The area of a poster board is (x2 + 3x − 10) square inches. Find the dimensions of the poster board if x = 16. The dimensions of the poster board are

On the basis of their sides, we may similarly determine the areas of various shapes like rectangles, parallelograms, triangles, and any polygon.

The space that the object occupies is called the area. It is the area that any shape resides in. We only take into account a square's side length when calculating its area. Since a square's area is equal to the square of each of its equal sides, it is a square.

On the basis of their sides, we may similarly determine the areas of various shapes like rectangles, parallelograms, triangles, and any polygon. Based on the radius or the separation of the surface's outer line from the axis for curved surface objects, the area of the surface is determined.

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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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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?

x=-2+3√2/2 and x=-2-3√2/2 are solutions of the quadratic equation 2x²+4x=7.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is 2x²+4x=7

Subtract 7 from both sides of the equation.

2x²+4x-7=0

Use the quadratic formula to find the solutions.

x=-b±√b²-4ac/2a

x=-4±√16-4(2)(-7)/2(2)

x=-4±√16+56/4

x=-4±√16+56/4

x=-2±3√2/2

x=-2+3√2/2 and x=-2-3√2/2

Hence, x=-2+3√2/2 and x=-2-3√2/2 are solutions of the quadratic equation 2x²+4x=7.

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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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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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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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Answer: x = 32/2

Step-by-step explanation:

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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Therefore, square are results multiplying the number by itself whereas square root component of the number.

What is  square root ?

The square root of a number or a root of an equation is the component of the number that results in the original number when multiplied by itself. Exponents are specifically squares and square roots. Consider the number 9. You can write this as or as 3 × 3.

According to the given question:

When you multiply an integer by itself, you get squares.

Alternatively, the square root of an integer is a value that, when multiplied by itself, returns the original value.

This makes both vice-versa approaches.

The square of two is four, for instance, while the square root of four is two.

Therefore , the difference between squaring a number and finding the square root of a number is square are results multiplying the number by itself whereas roots its vice versa.

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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

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

A General Rule for Solving Equations

x= 9, y= 15

-4x +3y= 8 -----(1)

2x +5y=-3-----(2)

(1) ×2:

-8x +6y= 16 -----(3)

(3) -(2):

-4x +6y -(-8x +6y)= 16 -1

-4x +6y +4x -5y= 15

y= 15

Substitute y= 15 into (1):

-4x +3(15)= 8

-4x+45=8

4x+45-8

4x=37

x=37÷4

x=9

b = 2(9) + 5(15)  + 3

b = 13 + 75 + 3 = 91

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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

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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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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The measure of the length AC is 60.

Z = 60

It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

BY = YC = 50/2 = 25

BX = XA = 42/2 = 21

Now,

XY is parallel to AC.

BX/XY = BA/AC

21/30 = 42/AC

1/30 = 2/AC

AC = 60

Z = 60

Thus,

The length of the AC is 60.

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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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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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The slope of a line is the change in the line's y coordinate from its x coordinate.

The shift from the line's y coordinate to its x coordinate is referred to as the slope of a line. The following mathematical formula is used to express the slope of a line:

Slope: y₂-y₁/x₂-x₁

For instance using the coordinate points(0, 0) and (1, 3), respectively, into the formula to obtain:

Slope = 3-0/1-0

Streamline to have:

Slope = 1/3

Slope = 3

As a result, the slope of the line passing the coordinates is 3.

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The time required for the balance of the account to be $6000 is 19.5 years.

The simple interest method, which adds interest to the starting principal amount at the same rate every day, is a quick and easy technique to calculate the interest on that money.

Simple interest is a way to calculate the amount of interest that will be charged on a certain amount of money at a certain rate and for a certain period of time.

As per the information in the question,

Principal amount, p = $3500

Rate, r = 8.75%

End amount = $6000

SI = (p × r × t)/t

6000 = 3500 × 8.75% × t

t = (6000 × 100)/(3500 × 8.75)

t = (600000)/(3500 × 8.75)

t = 19.5 years.

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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 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:

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:

Therefore, the  Uppercase delta (Δ) in calculus denotes the change of variable.

Calculus is a discipline of mathematics that, in its most basic form, deals with rate of change. As an illustration, suppose you wanted to figure out how fast an automobile would slow down as it approached a stop sign. You may determine that change using calculus. Yes, calculus incorporates movement into math.

Here,

Given: Uppercase delta (Δ)

In math, the uppercase letter delta () typically denotes "change" or "the change."

Consider a scenario where the variable x represents an object's motion.

Consequently, "Δx" denotes "the change in movement." This mathematical interpretation of delta is used by scientists in a variety of scientific fields.

Therefore, the  Uppercase delta (Δ) in calculus denotes the change of variable.

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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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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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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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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.