick marks to the right of 0.

d
Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed is placed between the 5th and 6th tick marks to the left of 0. A point labeled T is placed on the 2nd tick mark to the right of 0.

Answers

Answer:

Step-by-step explanation:

Need to give more information to solve this problem

There may be more then one answer
Will give brainlest

Answers

Answer:

the 3(2m+1m) and 9m.

Step-by-step explanation:

please help, I don’t know my properties very well. The choices are
associative property of addition
Commutative property of addition
Associative property of multiplication
Commutative property of multiplication

Answers

Answer:

C) Associative property of multiplication

Step-by-step explanation:

Given equation:

- 3x * 2 = 2

The first step:

- 3 * 2x = 2

We see right side is same and changes on the left side, similar to:

(ab)c = a(bc),

where the factors are differently grouped, but it doesn't change the product.

This property is called:

Associative property of multiplication

The matching choice is C

Using trigonometry what is the value of t

Answers

Answer: t≈8.93 units

Step-by-step explanation:

The cosine of an angle (cos) is the ratio of the adjoining leg of a right triangle to the hypotenuse

Hence,

[tex]\displaystyle\\cos56^0 =\frac{5}{t} \\[/tex]

Multiply both parts of the equation by t(t≠0):

[tex]\displaystyle\\cos56^0(t)=\frac{5}{t} (t)\\\\t(cos56^0)=5[/tex]

Divide both parts of the equation by cos56°:

[tex]\displaystyle\\t=\frac{5}{cos56^0} \\\\t\approx\frac{5}{0,56} \\\\t\approx8,93\ units[/tex]

Jenny's school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 6 senior citizen tickets and 4 student tickets for a total of $118. The school took in $258 on the second day by selling 14 senior citizen tickets and 8 student tickets. Find the price of a senior citizen ticket and the price of a student ticket.

Answers

The cost of tickets for senior citizen and students are $11 and $13 respectively.

System of equations

To solve this problem, we have to write out system of equations and solve the value of the unknown.

Let;

x = senior citizen tickety = student tickets.

We can express the problem mathematically as;

[tex]6x + 4y = 118..eq(i)\\14x + 8y = 258 ...eq(ii)[/tex]

Solving for x and y;

[tex]6x + 4y = 118..eq(i)\\14x + 8y = 258 ...eq(ii)\\x = 11, y = 13[/tex]

From the calculations above, the value of x and y are 11 and 13 respectively.

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Change 7/3 from an improper fraction to a mixed number.
7 0/3
2 1/3
3 1/2
2 3/1

Answers

Answer:

Step-by-step explanation:

Here is what the mixed number looks like. [tex]W\frac{R}{D}[/tex]

W- whole numbers (that is the integers)

R- remainder

D- denominator

If you ever want to convert an improper fraction to a mixed number, here are the steps.

Step 1: Use traditional division. How many does 3 goes into 7? 2 times with remainder, R=1 (how many is left over after dividing).

Step 2: Replace the unknowns with D=3

Note: the denominator always stays the same!

[tex]2\frac{1}{3}[/tex]

Graph the function. Find the y-intercept and state the domain and range. y = 4(2x) + 1

Answers

The domain and the range of the function y = 4(2x) + 1 are oo < x < oo and oo < y < oo

How to determine the domain and the range?

The function is given as

y = 4(2x) + 1

Rewrite as a function

f(x) = 4(2x) + 1

Next, we plot the graph of the function (see attachment)

From the graph, we can see that the graph is a linear graph

This means that the function has a domain and a range of all set of real values

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-15 turned into a rational number as a/b

Answers

Answer:

-15/1 is a rational number that gives you the answer. There is other answers such as -45/3 to get -15, but -15/1 is much simpler.

Step-by-step explanation:

-15/1 is a rational number that gives you the answer. There is other answers such as -45/3 to get -15, but -15/1 is much simpler.

The table shows a proportional relationship.


x 15 9 21
y 5 3 7


Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (15, 5).
A line passes through the point (0, 0) and continues through the point (7, 21).
A line passes through the point (0, 0) and continues through the point (5, 15).
A line passes through the point (0, 0) and continues through the point (3, 9).

PLS HELP

Answers

The statement that describes the graph of the proportional relationship is:

"A line passes through the point (0, 0) and continues through the point (15, 5)."

How the proportional relationship would look like?

We have a proportional relationship defined by the following table:

x: 15, 8, 21

y: 5, 3, 7

Remember that a general proportional relationship is given by the formula:

y = k*x

Where k is the constant of proportionality.

If we take x = 0, we always get:

y = k*0

y = 0

So the line always passes through the point (0, 0).

And by using the information on the table, we also know that the line passes through (15, 5), (9,3) and (21, 7).

Then the correct option is:

"A line passes through the point (0, 0) and continues through the point (15, 5)."

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20 POINTS IF U ANSWER ALL PLEASE

Answers

1.The two sides of the triangle that form the right angles. Are always the two shortest lengths given - Legs

2.The sides that's opposite the right angle. The length of this is always greater than the length of either leg.- Hypotenuse.

3. The triangle that contains a right angle(90°) - Right triangle.

4.In a right triangle the sum of the squares of the lengths of the legs equals the square of the lengths of the hypotenuse. - Pythagorean Theorem.

What is a right triangle?

If one of the triangle's angles is 90 degrees, the triangle is said to have right angles.The triangle with a right angle is known as a right triangle because a right angle is 90 degrees. Using the Pythagorean rule, it is simple to understand how the different sides of this triangle relate to one another. The greatest side of a right angle is known as the hypotenuse, and it is opposite the right angle.The right triangle's base, altitude, and hypotenuse are added to determine its perimeter.

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Dalvin is going to invest in an account paying an interest rate of 3.1% compounded annually. How much would Dalvin need to invest, to the nearest dollar, for the value of the account to reach $1,620 in 20 years?

Answers

Answer:

$880

Step-by-step explanation:

[tex]p( {1.031}^{20} ) = 1620[/tex]

[tex]p = \frac{1620}{ {1.031}^{20} } = 879.71[/tex]

To the nearest dollar: $880

PLEASE HELP DUE SOON
(a lot of points)

Answers

Answer:Im not sure, but i think it's 443,17$

Step-by-step explanation:

She worked 37 Hours
37*9,25 (9,25 is the money she got by each hour) = 342,25

The sum of all sales is 3,364$, 3% of that is 100,92


342,25 + 100,92 = 443,17

Find the simple interest and the future value for principal amount $6000, rate 4%, and time 1 year. The simple interest is $The future value is $

Answers

We have the following equation to find the simple interes:

[tex]I=P\cdot n\cdot r[/tex]

where P is the principal amount, r is the rate and n is the time period.

In this case, we have the following:

[tex]\begin{gathered} P=6000 \\ n=4\%=0.04 \\ n=1 \\ \Rightarrow I=6000\cdot0.04\cdot1=240 \\ I=240 \end{gathered}[/tex]

thus, the interest after 1 year is $240.

To find the future value, we can add the interest to the principal amount to get:

[tex]F=6000+240=6240[/tex]

therefore, the future value is $6240

Can you please tell me what to fill in the blank

Answers

Use proportions to find the values that must be in the blanks.

For the first blank, 2 is to 5 as the value is to 10:

[tex]\begin{gathered} \frac{2}{5}=\frac{x}{10} \\ x=\frac{2}{5}\cdot10 \\ x=4 \end{gathered}[/tex]

The first blank must be filled with 4.

For the second blank, 2 is to 5 as 6 is to the value:

[tex]\begin{gathered} \frac{2}{5}=\frac{6}{x} \\ x=6\cdot\frac{5}{2} \\ x=15 \end{gathered}[/tex]

The second blank must be filled with 15.

For the last blank, 2 is to 5 as the value is to 25:

[tex]\begin{gathered} \frac{2}{5}=\frac{x}{25} \\ x=\frac{2}{5}\cdot25 \\ x=10 \end{gathered}[/tex]

The last blank must be filled with 10

find m

how would i solve these? do i use the exterior angle theorem? pls help

Answers

Um maybe try it out then ask for help from the teacher

Maybe ask a teacher that question

5. Every year 3% of university students drop out of their course at
CleverClogs University. This year 12 people dropped out. How
many people started at the beginning of the year?

Answers

Total number of people 400 started at the beginning. To calculate the percentage, divide the value by the total value and multiply the result by 100.

What is meant by Percentage?A percentage is a number or ratio that can be expressed mathematically as a fraction of 100. Divide the number by the whole and multiply by 100 to get the percentage.As a result, the percentage represents a part out of 100. % stands for one hundred percent. The symbol "%" represents it. A percentage is a relative value that represents one-hundredth of a whole. One percent (symbolized 1%) represents one hundredth part; thus, 100 percent

Therefore,

Percentage of students dropped = 3%

Number of people dropped this year= 12

To find Total students = (12/3) * 100 = 400

That is to find how many people dropped is = 400 *(3/100) = 12

so we  can rearrange the  formula .

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Can someone help me on Rate of change

Answers

Answer:

slope is cost per hamburger, $3.00.total cost is $15.50.initial cost is ticket price, $3.50.

Step-by-step explanation:

Given incorrect statements regarding cost relationships involving tickets and hamburgers at a basketball game, you want the corrected versions.

Each given relation involves two elements of the costs in the given situation. The incorrect relation can be resolved two ways: changing one of the elements, or changing the other one.

a. slope = total cost

This can be corrected by identifying what the slope represents:

  The slope represents Arlie's cost per hamburger.

Or, by saying what represents total cost.

  The value of the cost function represents total cost.

b. total cost = $12

This can be corrected by identifying the cost of 4 hamburgers:

  If Arlie buys 4 hamburgers, his cost of hamburgers will be $12.

Or, by saying what the total cost is with 4 hamburgers:

  If Arlie buys 4 hamburgers, his total cost is $15.50.

c. initial cost = price per burger

This can be corrected by identifying Arlie's initial cost at the game:

  Arlie's initial cost at the game is the price of the ticket.

Or, by saying the price per burger:

  Arlie found that $3.00 at the game is the price per burger.

24x - 30 + 45-81x - 320x + 80

Answers

-377x + 95 hope this helps :)

Find the value of m.
28
3
35°
| | (1 d.p.)

Answers

The value of the base in the given triangle is 22.96.

What is a triangle?

Three edges and three vertices make up the three sides of a triangle, which is a three-sided polygon in geometry. The fact that a triangle's internal angles can be added up to equal 180 degrees is its most significant characteristic. Triangle's angle sum property is what this characteristic is known as.

We have given to find m, we will use cosine rule

cos ∅ = base/hypotenuse

Here ∅ = 35°

Base = m

Hypotenuse = 28

lets substitute the values and we get,

⇒ cos 35° = m/28

⇒ m = cos 35°  × 28

⇒ m = 0.82 × 28                   ( cos 35° = 0.82)

⇒ m = 22.96

Thus, the value of the base in the given triangle is 22.96.

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What part of the expression has a quotient: 5.3t-(20/4)+11

Answers

Answer:

(20/4)

Step-by-step explanation:

The term "quotient" implies division, which is present in the (20/4) part of the expression.

Which situations can be represented by an exponential function?

The sales at an auction website double each year.

In a stadium section, each row has 3 more seats than the previous row.

The value of a home increases by 7.5% per year.

Karen increases her running distance by 0.5 km per week.

Answers

The mathematical expression f(x)=exp or ex denotes the exponential function. A function is said to be an exponential function when the value of the function increases/decreases rapidly.

What is exponential function?

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

When the input variable x appears as an exponent in the formula f(x) = ax, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. x can be any real number in the case when a>0 and a=1 are true.

A function is said to be an exponential function when the value of the function increases/decreases rapidly.The situations that can be represented by an exponential function are:An event organizer finds each year's attendance for the past five years is about 4/5 of the previous year's attendance.A toad population is increasing by about 7.5% each year.

The complete question is,

Which situations can be represented by an exponential function? select each correct answer. an event organizer finds each year's attendance for the past five years is about 45 of the previous year's attendance. on the highway, Kareem's car gets 38 mpg. shu fang has $25.75 deducted from her checking account every month. a toad population is increasing by about 7.5% each year?

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how long will it take for them to get the same number of followershow many followers will they have

Answers

Answer:

Explanation:

Let's refer to 1st the handle as A and the 2nd handle

(4.2x10^2) + (2.3x10^4)

Answers

Answer:

23,420

Step-by-step explanation:

10^2=100

4.2×100=420

10^4=10,000

2.3×10,000=23,000

420+23,000=23,420

Square abcd, shown below, contains eleven smaller, un-shaded squares. The side length of each small square is of the side length ofsquare abcd. What percentage of square abcd is 1 5 shaded?

Answers

Answer:%56

Step-by-step explanation:

please my teacher will know its not me writing please make the explanation simple



A rabbit's fur grows at the rate of 5 over 2 inches per month.

How many months will it take the rabbit's fur to grow 15 over 4 inches?

Explain your answer using words, and show your work using division of fractions. (10 points)

Your answer:

Answers

Step-by-step explanation:

can we become friends????

roman spun the spinner 34 times and landed on 4 a total of six times what is romans experimental probability

Answers

Romans experimental probability is 0.176.

What is probability?

Probability simply means the likelihood that something will happen or take place.

In this case, Roman spun the spinner 34 times and landed on 4 a total of six time.

The probability will be:

= Number of occurence / Total available value

= 6 / 34

= 0.176

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Please explain the law of detachment and the law of syllogism.
Please also give 1 example for each law.

Answers

Law of Syllogism

The law of syllogism, also called reasoning by transitivity, is a valid argument form of deductive reasoning that follows a set pattern. It is similar to the transitive property of equality, which reads: if a = b and b = c then, a = c.There are also three parts involved in the law of syllogism, and each of these parts is called a conditional statement. A conditional statement has a hypothesis, which follows after the word if, and it has a conclusion, which follows after the word then. A letter is used to represent each phrase of the conditional statement. Let me introduce the pattern, and then we can look at some examples. Statement 1: If p, then q. Statement 2: If q, then r. Statement 3: If p, then r. Statements 1 and 2 are called the premises of the argument. If they are true, then statement 3 must be the valid conclusion.

Law of Detachment

The law of detachment states that if a conditional statement is true and its antecedent is true, then the consequence must also be true.There are endless examples both in mathematics and beyond of the law of detachment. One example is a coffee shop that gives a free drink to every 25th customer. As a conditional statement, this is “If someone is the 25th customer, then they get a free drink. ”Thus, if you are the 25th customer, you know you will get a free drink. Likewise, if your friend is the 25th customer, you know he will get a free drink.

Sources: https://www.storyofmathematics.com/law-of-detachment/

https://study.com/academy/lesson/law-of-syllogism-in-geometry-definition-examples.html

Refer to the attachment

Please answer the questions in photo ( will mark brainliest )

Answers

Answer: 4 =division 5=multiplication6=subsitution

Step-by-step explanation:

Simple rules

Solve for x.
5x +13
x = [?]
X+23.

Answers

Answer:

5/2

Step-by-step explanation:

Use The image to the right to answer Questions 1 - 4
1. Name two points collinear to point D.
2. Give another name for line p.
3. Name the intersection of line r and plane K.
4. Name a point non-coplanar to plane K.

Answers

Considering the given line and plane, it is found that:

1. Points E and F are colinear to point D.

2. Another name for line p is line AB, as these two points form the line.

3. The intersection of line r and plane K is at point X.

4. One point non-coplanar to plane K is of W.

Item 1

Two points are colinear if they belong to the same line. In the context of this problem, points D, E and F belong to line q, hence points E and F are colinear to point D.

Item 2


Given two points, there is only one line that can pass through these points. Line p in this problem is composed by points A and B, hence the line can also be called line AB.

Item 3

The intersection of a plane and a line is at a single point, and the point of line r that is coplanar to plane K is point X, hence it is the intersection of the line with the plane.

Item 4

A point is coplanar to a plane when the point belongs to the plane. In this problem, points W and Y do not belong to plane K, hence both are non-coplanar to plane K.

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