How many non negative integer solutions are there to the equation 2x1 2x2 x3 x4 12?

Answers

Answer 1

There are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

NON NEGATIVE INTEGER SOLUTIONS

The number of non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the number of solutions to the equation x1 + x2 + x3 + x4 = 6, which is the number of ways to place 6 distinguishable balls into 4 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

The equation 2x1 + 2x2 + x3 + x4 = 12 is equivalent to the equation x1 + x2 + (x3/2) + (x4/2) = 6. The variables x1, x2, x3 and x4 are non-negative integers, thus (x3/2) and (x4/2) are also non-negative integers.

The number of solutions to x1 + x2 + (x3/2) + (x4/2) = 6 is equivalent to the number of ways to place 6 distinguishable balls into 3 distinguishable boxes. This is equivalent to the number of ways to choose 3 balls to not place in the first box, which is (6 choose 3) = 20.

Because each of x1 and x2 are integers and (x3/2) and (x4/2) are integers, it ensures x1, x2, x3, and x4 are also integers. Therefore, there are 20 non-negative integer solutions to the equation 2x1 + 2x2 + x3 + x4 = 12.

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Related Questions

Sue downloads music videos on her phone.
The cost of the video downloads (in dollars) is given by the equation c = 2v, where c is the total cost of the videos and v is the number of videos. The constant of proportionality in the equation in terms of cost per video is (1/2, 1, 2, 4) In this example, the constant of proportionality is also the (total price, unit price) of the videos.

Answers

The constant of proportionality in the equation in terms of cost per video is 2.

Option C is the correct answer.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 4 is an equation.

We have,

The cost of the video downloads (in dollars) is given by the equation.

c = 2v

where c is the total cost of the videos and v is the number of videos.

Now,

c = 2v can be written as,

c ∝ v

This means,

2 is the constant of proportionality.

Thus,

The constant of proportionality is 2.

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A street traffic coordinator records data about the number of vehicles with 4 wheels and the number of vehicles with more than 4 wheels that drive over a bridge. Her data is shown.

Answers

The percentage of vehicles that have four wheels are trucks is 30%.

What is Percentage?

Percentage is defined as the parts of a number per fraction of 100. So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Number of trucks that are four wheels = 127 - 76 = 51

Number of trucks that have more than four wheels = 76

Total number of trucks = 127

Number of non trucks that are four wheels = 120

Number of non trucks that have more than four wheels = 18

Total number of non trucks = 138

Total number of four wheels = 51 + 120 = 171

Number of trucks that are four wheels = 51

Percentage of vehicles that have four wheels are trucks = (51 / 171) × 100 = 29.82 ≈ 30%

Hence 30% of the for wheeler vehicles are trucks.

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The complete question is as follows :

A street traffic coordinator records data about the number of vehicles with 4 wheels and the number of vehicles with more than 4 wheels that drive over a bridge. Her data is shown.

Of the 127 trucks that drive over the bridge, 76 have more than 4 wheels. Of the 138 non-trucks that drive over the bridge, 120 have 4 wheels

What percentage of vehicles that have four wheels are trucks? Round your answer to the nearest whole percent.

Over the next 15 months you have to read more than 90 books. You have to read x books per

month. The inequality 15x > 90 represents this situation. Solve the inequality to find the number of

books you have to read per month.

Answers

You have to read at least 6 books per month.

Now, According to the question:

What is an Inequality?

A statement involving the symbols '>', '<', ' ≥', '≤' is called an inequality. For example 5 > 3, x ≤ 4, x + y ≥ 9. (i) Inequalities which do not involve variables are called numerical inequalities. For example 3 < 8, 5 ≥ 2.

Now,

Over the next 15 months you have to read more than 90 books.

The inequality is given as:

The inequality 15x > 90 represents this situation.

Solve the Inequality:

Divide by 15 on both sides:

15x ÷ 15 > 90 ÷ 15

x > 6

Hence, You have to read at least 6 books per month.

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What is 13 1/2 - 5 6/8

Please explain the process.

Answers

Answer: 31/4

Step-by-step explanation:

Convert both into improper fractions:

(13*2+1)/2 - (5*8+6)/8

= 27/2 - 46/8

Simplify 46/8:

27/2 - 23/4

Same denominator:

54/4 - 23/4

= 31/4

which of the following is not always true? if you know the z score, you can determine a percentile by looking at a conversion chart. if you know the z score, you can determine most common standard scores (e.g., t score, diq, sat, nce, etc.). if you know the z score, you can determine the standard deviation of the test.

Answers

The statement that is not always true is C. If you know the z score, you can determine most common standard scores (e.g., T score, DIQ, SAT, NCE, etc.).

How can Z-Score be described?

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

You can calculate the test's standard deviation if you know the z score. If you know the z score, you can use a conversion chart to find the percentile.

Therefore, option C is correct.

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missing options:

a. All of these are true.

b. If you know the z score, you can determine the standard deviation of the test.

c. If you know the z score, you can determine most common standard scores (e.g., T score, DIQ, SAT, NCE, etc.).

d. If you know the z score, you can determine a percentile by looking at a conversion chart.

an acute triangle has a side length of $8,$ and a side length of $15.$ the third side length is also a positive integer. how many different possible values are there for the third side length?

Answers

There are 16 possible values are there for the third side length.

In an acute triangle, the three angles are less than 90°.

The minimum length of the third side is if the other two sides form the lowest possible angle (close to 0 degrees), in which case the length approximates zero, so if the number is an integer, the minimum length of the third side is 1.

The maximum length of the third side is if it is close to the hypotenuse of a right triangle with legs 8 and 15 =>

hypotenuse² = 15² + 8² = 289 => hypotenuse =17. So, the length of the third side must be less than 17.

So, the possible lengths of the third side are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16.

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6.04 Unit Test: Introduction to Functions math

Answers

Relation is a function if it has only One y-value for each x-value.

What is a function?

A relation is a function if it has only One y-value for each x-value.

The domain is the set of all possible inputs of a function, whereas the codomain is the set of its possible outcomes or results.

The range of a function refers to all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.

Hence, relation is a function if it has only One y-value for each x-value.

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Eliminate the parameter in the equations x=cos(t)-5 and y=3sin(t)+6. How can the rectangular equation be described?


1) circle

2) ellipse

3) parabola

4) hyperbola

Answers

Answer:

Eliminate the parameter in the equations x = cos (t) – 5 and y = 3sin (t) + 6. How can the rectangular equation be described? Options: A. Circle B. Ellipse C. Parabola D. Hyperbola 2 See answers Advertisement poojatomarb76 The parameters indicate a circle with a radius of 5 units and a center of (-7,9), using the equation (x + 7)² + (y - 9)² = 5².

Step-by-step explanation:

Can somebody please help? It’s due tomorrow.

Answers

The two sets “ a ” and “ B triangle must have identical items triangle , but this does not require that they be put in the exact order for the groups to be equal.

Describe the triangle.

A triangle is a 2D shape with three vertices, three straight edges, and three straight edges. A main aspect of these shapes is that each type of triangle has three internal angles which thus add near to 180° in these designs. during their math classes about these angles and how to employ this quality to spot missing values.

Here,

Given:

Triangle 1 contains two angles, one measuring 34 degrees and another 48 degrees.

The third angle is therefore 1803448=98.

Triangle 2 has an angle of 34 and another of 48, where an.

To put it another way, the 3rd angle is 18034a=146a14648=98.

Triangles 1 & 2 cannot be compared, according to Jennifer, given the information at hand.

They are comparable when 34,98,48=34,a,146a.

How many degrees will it take for Jennifer's claim to be deemed false? a = to equalize the triangles

Because of this, it's important to understand that while aspects in two sets “ a ” and “ B must match, the sets need not be equal if the elements are listed in the same order.

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solving quadratics by factoring worksheet answer key

Answers

Factorization is a step in the process of locating the roots of a quadratic equation.

Why is quadratic equation by factoring?

Finding the roots of a quadratic equation involves the process of factorization. When factoring quadratic equations, the original quadratic expression is changed into the product of two linear factors.

A quadratic function has the formula f(x) = ax² + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.

Breaking down the factors, or numbers, that multiply to create another number is a frequent mathematics operation known as factoring. Various things affect some figures.

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Roberto is making a rectangular box with measurements as shown below.
5in
3in
3 in

Answers

The volume of the rectangular box is 45 cubic inches  

What is a cuboid?

A cuboid is a three-dimensional geometric shape with 6 rectangular faces, 8 corners, and 12 sides. This is a special type of right angle prism. That is, two pairs of parallel, congruent faces form a rectangle. Opposite faces of a cuboid have the same length, width, and height. A cuboid can be visualized as a box with different dimensions of length, width and height. The length of a cuboid is the distance along the longest side, the width is the distance along the shortest side, and the height is the distance along the side perpendicular to the length and width. The volume of a cuboid can be calculated by multiplying its length, width and height.

length, l= 5 in

width, w= 3 in

height, h = 3 in

Volume = l*w*h= 5*3*3 = 45 cubic inches

The volume of the rectangular box is 45 cubic inches  

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A triangle has two sides with lengths of 8 and 17. Complete the compound inequality to expresses the possible values for the lengths of the third side, x.

Answers

The possible value of third side of triangle c lies between 9 and 25 by the triangle inequality theorem. 9 < c < 25 is correct.

According to triangle inequality theorem that, given two sides length of a triangle, the length of the third side of the triangle must be larger than the difference and smaller than the sum of the two given sides.

for two sides length a and b of a triangle and third side is c,

then according to triangle inequality theorem

(a-b) < c < (a+b)

in the given example we have two sides of triangle are 8 and 17.

let a=17

b=8 and unknown side is c

from triangle inequality theorem

(17-8) < c < (17+8)

9 < c < 25.

thus, the length of third side of triangle lies between 9 to 25.

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Can you help me with this, 30 POINTS!!!

Answers

Answer: domain- 2-7 or 5 and the range is -1-10 0r 11

Step-by-step explanation: depends how your teacher writes it

Answer: domain- 2-7 or 5 and the range is
-1-10 Or 11

Is the distance between two numbers always positive?

Answers

Distance is never a negative. The distance between two values, a, and b, on the same line, is.

What is the distance?

Regardless of direction, an object's total velocity determines its distance.

Distance is the amount of space an object has traveled, regardless of where it began or concluded.

Knowing how far an object is from us allows us to estimate its actual size.

Place the subject always to the left of the lens.

There is a pole in the mirror from which the distances are determined.

Distance is never a bad thing.

Distances that are positive are those that are recorded in the incident ray's direction, and negative distances are those that are recorded in the opposite direction.

Distance is never a negative. On the same line, the separation between two values, a, and b, is.

Therefore, distance is never a negative. The distance between two values, a, and b, on the same line, is.

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Malcolm is trying a very low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:

50 < 2x + 10 and 2x + 10 < 110

Solve for x in this inequality, and explain what the answer represents.

Answers

Malcolm must consume more than 20 grams of carbohydrates but fewer than 50 grams of carbohydrates because x > 20 and x 50.

Find an inequity by what method?

Isolate the variable and place all other constants on the other side of the inequality to solve it. This can be done by manipulating the inequality by doing opposing procedures.

To begin, multiply each side by two to first isolate the x. You must always consider the other side while doing something to one.

Explanation:

The following inequalities

Fill up each inequality.

The inequality is reduced by 10 on each side (1).

Subtract 2 from both sides.

X is greater than twenty.

The inequality is reduced by 10 on each side (2).

Subtract 2 from both sides.

X is not greater than 50 in value.

Malcolm must consume more than 20 grams of carbohydrates but fewer than 50 grams of carbohydrates because x > 20 and x 50.

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Given the area of the field is 5100m²,calculate the cost of fencing the field if the cost of the mesh wire used is RM20 per metre. ​

Help me!!plsss

Answers

The cost of fencing the field if the cost of the mesh wire used is RM 20 per metre is RM 102000.

Area of the field = 5100 m²

Cost of the mesh wire used = RM 20 per metre

To calculate the cost of fencing the field, we need to multiply the area of the field by the cost of the mesh wire used, that is

Cost of fencing the field =  Area of the field × Cost of the mesh wire used

Cost of fencing the field = 5100  × RM 20

Cost of fencing the field = RM 102000

Hence, the cost of fencing the field is RM 102000.

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You buy 1 box of dog food and 2 cans of cat food for $23. Your friend buys 2 boxes of dog food and 1 can of cat food for $22. What is the cost of each box of dog food? of each can of cat food? Please answer this ASAP

Answers

The cost of 1 box of dog food is $ 7 and cost of 1 can of cat food is $ 8  

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

here, we have,

Given data ,

Let the cost of 1 box of dog food be = x

Let the cost of 1 can of cat food be = y

The cost of 1 box of dog food and 2 cans of cat food = $ 23

The cost of 2 boxes of dog food and 1 can of cat food = $ 22

So , the equation will be

1x + 2y = 23   be equation (1)

2x + 1y = 22   be equation (2)

Now , Multiply equation (1) by 2 , we get

2x + 4y = 46   be equation (3)

On Subtracting equation (2) from equation (3) , we get

3y = 24

Divide by 3 on both sides , we get

y = $ 8

Substituting the value of y in equation (1) , we get

x + 2 ( 8 ) = 23

x + 16 = 23

Subtracting 16 on both sides , we get

x = $ 7

Therefore , the value of x is $7 and value of y is $ 8

Hence , the cost of 1 box of dog food is $ 7  and the cost of 1 can of cat food is $ 8  

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Dave has a lawn mowing business. Based on daily sales figures for the past two summers, he has developed
the following probability distribution for X = number of lawns mowed on a randomly selected day.
Number of Lawns .xi
Probability pi
0
0.2
(a) Make a histogram of this probability distribution.
1
0.4
2
0.3
310.
3
0.1

Answers

a) The histogram is given by the image presented at the end of the answer.

b) The probability of at least one lawn is P(X > 0) = 0.8.

c) The probability of at most one lawn is: P(X ≤ 1) = 0.6.

How to obtain the probabilities?

The distribution, giving the probability of each outcome, is presented as follows:

P(X = 0) = 0.2.P(X = 1) = 0.4.P(X = 2) = 0.3.P(X = 3) = 0.1.

The probability of at least one lawn is given as follows:

P(X > 0) = P(X = 1) + P(X = 2) + P(X = 3)

P(X > 0) = 0.4 + 0.3 + 0.1

P(X > 0) = 0.8.

The probability of at most one lawn is obtained as follows:

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X ≤ 1) = 0.2 + 0.4

P(X ≤ 1) = 0.6.

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Please help me with this please

Answers

Step-by-step explanation:

when dividing terms of the same base, we subtract the exponents (when multiplying we add the exponents).

so, it tells us

-55 - a = -43

-a = 12

a = -12

the rule of exponent when the result is the quotient of the numerator to the power and the denominator to the power is_____.

Answers

Answer:4

Step-by-step explanation:

Parallel, Perpendicular or neither y=1/3x+9 x-3y=3

Answers

Answer:

Parallel

Step-by-step explanation:

First ecuation

[tex]y=\frac{1}{3} x+9[/tex]   slope = 1/3

Second equation:

[tex]x-3y=3[/tex]

[tex]-3y=-x+3[/tex]  

[tex]y=\frac{-x+3}{-3}[/tex]

[tex]y=\frac{1}{3} x-1[/tex]  slope = 1/3

Both equations represent parallel lines because they have the same slope

Hope this helps

It is multiple choice.

Answers

The expressions that are equivalent to 25 + 3(a-5) + 7a are:

10a + 10, 5(2a + 2) and 2(5a + 5)

How to determine the equivalent expressions?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

The expression 25 + 3(a-5) + 7a can be written as follow:

25 + 3(a-5) + 7a = 25 + 3a -15 + 7a

                          = 10a + 10

Thus, 10a + 10 is equivalent to 25 + 3(a-5) + 7a

Since 5(2a + 2) =  10a + 10. Thus, 5(2a + 2) is equivalent to  25 + 3(a-5) + 7a

Also, 2(5a + 5) = 10a + 10. Thus, 2(5a + 5) is equivalent to  25 + 3(a-5) + 7a

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A fitness center piloted two new programs to help people reduce stress levels and maintain a healthy lifestyle. After one month, 112 of the 125 people who volunteered for a program in mindfulness reported a reduction in stress levels, and 110 of the 135 people who volunteered for a yoga program reported a reduction in stress levels. The fitness center wants to investigate whether there is a significant difference between the proportions of all people in the two programs who would report reductions in stress levels. Have the conditions for inference been met?

Answers

The conditions for inference have not been fully met based on the information provided.

Independence: It is not specified whether the participants in the mindfulness program and the yoga program were randomly assigned, or whether they were self-selected. Without random assignment, we cannot assume that the two groups are independent, so we cannot make any conclusions about the population from the sample.

Normality: It is also not specified whether the data follows a normal distribution, which is a requirement for many statistical tests.

Sample size: It is not specified whether the sample size is large enough to make valid inferences.

In order to make valid inferences, the fitness center should ensure that the sample was randomly selected, the data is approximately normally distributed, and the sample size is large enough.

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Solve please:
1/5n + 2/3 -2 = n - 2/5

Answers

Answer:

[tex]\boxed{n = 6}[/tex]

Step-by-step explanation:

Given equation is:

[tex]\dfrac{1}{5}n\:+\:\dfrac{2}{3}-2\:=\:n\:-\dfrac{2}{5}[/tex]

First let's get rid of the fractions by multiplying by 15 which is the LCM of 3 and 5 and is simply 3 x 5. The LCM of two prime numbers is the product of the primes

Multiplying throughout by 15:
[tex]15\cdot \dfrac{1}{5}n\:+15 \cdot \:\dfrac{2}{3}- 15\cdot 2\:=\:15\cdot n\:-15\cdot \dfrac{2}{5}[/tex]

==> [tex]3n+10-30 = 15n - 6[/tex]

==> [tex]3n -20 = 15n - 6[/tex]

Move 3n to the right side(subtract 3n from both sides) and move -6 to the left side(same as adding -6 on both sides):

==> [tex]3n - 3n -20 + 6 = 15n - 3n - 6 + 6[/tex]

==> [tex]-14 = 12n\\[/tex]

Divide by 12:

[tex]\implies n = \dfrac{-14}{12} = -\dfrac{7}{6} = -1.16666....[/tex]

Answer:
[tex]\boxed{n = 6}[/tex]

what's the answer to 3-10(-x+2)?

Answers

The expression 3-10(-x+2) is simplified to 10x - 17

What is an arithmetic operator?

An arithmetic operator can simply be defined as a mathematical function which takes two operands and also performs a calculation on them simultaneously.

There are several arithmetic operators, they include;

AdditionSubtractionMultiplicationModulusDivisionFloor divisionExponentiation

From the information given, we have the operation;

3-10(-x+2)

expand the bracket

3 + 10x - 20

Now, collect like terms

10x + 3 - 20

subtract like terms

10x - 17

Hence, the expression is 10x - 17

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What is the place and face value of 7?

Answers

7 is a digit and has no face value.  A number is made up of digits and has a face value, which is the numerical value of a digit in a number. However, 7 is just a digit and has no face value.

7 is a digit and not a number. A number is made up of digits and has a face value, which is the numerical value of a digit in a number. However, 7 is just a digit and has no face value.

7 is a digit and not a number. A number is made up of digits and each digit has a face value, which is the numerical value of a digit in a number. Digits are the building blocks of a number and, without them, a number would not exist. When combining different digits together, the face value of each digit changes based on its position in the number, with the face value of the first digit being the most significant. However, 7 is just a digit on its own and does not have any face value. It is only when 7 is combined with other digits that it takes on a face value, which is determined by its position in the number. Therefore, 7 is a digit and has no face value.

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What is the value of 152 + (−53) + (−15)?

220
190
114
84

Answers

Answer:84

Step-by-step explanation:

the answer to the 152 + (-53) + (-15) is 84

Mr. Morgan earns $42,000 a year as a teacher. The state
income tax rate is 2.6% of taxable income and he has $3,600 in
personal exemptions (not taxable). How much is deducted from
his biweekly paycheck in state taxes?

Answers

Mr. Morgan has to pay a state tax of $ 38.4 in a biweekly basis on his $42000 yearly income.

What is State Income Tax ?

State income taxes are a proportion of your income that you pay to the state government based on how much money you earn from your work, and they vary from state to state.

Tax exemption is the reduction or elimination of a requirement to make a required payment that would otherwise be imposed on individuals, properties, income, or transactions by a ruling power. Tax-exempt status might offer full tax exemption, reduced rates, or tax on only some things.

The more children you have, the more taxes you pay since children are exemptions or deductions on tax forms. Some non-profit organizations are tax-exempt, which means they don't have to pay any taxes. People are also exempt from participating in certain vocations and battles. You are excused if you have an exemption.

Personal Exemption is non taxable = $ 3600

Total income = $ 42000 yearly

Total taxable income = 42000 - 3600 = $ 38400

Total tax yearly = 2.6 % of 38400 = (2.6/100)*38400 = $ 998.4

Total tax generated biweekly is = (998.4/52)*2 = $ 38.4

Mr. Morgan has to pay a state tax of $ 38.4 in a biweekly basis on his $42000 yearly income.

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What is the inverse to
y=log6(2x)

By the way, the 6 is the base of the log
Also, can I have step by step explanation I need this so don't fake answer pls

Answers

Answer:

f-1(x)=x/2

Step-by-step explanation:

y=log6(2x)

interchange x and y

x=log6(2y)

making y the subject in the eqn

x=2y

y=x/2

Answer (my view): If it's an inverse f(-1)(x) = 6^x/2

Explanation: The function is f(x) = log6(2x), an inverse of a function (i. e: f(-1)(x)) can be defined as a function that takes an output of it's main function (i. e: f(x)) as its input and returns the original input plotted in the main function. Any logarithm can be interpreted as an exponentiation, so log6(2x) would be equal to 6^f(x) = 2x, the function f(-1)(x) would take this exponent of 6 returned by the main function and return a half of the base of the function times 1/2, letting this exponent (output of the main function) be x, f(-1)(x) = 6^x/2.

Algebraically, however: f(x) = log6(2x), and f(f^(-1)(x)) = x.

So log6(2(f^(-1)(x))) = x, then 6^x = 2(f^(-1)(x)), (6^x)/2 = (f^(-1)(x)).

A very, very hungry guy goes to a fast food place and orders 2 chicken sandwiches
and 4 tacos, at a total cost of $6.60. Three days later, he's ready to eat again. This
time, he buys 5 chicken sandwiches and 2 tacos, at a total cost of $9.30. Write and
solve a system of linear equations. Identify the cost of one chicken sandwich, and the
price of one taco.

Answers

Answer:Burgers are $1.50 and tacos are $0.90

Step-by-step explanation:Let b denote burgers and t denote tacos. Our equations are then:2b+4t=6.605b+2t=9.30Multiply bottom equation by 2 to get 10b+4t=18.60. Subtract the two equations to get:-8b=-12b=12/8=1.5Plug this back into either equation, I'll use the first one, 2(1.5)+4t=6.60. t=0.90.

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