A rectangle has an area of 45x2 − 42x − 48 and a width of 5x − 8. what is the length of the rectangle? to find the length of the rectangle, use 45x2 − 42x − 48 as the and 5x − 8 as the .

The lengths that represents the side length of a right triangle are 7, 24, 25 and 5, 12, 13.

A right triangle is a triangle that has three sides known as the opposite, adjacent and hypotenuse. The hypotenuse is the longest sides of the triangle. The opposite side is the side that faces an angle. The adjacent side is the third side.

7² + 24² = 25²

5² + 12² = 13²

9² + 16² = 18.4²

16² + 22² = 27.2²

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Answer:

She has 17 turtles

Step-by-step explanation:

You have to divide 102 by 6 which equals 17.

b is a diagonal of a square. Diagonal is just \(a\sqrt{2}\) which means that b is equal to \(7\sqrt{2}\).

To apply the power rule for differentiation to the function f(x, y) = 5x^4y^3 + 3x^2y + 4x + 5y, we differentiate each term with respect to x while treating y as a constant.

The power rule states that if we have a term of the form x^n, where n is a constant, then the derivative with respect to x is given by nx^(n-1).

Let's differentiate each term one by one:

For the term 5x^4y^3, the power rule gives us:

d/dx (5x^4y^3) = 20x^3y^3.

For the term 3x^2y, the power rule gives us:

d/dx (3x^2y) = 6xy.

For the term 4x, the power rule gives us:

d/dx (4x) = 4.

For the term 5y, y is a constant with respect to x, so its derivative is zero.

Putting it all together, we have:

fx(x, y) = 20x^3y^3 + 6xy + 4.

Therefore, the derivative of the function f(x, y) with respect to x is fx(x, y) = 20x^3y^3 + 6xy + 4.

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The best way to select a random sample of students is "Ask every 20th student during lunch in the school cafeteria".

The model approach to picking a random sample of students to gather data on teens' music tastes is to ensure that each student has an equal chance of getting chosen. This is known as random sampling, and it assists in reducing biases and ensuring that the sample is representative of the total population.

Option C, Asking every 20th kid during lunch in the school cafeteria, would be the best decision among the possibilities presented.

By picking every 20th student, a decent amount of randomization is achieved, and each student has an equal chance of being included in the sample.

When compared to the other choices, this technique generates a more representative sample.

Hence, the correct answer is C.

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The exact length of the curve is given by the integral of √(dx/dt)^2 + (dy/dt)^2 from t = 0 to t = 3.

130 words: To find the exact length of the curve defined by x = 6 + 3t^2 and y = 4 + 2t^3, where t ranges from 0 to 3, we can use the formula for arc length. The arc length, denoted as L, is given by the integral of the square root of the sum of the squares of the derivatives of x and y with respect to t, integrated over the range of t.

L = ∫[0 to 3] √((dx/dt)^2 + (dy/dt)^2) dt

First, we find the derivatives:

dx/dt = 6t

dy/dt = 6t^2

Substituting these derivatives into the arc length integral, we have:

L = ∫[0 to 3] √((6t)^2 + (6t^2)^2) dt

L = ∫[0 to 3] √(36t^2 + 36t^4) dt

Simplifying the expression under the square root, we get:

L = ∫[0 to 3] √(36t^2(1 + t^2)) dt

L = ∫[0 to 3] 6t√(1 + t^2) dt

Evaluating this integral will give us the exact length of the curve.

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The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.

The ratio of boy to girl who play kickball at race is 6 to 2

6 boys: 2 girls

Multiply the number of girls by the ratio:

18 girls x (6 boys / 2 girls) = 18 x 3 = 54

Subtract the number of girls from the total to get the number of boys:

54 - 18 = 36

Therefore, there are 12 boys who play kickball at race.

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ANSWER:

STEP-BY-STEP EXPLANATION:

Degrees and radians are two different systems for measuring angles. An angle of 360 ° equals 2π radians; an angle of 180 ° equals π radians.

Therefore the formula is the following:

Answer:

Hey there!

33 is a composite number. It can be broken down to 3 and 11.

Let me know if this helps :)

Answer:

33

Step-by-step explanation:

whenever you divide 13,23,or 43, you get a decimal or fraction. You can divide 33 by 3 or 11.

Answer:

The maximum value for the function on the interval [-2,3] is at x=-1 where the value of the function is 2 (local maximum)

Step-by-step explanation:

When the following equations are solved with elimination method, the values of X and y are as follows:

1.)X= 2; y = 9

2.) X= 2 ; y = 1

3.) X = 38.8; y =-6.7

For question 1;

y = 6x-3

5x = 2y-8

Rewrite each equation in the form Ax + y = C.

3 = 6x-y ---> equation 1

8 = -5x+2y----> equation 2

Multiply the first equation by 2 so that the coefficients of y in each equation will be opposites with a sum of 0.

2(3) = 2(6x-y)

6 = 12x -2y

Add the two equations to eliminate the variable y. Then solve for x.

12x -2y = 6

+ -5x+2y = 8

7x = 14

X = 14/7 = 2

Substitute x into the first equations and solve for y.

y = 6(2) -3

y = 12-3

y = 9.

For question 2;

12x+4y= 28

y = 3x-5

Rewrite each equation in the form Ax + y = C.

28 = 12x+4y

5 = 3x-y

Multiply the second equation by 4 so that the coefficients of y in each equation will be opposites with a sum of 0.

4(5) = 4(3x-y)

20 = 12x- 4y

Add the two equations to eliminate the variable y. Then solve for x.

12x+4y= 28

+ 12x- 4y = 20

24x = 48

X = 48/24 = 2

Substitute x into the first equations and solve for y.

Y = 3(2)-5

y = 6-5 = 1

For question 3;

4x = 2y + 12

4y = 12-x

Rewrite each equation in the form Ax + y = C.

12 = 4x -2y

13 = X + 4y

Multiply the second equation by -4 so that the coefficients of x in each equation will be opposites with a sum of 0.

-4(13) = -4(x+4y)

-52 = -4x-4y

Add the two equations to eliminate the variable x. Then solve for y.

4x -2y = 12

+ -4x-4y = -52

-6Y = 40

y = -40/6 = -6.7

Substitute y into the first equations and solve for X.

4(-6.7) = 12-x

-26.8 = 12-X

X = 12+26.8

X = 38.8

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To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.

To increase usability in a spreadsheet, you can utilize the following techniques:

1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.

2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.

3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.

4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.

5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.

6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.

7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.

By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.

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Answer:

smh 2

Step-by-step explanation:

Answer:

HI

Step-by-step explanation:

u need two answers to give brainliest

Answer:

507

Step-by-step explanation:

Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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Answer:

First option

Third option

Step-by-step explanation:

First simplify the given expression:

6 - x + 2x - 7 + 2x

6 + x - 7 + 2x

-1 + 3x or 3x - 1

Then find the other expressions that are equivalent to that

Answer:17

Step-by-step explanation:my teacher explained how 20 is wrong

Answer:

It is 17 percent.

Step-by-step explanation:

Confirming the other answer is right and just saying it's right for other people who might not trust em. :D

The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers.

The diagram that is best at displaying data dispersion is a box plot. Here's the main answer:When there is a need to compare the distribution of data, a box plot is often the best method.

A box plot is a diagram that shows how a dataset is distributed. It shows how data is spread out and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal (not evenly distributed).

A box plot is a great way to summarize large amounts of data and it is also very easy to read and interpret. It shows a number of statistical values, including the median (the middle value of the data set), the quartiles (the values that divide the data set into four equal parts) and the range (the difference between the maximum and minimum values).

Additionally, it can identify any outliers in the data, which are values that are significantly different from the rest of the data.A box plot is created by drawing a rectangle between the first and third quartiles (the middle 50% of the data) with a line drawn inside it to show the median.

Lines are then drawn from the edges of the rectangle to the minimum and maximum values. Any outliers are marked with a point outside of the rectangle.

The box plot is a great way to compare data sets and to visualize the dispersion of the data

The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal. A box plot is created by drawing a rectangle between the first and third quartiles with a line drawn inside it to show the median.

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Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

The correlation between the time spent waiting at traffic lights and total cycling time was 0.50.

This means that there is a moderate positive correlation between the two variables.

This indicates that as the time spent waiting at traffic lights increases, so does the total cycling time.

Similarly, as the time spent waiting at traffic lights decreases, the total cycling time decreases as well.

The correlation coefficient measures the degree of association between two variables.

The value of the correlation coefficient ranges from -1 to +1.

A correlation coefficient of +1 indicates a perfect positive correlation between the variables.

A correlation coefficient of -1 indicates a perfect negative correlation between the variables.

A correlation coefficient of 0 indicates no correlation between the variables.

In this case, a correlation coefficient of 0.50 indicates a moderate positive correlation between the time spent waiting at traffic lights and total cycling time.

The strength of the correlation indicates that the two variables are related, but not perfectly related.

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For the given op amp circuit with v0 = 0 and upsilons = 3 V, the value of upsilon(t) for t > 0 can be calculated using the concept of virtual ground and voltage divider rule.

In the given circuit, since v0 = 0, the non-inverting input of the op amp is connected to ground, which makes it a virtual ground. Therefore, the inverting input is also at virtual ground potential, i.e., it is also at 0V. This means that the voltage across the 1 kΩ resistor is equal to upsilons, i.e., 3 V. Using the voltage divider rule, we can calculate the voltage across the 2 kΩ resistor as:

upsilon(t) = (2 kΩ/(1 kΩ + 2 kΩ)) * upsilons = (2/3) * 3 V = 2 V

Hence, the value of upsilon(t) for t > 0 is 2 V. The output voltage v0 of the op amp is given by v0 = A*(v+ - v-), where A is the open-loop gain of the op amp, and v+ and v- are the voltages at the non-inverting and inverting inputs, respectively. In this case, since v- is at virtual ground, v0 is also at virtual ground potential, i.e., it is also equal to 0V. Therefore, the output of the op amp does not affect the voltage across the 2 kΩ resistor, and the voltage across it remains constant at 2 V.

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Hence,  when \(n=10\) the given inequality is true.

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

Which integer will make the inequality \(2(n + 2) < 5(n -1)\) true.

So,

\(2(n + 2) < 5(n-1)\)

When

\(n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45\)

Hence,  when \(n=10\) the given inequality is true.

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Polynomial functions and rational functions are both types of functions that are commonly studied in mathematics. However, there are fundamental differences in the graphs of these two types of functions.

A polynomial function is a function of the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where n is a non-negative integer, and the a_i's are coefficients. The graph of a polynomial function is a smooth curve that can have any number of turns, but does not have any breaks or holes.

Polynomial functions can have degree 0 (a constant function), degree 1 (a linear function), degree 2 (a quadratic function), and so on.

On the other hand, a rational function is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are both polynomial functions. The graph of a rational function can have breaks or holes where the denominator is zero. The degree of the numerator and denominator can be the same, but it is not a requirement.

One fundamental difference in the graphs of polynomial functions and rational functions is that polynomial functions have a defined end behavior, while rational functions do not. The end behavior of a polynomial function depends on the degree and leading coefficient of the function. Rational functions, however, can approach vertical asymptotes as x approaches certain values, making the end behavior undefined.

Another difference is that the domain of a polynomial function is all real numbers, while the domain of a rational function excludes any value of x that makes the denominator zero. This means that the domain of a rational function can have "holes" in the graph where the function is undefined.

In summary, polynomial functions and rational functions are both important types of functions in mathematics, but they have fundamental differences in their graphs. Polynomial functions have a smooth curve and defined end behavior, while rational functions can have breaks and holes in the graph and undefined end behavior.

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The text describes various techniques for identifying potential sites for plants or facilities. These techniques include the centroid method, factor-rating systems, linear programming, the transportation method of decision analysis, and regression analysis.

However, the text does not mention one of these techniques as a way to identify potential sites. The technique that is not mentioned in the text is option D, the transportation method of decision analysis. The transportation method is a mathematical technique used to determine the optimal transportation of goods from one location to another. It involves minimizing transportation costs while meeting supply and demand requirements. While this technique can be useful in logistics and supply chain management, it is not typically used to identify potential sites for plants or facilities.

In summary, the techniques mentioned in the text for identifying potential sites are the centroid method, factor-rating systems, linear programming, and regression analysis. The transportation method of decision analysis is not mentioned in the text as a technique for identifying potential sites.

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Given:

Annual earnings = $17,500

Asked: What is the gross amount of her semimonthly paycheck?

Solution:

To find the answer, we need to divide first the annual earnings by 12 to get the monthly paycheck. After that, we will divide it by 2 because we are looking for the semimonthly paycheck.

ANSWER: C. $729.17