onsider the system Ax =b, where A = 1 4 3 1 -1
3 9 3 0 9
2 6 2 4 -2
1 3 1 2 -1 b1
b2
B= b3 b4 find all possible values of b so that rank(a) = rank[a| b]. (b) find all possible values of b so that the system ax = b is inconsistent.

A number is a restriction on a rational expression if the number makes the denominator of the rational expression equal to zero.

Hence, option (b) is correct choice.

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.

A rational expression's denominator is undefined when it equals zero, hence it cannot be employed in the expression.

For that particular value of the number, the limitation renders the value of the rational statement undefinable.

To put it another way, the number is a limitation since it cannot be used as the input for the rational expression because the output would be an undefined value.

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The missing option may be:

(a) 1

(b) 0

(c) always positive

(d) Indefinite

The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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Answer:

In a triangle, the sum of the measures of the angles is always 180 degrees. So we can write an equation:

28° + 104° + x = 180°

Simplifying, we get:

x + 132° = 180°

Subtracting 132° from both sides:

x = 48°

Therefore, x is 48 degrees

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

The point (5, 10) has not been translated in the given figure.Hence this statement is false.

The graph shows five points.

A point has been translated right and up.

Now, the statements that are true based on the graph are as follows:

The point (9, D) has been translated right and up.Answer: False

There is no information given about point (9, D).

So, we cannot say anything about the translation of point (9, D).

The point (1, 8) has been translated right and up.Answer: True

As explained above, the point (1, 8) has been translated 7 units to the right and 2 units up to get the new point (8, 10). So, this statement is true.

The point (2, 9) has been translated right and up.Answer: False

The point (2, 9) has not been translated in the given figure.

So, this statement is false.

Statement 4: The point (8, B) has been translated right and up.Answer: True

The point (8, B) has been translated 1 unit up in the given figure. So, this statement is true.

The point (5, 10) has been translated right and up.Answer: False

The point (5, 10) has not been translated in the given figure.

So, this statement is false.

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Using rounding concepts, the rounding of $13.59582 to cents is of $13.60.

To round a number to the nearest cent, we have to look at the third decimal digit.

In this problem, the third digit is of 5, which means that one should be added to the second digit, since the sum results in 0 we add to the first digit, hence the rounding of $13.59582 to cents is of $13.60.

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Answer:

6×4 = 24 m^3

..............................

Answer:

24 units

Step-by-step explanation:

because 6x4=24 units

Answer:

100-x

Step-by-step explanation:

Hope this helps:)

Long division is a method of dividing large numbers by hand. It can be done using several different methods, but the standard algorithm is the most common.

The steps for the standard algorithm are as follows:

1. Begin by writing the dividend (the number to be divided) above the division bar and the divisor (the number that the dividend is being divided by) below the division bar.

2. Divide the leftmost digit of the dividend by the divisor. Write the result of this division to the left of the division bar.

3. Multiply the divisor by the quotient from the previous step, and write the result of this multiplication below the dividend.

4. Subtract the product from the dividend and write the result below the dividend.

5. Bring down the next digit of the dividend to the remainder and repeat steps 2-4 until the remainder is 0.

6. The result of the division is the quotient written to the left of the division bar.

Long division is a method of dividing large numbers by hand.

It involves dividing the leftmost digit of the dividend by the divisor, multiplying the divisor by the quotient, subtracting the product from the dividend, and repeating these steps until the remainder is 0. The result is the quotient written to the left of the division bar.

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The value of Hope's car decreased by 82%. Therefore, the correct answer choices are:

A. Decreased.

A. 82%.

In Mathematics and Statistics, a physical asset such as a car that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:

\(P(t) = I(1 - r)^t\)

Where:

By substituting given parameters, we have the following:

\(A = 19,995(0.82)^t\)

By comparison, we have:

Rate of change per unit interval, r = 0.82 = 82%.

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Answer:

25

Step-by-step explanation:

As per the given 4 x 5 matrix, the reduced row echelon form of A is \(\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right]\)

The term matrix in math refers a set of numbers arranged in rows and columns so as to form a rectangular array.

Here we have the 4 x 5 matrix.

And here we also know that a1,a2,a4 are linearly independent and the value of a3=a1+2a² and a5=2a1-a²+3a⁴.

Now, we have to apply the value of

a1 = 1, a2 = 0, a3 = 0, a4 = 0, a5 = 1, a6 = 0, a7 = 0, a8 = 0, and a9 = 1.

Then we get the matrix of 3 x 3 looks like the following,

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\)

Now, we have to do the following steps in order to get the reduced row echelon form of A,

The first and foremost steps is to take the non-zero number in the first row is the number 1.

Then we have to place any non-zero rows are placed at the bottom of the matrix.

This steps are repeated until the final row becomes zero.

Then we get the resulting matrix as \(\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right]\)

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Answer:

She's wrong because she didn't distribute correctly. She was supposed to multiply 4 and 12, which makes 48.

The proper answer should be 4x+48

To find the monthly difference in median income find the median income of a woman with a bachelor's degree and one without it then subtract. To find the hourly difference find the hour income of women and men with an advanced degree and then subtract.

The median refers to the value that is placed right in the middle of other values. For example, if the values are 5, 9, 4 the median is 9.

This question requires you to:

This quetion requiers you to:

Note: This question is incomplete because there is no information provided about women's income; due to this, I answered based on general knowledge.

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Answer:

the answer is 86

Step-by-step explanation:

i did the assignment on gradpoint

L is the slope 1 and K is the slope 2.

Given,

From the graph:

To find the graphing lines  and slopes

Now, According to the question:

Analysis the graph :

1) we can see that the line L : when level changed by one the vertical changed by one. The change in both directions is the same.

So, The slope is 1 .

The line K has aslope 2: when level changed by one, the vertical changed by two.

2) Slope is 1/3 : It means that when level changed by three, the vertical changed by one .

and, To see the graph.

Hence, L is the slope 1 and K is the slope 2.

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Answer:

LN = 6

Step-by-step explanation:

Since M is on LN, then

LN = LM + MN = 4 + 2 = 6

Answer:

\(\huge \boxed{6}\)

Step-by-step explanation:

Point M is on the line segment LN.

LM = 4

MN = 2

LN = LM + MN

LN = 4 + 2 = 6

Answer:

The slope is negative, and m = -3/5

Step-by-step explanation:

The line is going down, so the slope is negative, and using the slope formula, m = -3/5.

The inverse of (x-A)^c = B, where A = 2x + 1, is x = -(B^(1/c) + 1).

To find the inverse of the expression in (x - A)^c = B, where A = 2x + 1, we can use the following steps:

First, solve for x in terms of A

x = (A - 1) / 2

Substitute the expression for A into the original equation

(x - (2x + 1))^c = B

Simplify

(-x - 1)^c = B

Take the c-th root of both sides

-x - 1 = B^(1/c)

Solve for x

x = -(B^(1/c) + 1)

Therefore, the inverse of the expression in (x - A)^c = B, where A = 2x + 1, is given by

x = -(B^(1/c) + 1)

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--The given question is incomplete, the complete question is given

" Inverse of this in (x-A)^c = (B)

—-

where A = 2X+1 "--

Answer: Slope = -3/4

Step-by-step explanation:

Background information

The given equation [y = -3/4x + 2] is in the form of slope-intercept form of linear equation.

The slope-intercept form of a linear equation is where one side contains just [y]. So, it will look like: y = mx + b where [m] is the slope and [b] is the y-intercept.

Match the given equation with the base form of the equation

y = (-3/4)x + 2

y = m x + b

Finalize the match result

m = -3/4

b = 2

Therefore, the slope of the equation [y = -3/4x + 2] is \(\boxed{-\frac{3}{4} }\)

Hope this helps!! :)

Please let me know if you have any questions

The answers are:

a) it has a absolute maximum/minimum, it does not decrease for x > 0.

b) it does not have a absolute maximum/minimum, it does decrease for x > 0.

c) it does not have a absolute maximum/minimum, it does decrease for x > 0.

One rule we can use to know if there are absolute minimums/maximums is to look at the degree.

If it is even, we can have absolute minimums/maximums, if it is odd, we can't.

So the first option has, and the second and third don't

Now the behavior for x > 0.

The first function is x^2, and it increasese when x increases.

The second function is -5x^3, due to the negative sign, it decreases for positive values of x.

The last function is a linear one; -2x + 2, again, for the negative sign, it decreaess for x > 0.

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Answer:

.22222 or \(\frac{2}{9}\)

Step-by-step explanation:

\(2(\frac{1}{3^{2} })\\\\2(\frac{1}{9})\\\\= .22222 \\\) or  \(\frac{2}{9}\)

The completed statement on the exponential model that fits the data in the question is presented as follows;

The exponential model indicates that the plastic production has a 7.88% growth per year. The model predicts that the production 15 years after 1960 was closest to 30 million metric tons, because the correlation coefficient indicates a strong correlation between the model and the data, this prediction is correct.

The correlation coefficient is an indication of the level at which the variables are interdependent.

The table of values in the question can be entered into a spreadsheet application as follows;

The equation for the trendline obtained from MS Excel is presented as follows; f(x) = 9.2179·e^(0.0788·x)

The growth rate from the above exponential function is 7·88% per year

The production 15 years after 1960 is therefore;

f(15) = 9.2179·e^(0.0788 × 15) ≈30.06

The number of plastic produced 15 years after 1960 is about 30 million metric tons

The correlation coefficient obtained from MS Excel is R² = 0,9157, which indicates a strong correlation between the data and the model

The prediction is correct based on the strong correlation between the year and the number of plastic produced.

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The largest possible side length of the tiles that can be used is `12` inches as it can cover the entire bathroom without any gaps or cutting of tiles.

The largest tile that can be used is a square tile. To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4.

`48/4 = 12`

`60/4 = 15`

The largest possible side length of the tiles that can be used is `12` inches. Jayla's parents are replacing their bathroom floor with square tiles. The floor is a rectangle that is `48` inches by `60` inches. To cover the entire bathroom with no gaps, and without having to cut any of the tiles, they need to use a tile that is the same size as the largest possible tile that can cover the entire floor without any gaps.

To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4. This is because a tile needs to cover 4 sides of the floor without any gaps, so the side length of the tile needs to be equal to the length divided by 4, or the width divided by 4.

In this case, the side length of the largest possible tile is `12` inches. This is because `48/4 = 12`, and `60/4 = 15`. As `15` is larger than `12`, the side length of the largest possible tile is `12` inches. This means that the tiles need to be `12` inches by `12` inches in size to cover the entire bathroom without any gaps.

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The length of the rectangle is \(8x^2y^3\) inches when  the area of the rectangle is \(48x^3y^5\) square inches.

To find the length of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

We are given that the area of the rectangle is \(48x^3y^5\) square inches, and its width is \(6xy^2\) inches. Therefore, we can substitute these values into the formula to get:

\(48x^3y^5 = length * 6xy^2\)

Simplifying this equation, we can cancel out the common factors of 6x and \(y^2\) on both sides to get:

\(8x^2y^3 = length\)

Therefore, the length of the rectangle is \(8x^2y^3\) inches.

To verify our answer, we can substitute the length and width back into the formula for the area of a rectangle and check if it matches the given area:

Area = length x width = \((8x^2y^3) * (6xy^2) = 48x^3y^5\)

Since this matches the given area, we can be confident that our answer is correct. Therefore, the length of the rectangle is \(8x^2y^3\) inches.

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Answer:

26

Step-by-step explanation:

It started with x apples.

8 were given away.

Now there are x - 8 apples.

Two thirds of the remainder is (2/3)(x - 8).

That is equal to 12.

(2/3)(x - 8) = 12

x - 8 = 18

x = 26

There were originally 26 apples.

Answer:

26, if I understood the question correctly.

John has an amount of apples, gave 8 to her friend, and noticed that two thirds of the remainder is a dozen.

Step-by-step explanation:

If 2/3 of the remainder is 12, then we can set this up as an algebraic equation to see what the remainder started with.

x*2/3=12

Now we can see that we need to divide the 2/3 to get the answer for what x is equal to.

\(x=12/(\frac{2}{3} )\)

To divide fractions, you multiply by the reciprocal, (or the fraction upside down)

\(x=12*(\frac{3}{2})\)

When we multiply 12 by 3/2, we get 36/2, and when we reduce, we get 18.

If the entire remainder is 18, then the original total would be 18 plus the 8 that John gave to her friend.

18+8=26

Kind of a strangely worded question, I hope I understood correctly

The confidence interval is from 3.44 to 4.06 minutes.

According to the statement

we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%

and we have to find the mean interval.

So, We know that the

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.

We know that the z value for 90% confidence interval is 1.64.

so, The formula to calculate margin of error is

MOE = Z*standard deviation/ (n)^1/2

put the values in it

MOE = Z*standard deviation/ (n)^1/2

MOE = 1.64*0.5/ (7)^1/2

MOE = 1.64*0.189

MOE = 0.310

And to find the interval the formula is

Confidence interval = sample mean ± margin of error

Confidence interval = 3.75 ± 0.310

Confidence interval = (4.06,3.44)

So, The confidence interval is from 3.44 to 4.06 minutes.

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To determine the differential dy for x=1 and dx=0.15, we need to use the formula for the differential of a function: dy = f'(x) dx, where f'(x) is the derivative of the function with respect to x.

In this case, the function is y=7x^2/(x-2), so we need to find its derivative:

y' = (14x(x-2) - 7x^2)/((x-2)^2)

y' = -14x/(x-2)^2

Now, we can substitute x=1 and dx=0.15 into the formula for the differential:

dy = f'(x) dx

dy = (-14(1))/(1-2)^2 (0.15)

dy = 0.735

Rounded to four decimal places, the differential dy is 0.7350.
Hello! I'd be happy to help you with your question. To determine the differential dy, we will first find the derivative of the given equation, and then plug in the values for x and dx. Here's the step-by-step explanation:

1. Given equation: y = 7x * (2/x - 2)
2. Simplify the equation: y = 14 - 14x
3. Find the derivative (dy/dx) of the simplified equation: dy/dx = -14
4. Given values: x = 1 and dx = 0.15
5. Calculate the differential dy: dy = (dy/dx) * dx = (-14) * (0.15)

dy ≈ -2.1

So, the differential dy is approximately -2.1 when x = 1 and dx = 0.15.

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Answer:

n = 3

Step-by-step explanation:

Starting equation:

2n + 4 = n + 7

Subtract by n on both sides:

n + 4 = 7

Subtract 4 on both sides

n = 3

Check to see if the answer works:

2(3) + 4 = 3 + 7

6 + 4 = 3 + 7

10 = 10

The solution works

n = 3

Answer:

f(x) = 1750 x 0.88^x

It will be worth $629.36 in 2020.

Step-by-step explanation: