a. what is the area of the window seat when x=3
b. write a polynomial that helps represent the area of the window seats

A graph of the quadratic function g(x) = 2x² - 4x - 16 which shows a parabola with the vertex (1, -18) is shown in the image attached below.

Mathematically, the standard equation of the directrix lines for any parabola is given by this mathematical expression:

x = a(y - k)² + h or y = a(x - h)² + k.

Where:

A quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.

In this scenario, we would use an online graphing calculator to plot the graph of the given quadratic function g(x) = 2x² - 4x - 16 and we can observe that it shows a parabola.

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The slope of the line 4y - 3x = 1 is 3/4.

A line's slope is the ratio of how much y grows as x grows by a certain amount. You may determine a line's slope by looking at how steep it is or how much y grows as x grows. Anywhere along the line, the slope is uniform. In mathematics, measuring steepness is a common goal. It is obvious that slopes B and C are steeper than slope A. They both stand seven units tall, although slope A is only four. Therefore, it would seem that steepness and height are related.

Given

Equation

4y - 3x = 1

3x added to both sides,

4y = 1 + 3x

Dividing by 4,

y = 3/4x + 1/4

Using slope intercept form,

y = mx + b

m = slope

m = 3/4

The slope of the line 4y - 3x = 1 is 3/4.

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There is a limit in Microsoft Excel on the number of rows and columns an Excel file can contain. An Excel file may have upto 256 columns and 65536 rows.

Now, According to the question:

There is a limit in Microsoft Excel on the number of rows and columns an Excel file can contain. An Excel file may have upto 256 columns and 65536 rows.

Excel sheet:-

In Microsoft Excel, a sheet is often called a worksheet. A sheet is a single page that contains its own collection of cells to help you organize your data. There can be many sheets in your Excel document and you can see the sheets listed as tabs along the bottom of your document.

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Therefore, the formula for solving the area of quadrilateral is given by

area of quadrilateral = 1/2(sum of perpendicular drawn from residual two vertices).

What is quadrilateral?

A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. It is made up of four linked non-collinear points. The sum of the internal angles of quadrilaterals is always 360 degrees.

According to the given question:

When the diagonal and the sum of the lengths of the perpendiculars traced from the remaining two vertices are known,

The area of the quadrilateral can be calculated as follows:

Area of quadrilateral = (1/2) diagonal length sum of the lengths of the perpendiculars drawn from the residual two vertices.

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The ratio in which P (1,2) divides AB at (2,1) and (7,4) is 1:6.

Ratio is the term for the proportion between two or more things in terms of number, amount, or size.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.

Given,

Point P → (1, 2)

Point A → (2, 1)

Point B → (7, 4)

Let m1:m2 be the ration

The formula that is used is:

[tex]x=\frac{m1x2+m2x1}{m1+m2} ; y=\frac{m1y2+m2y1}{m1+m2}[/tex]

Now we have been given the Point P → (1, 2), hence x = 1 and y = 2

Also, (x₁, y₁) = (2, 1) and (x₂, y₂) = (7, 4)

[tex]1=\frac{7m1+2m2}{m1+m2} ; 2=\frac{4m1+m2}{m1+m2}[/tex]

m₁ + m₂ = 7m₁ + 2m₂

0=6m1-m2

m2=6m1

1/6=m1/m2

The ratio in which P divides AB is 1:6.

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Pipe will take 21.5 hours to fill tank completely.

A tank can be partially filled in 1 hour = 1/x if it takes x hours to fill it completely.

If the tank must be emptied in y hours, then the portion drained in an hour is equal to 1/y.

If a pipe can fill a tank and drain it in x and y hours, respectively.

When both pipes are opened simultaneously, the tank's net volume is filled in one hour using the formula (xy) / (y-x), provided y>x.

If a pipe can fill a tank and drain it in x and y hours, respectively.

When both pipes are opened simultaneously, the tank's net volume is filled in one hour using the formula (xy) / (x-y), provided x>y.

Net work completed equals the sum of all inlets' work (Sum of work done by Outlets)

Volume of tank be V

Pipe A and Pipe B together fill (1/9)V in one hour.

Pipe A fills (1/15)V in one hour.

Pipe B fills (1/9 - 1/15)V in one hour.

Solving for pipe B, we get

1/9 - 1/15

[tex]=\frac{15-9}{15*9}\\=\frac{6}{15*9}\\=\frac{2}{45}\\[/tex]

So, tank B will take total 21.5 hours to fill tank individually.

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3 to 1 slope means: there are three horizontal units for every one vertical unit.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

That is to say,

"Ratios like 3:1 are used to represent slopes. This indicates that there is a 1 unit (foot or meter) vertical shift, either up or down, for every 3 units (feet or meters) of horizontal distance."

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The complete question is as follows:

How do you do a 3 to 1 slope?

The types of continuity of a function are: pointwise continuity, uniform continuity, absolute continuity, and uniform convergence.

The types of continuity of a function are: pointwise continuity, uniform continuity, absolute continuity, and uniform convergence. Pointwise continuity means that the function is continuous at each point in its domain. Uniform continuity means that the function is continuous over some larger region. Absolute continuity means that the function is continuous over its entire domain. Finally, uniform convergence means that the function converges to a limit value over a range of values. Pointwise continuity is the weakest form of continuity and uniform convergence is the strongest. All of these types of continuity are important for understanding the behavior of functions and their properties.

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The nature of the roots of 2x² 3x 5 0 are imaginary, as it is not possible to solve for real numbers.

To solve this equation, we first factor out the coefficients (2 and 5). Factoring out 2 gives us x² + 1.5x + 5 = 0. After that, we solve for x using the quadratic formula:

x

= -1.5 ± √(-1.5² - 4(1)(5)) / 2(1). This is reduced to x = -1.5 9.5 / 2, an imaginary number that cannot be solved using real values. This indicates that the equation's roots are fictitious.

x

= -1.5 ± √(-1.5² - 4(1)(5)) / 2(1)

x = -1.5 ± √9.5 / 2

x = -1.5 ± √(9.5)i / 2

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To solve a binomial expression, use the FOIL (First, Outer, Inner, Last) method to multiply the two terms together. Then use the distributive property to simplify the expression and combine like terms.

1.Identify the two terms of the binomial expression and write them in the correct order.

2. Use the FOIL method to multiply the two terms together:

the first term of each binomial is multiplied together first.

Outer: Divide the second term of the second binomial by the first term of the first binomial.

Multiplying the first term of the second binomial by the second term of the first binomial yields the inner product.

Lastly, combine the second terms of each binomial.

3. To make the expression simpler, use the distributive property.

4. Combine like terms, if applicable.

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Applying the properties of a parallelogram, the values of x and y are:

y = 81°

The shape given is a parallelogram, therefore:

3x = 2x + 33 [opposite angles]

3x - 2x = 33

x = 33

3x + y = 180 [adjacent angles]

Plug in the value of x

3(33) + y = 180

99 + y = 180

y = 180 - 99

y = 81°

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When 122 is decreased by five times a number, the result is equal to the number increased by 20 so the number is 17 .

Given :

Number :

A number is an arithmetic value used for representing the quantity and used in making calculations.

Let x be the number .

( 122- 5x ) = ( x + 20 )

122 - 5x = x + 20

122 - 6x = 20

122 - 20 = 6x

102 = 6x

divide by 6 on both sides

6x / 6 = 102 / 6

x = 102 / 6

x = 17

Hence the number is 17

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Answer:

6

Step-by-step explanation:

12*8=96

96/3= 3 remainder 6

As per the combination method, the number of ways can the ribbons be awarded is 24,024

The general formula to calculate the combination is written as,

nCr = n!/r! (n - r)!

where n refers the set or population and r refers subset of n or sample set

Here we have given that there are 14 dogs in a particular class at a dog show. blue, red, yellow, and white ribbons will be awarded to the first through fourth place finishers,

Here we need to find the number of different ways can the ribbons be awarded.

While we looking into the given question, the following details are given in it,

Total number of dogs = 14

Number of ribbons = 5

Which means that the value on n = 14 and the value of r = 5.

As per the given question we know that,

There are 14 possibilities for blue one

And then there are 14 - 1 = 13 possibilities for red ribbon.

And for the next yellow one has 12 possibilities

Then the white one has 11 possibilities.

Therefore, the total number of ways is

=> 14 x 13 x 12 x 11

=> 24024

Therefore, option (c) is correct.

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Answer:

C

Step-by-step explanation:

6x + y = - 30

36/6 x + 6/6 y = 24/6

6x + y = -30

6x + y = 4

If this system were graphed, the lines would be parallel, because they have the same slope

As per the concept of numbers, the way of explaining the greater than, less than, and equal to are defined below.

The term number in math is referred to an arithmetic value used for representing the quantity and used in making calculations.

Here we have to know that the greater than sign (>) denotes that the number after the more than sign is smaller than the number before the symbol whereas less than sign (<) denotes that the number after the sign is bigger than the number before the sign.

Similarly, to this definition, the term equal defines the number as being equal to each other or it can be used to assign the value to the variable that has been placed on the left-hand side.

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Answer:

3 1/8 lbs left

Step-by-step explanation:

[tex]5\frac{3}{4} -\frac{1}{8} -2\frac{1}{2}[/tex]

[tex]\frac{23}{4} -\frac{1}{8} -\frac{5}{2}[/tex]

[tex]\frac{46}{8} -\frac{1}{8} -\frac{20}{8}[/tex]

[tex]\frac{46-1-20}{8}[/tex]

[tex]\frac{25}{8}[/tex] lbs

Population parameters are used to estimate sample statistics, and this is true.

Population parameters are used to describe the characteristics of a population, such as the mean, median, and standard deviation, and are used to make inferences about a population. Sample statistics, on the other hand, are used to describe the characteristics of a sample of a population. For example, a sample statistic could be the mean of a sample of people's heights.

To estimate sample statistics, population parameters must first be known. For example, the sample mean can be estimated using the population mean. If the population means are unknown, then the sample means can be estimated using the sample mean.

In conclusion, population parameters are used to estimate sample statistics, and this is true. Population parameters provide useful information about a population that can be used to make inferences about a sample. Knowing the population parameters allows researchers to make more accurate estimates of sample statistics, which in turn can be used to make more reliable inferences about a population.

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Answer: x = 32/2

Step-by-step explanation:

Answer:

It takes 1 hour to drive 80mph at the rate Oliva is going

Step-by-step explanation:

To determine whether there are differences between more than two population variances, utilise anova is True

What is Anova?

A statistical technique called analysis of variance, or ANOVA, divides observed variance data into various components for use in further testing. When there are three or more data groups, a one-way ANOVA is used to find out how the dependent and independent variables are related.

Concept:

One-way ANOVAs are typically used when there are three or more categorical independent groups, although they can also be employed when there are only two groups (but an independent-samples t-test is more commonly used for two groups)

A statistical procedure called Analysis of Variance (ANOVA) is used to examine variations between the means (or averages) of several groups. It is used in a variety of situations to discover whether there are any differences between the means of various groups.

To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilised. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.

The absence of a difference in means is always the null hypothesis in an ANOVA. The alternative or research hypothesis, which is typically expressed in words rather than mathematical symbols, asserts that the means are not all equal. The research hypothesis involves any difference in means, such as when all four means are different from one another, one mean differs from the other three, two means differ, and so on. All scenarios other than the equality of all means described in the null hypothesis are covered by the alternative hypothesis, as it was previously illustrated.

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A statistical procedure called Analysis of Variance (ANOVA) is used to examine variations between the means (or averages) of several groups. It is used in a variety of situations to discover whether there are any differences between the means of various groups.

To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilised. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.

The lines intersect to form a rectangular prism, therefore the plane that is parallel to EFG is BCD. option D

We should know that in plane geometry, parallel lines do not intersect and intersecting lines form angles at the points of intersection.

To determine the similarity of the lines, Let us consider the following lines

From the rectangular prism

EF//AB

BC//FG

GH//CD

AD//EH

Each of the lines lies on opposite side of the rectangular prism.

Also, quadrilateral ABCD ≡ Quadrilateral EFGH

In conclusion, the plane that is parallel to EFG is BCD.

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The prediction is not reasonable and The prediction is an interpolation is correct

How to use a regression calculator to make a reasonable prediction given a data table?

Kardal used the trend line to predict that a man 72 inches tall would wear about a size 10. 5 shoe.

Given data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.

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Answer:

the answer is D i think

The formula in getting possible zeros in rational root theorem is given as ± p / q.

According to rational root theorem if a polynomial expression which is written in descending order of the exponents and has integer coefficients, then any rational zero must be of the form ± p / q

Here, p is a factor of the constant term or the numerator and q is a factor of the leading coefficient or the denominator.

As the name implies, the rational root theorem is used to find the rational solutions to a polynomial equation . Polynomial roots or zeros are the solutions we get when we solve a  polynomial equation. A polynomial does not need required rational zeros only.

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Answer:

x=4      y=-1

Simplify:

100+43y over 3 = 19

Step-by-step explanation:

-3x-8y=20

-5x+y=19

Percent of the daily value for saturated fat provided would be 48%

What is Percent Daily Value?

Daily Values are recommendations that specify the amounts of certain nutrients that the average person should obtain each day. Daily Values are only a general guide because they are calculated for the average person who consumes a total of 2,000 calories a day.

If the total saturated fat for the meal is 95 grams, this is equal to 95,000 milligrams of saturated fat.

To find the percent daily value for saturated fat from this meal, we can use the following formula:

percent daily value = (total saturated fat / recommended daily intake) * 100

= (95,000 / 2000) * 100

= 47.5

Rounded to the nearest whole number, the percent daily value for saturated fat from this meal is approximately 48%

This means that this meal provides approximately 48% of the recommended daily intake of saturated fat.

Hence, Percent of the daily value for saturated fat provided would be 48%

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The length of the arc of the curve from point p to point q is 14.

The length of the arc is calculated by using the differentiation of the curve expression.

Here we have given that expression y = 1/2 x²

And we need to find the length of the arc from the point P to Point Q.

In order to find the length we have to extract the x values from the given point then we get,

(x1, x2) = (-7, 7)

Here we have the curve of the arc as,

=> y = 1/2 x²

Now, we have to differentiate the expression to find the solution,

=> length of arc = ∫₋₇⁷1/2 x²

=> length of arc = 1/2 ∫₋₇⁷ x²

=> length of arc = 1/2 [2x]₋₇⁷

When we apply the values on x, then we get,

=> length of arc = 1/2 [2(7) - 2(-7)]

=> length of arc = 1/2 [28]

Therefore, the length is 14.

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An example of a horizontal asymptote is when the input values of a function f(x) is significantly large or significantly small.

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).

In Mathematics, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values approach negative infinity (-∞) to positive infinity (∞).

For instance, we can determine the horizontal asymptote of this function as follows;

y = 3/x

yx = 3

x = 3/y

x = 3/0

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Answer:

What is the quotient (3x2 + 4x - 15) ÷ (x + 3)? Summary: The quotient of (3x2 + 4x - 15) ÷ (x + 3) is 3x - 5.

Step-by-step explanation: