In the following diagram HI is parallel JK

If a graph moves arbitrarily near to a line in one direction (without necessarily crossing it), then the line is a(n) asymptote of the graph.

An object that serves as the limit of another line or curve in mathematics. Asymptotic to an axis, or the asymptote of a curve, refers to a falling curve that approaches but does not reach the horizontal axis.

An asymptote is a value that you approach steadily but never quite achieve. An asymptote is a line that a graph skirts but never touches in mathematics. It can be horizontal, vertical, or slanted. A graph that approaches a line but does not cross it is said to be an asymptote.

An asymptote of a curve in analytical geometry is a line along which the angle between the curve and the line decreases when one or both of the x or y coordinates tend to infinity. A line that is tangent to a curve at a point at infinity is said to be the asymptote of the curve in projective geometry and similar contexts.

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The number of units x that produces a maximum revenue is approximately 1890.56 units.

To find the number of units x that produces a maximum revenue R, you need to find the value of x that maximizes the function R = [tex]171x^2 - 0.06x^3.[/tex]

To do this, you can take the derivative of the function with respect to x and set it equal to 0. The derivative of a function gives us the slope of the function at a particular point, so setting the derivative equal to 0 will give us the points where the function is at a relative maximum or minimum.

The derivative of R with respect to x is:

R' = [tex]342x - 0.18x^2[/tex]

To find the value of x that maximizes R, we set R' equal to 0 and solve for x:

[tex]0 =[/tex] [tex]342x - 0.18x^2[/tex]

[tex]0.18x^2 = 342x[/tex]

[tex]x = \frac{342}{0.18}[/tex]

[tex]x = 1890.56[/tex]

Therefore, the number of units x that produces a maximum revenue is approximately 1890.56 units. Keep in mind that this is only a local maximum, and there may be other values of x that produce a higher revenue. To find the absolute maximum or minimum of the function, you would need to examine the behavior of the function over its entire domain.

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The number of seconds will it take the ball to hit the ground will be 2.078 seconds.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.

As per the given,

h(t)=-16t² + 14t + 40

The time when the ball hit the ground h(t) = 0

-16t² + 14t + 40 = 0

-8t² + 7t + 20 = 0

8t² - 7t - 20 = 0

t = (7 ± 26.25)16

t = 2.078 seconds

Since time can never be negative thus, 2.078 seconds will be correct.

Hence "The number of seconds will it take the ball to hit the ground will be 2.078 seconds".

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y=3 is the equation of a horizontal line that passes through the point (9, 3)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If a line passes through a point (x₁, y₁) and has a slope of m, then the

equation of the line is given by (y-y₁) = m(x-x₁).  

Because the question states the line is horizontal, the slope is zero, or m=0.

Plugging the information into the slope equation gives:

(y-(3)) = 0(x-(9)).

y-3= 0

y= 3.

Hence, y=3 is the equation of a horizontal line that passes through the point (9, 3).

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If you have to maintain the same average as in the first quarter of the year, you will have to spend $183 in the month of June.

Given is that your average monthly expenditure for gasoline during the first quarter was $167.70. You spent $147.20 in April and $172.90 in May.

Assume that you can spend $x in the month of June. So, we can write -

(147.2 + 172.9 + x)/3 = 167.7

147.2 + 172.9 + x =503.1

x = 183

Therefore, you can spend $183 in the month of June to have the same average.

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Answer:

B. 123

Step-by-step explanation:

⭐What does "divisible" mean?

Thus, we can find which number is divisible by 3 by dividing each number by 3 and seeing if the remainder is 0.

However, that process may be too long.

You can do it if you'd like, but there's a rule you can use:

⭐"If the sum of the digits is divisible by 3, the number is also."

Let's apply this rule:

A.

76

⇒ 7 + 6

⇒ = 13

13 is NOT divisible by 3. Therefore, 76 is NOT divisible by 3.

B.

123

⇒ 1 + 2 + 3

⇒ = 6

6 IS divisible by 3. Therefore, 123 IS divisible by 3.

C.

457

⇒ 4 + 5 + 7

⇒ = 16

16 is NOT divisible by 3. Therefore, 457 is NOT divisible by 3.

B.

9082

⇒ 9 + 0 + 8 + 2

⇒ = 19

19 is NOT divisible by 3. Therefore, 9082 is NOT divisible by 3.

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As per the volume of cylinder, the value of k is 3.06 centimeters.

Volume of cylinder:

According to geometry, the volume of a cylinder is defined as the capacity of the cylinder, which helps to find the amount of material that the cylinder can hold.

Given,

Here the glass pictured to the left can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.

Here we need to find the value of k, in centimeters.

While we looking into the given question we have identified that the value of the following,

Volume of the glass = 473 cubic centimeter

Height of the glass = 16 fluid ounces.

Radius of the glass = k

Then the value of k is calculated by using the volume of cylinder formula,

=> V = πr²h

Here we have to apply the values on the formula, then we get,

=> 473 = π x k² x 16

Apply the value of π = 3.14,

=> 473 = 3.14 x k² x 16

=> k² = 9.41

=> k = 3.06

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This city's data had the higher median monthly apartment cost of the two cities by $155.

The city of austin's data had the higher interquartile range of the two cities by $87.

The city of austin had the greater variability among monthly apartment costs because the standard deviation was $49.13 more than that of the other set of data.

The given data for the cost of renting a one-bedroom apartment in Dallas in ascending order is as follows;

$994, $1,322, $1,075, $1,189, $1,172, $1,465, $1,215, $930, $1,090, $1,288

$930, $994, $1,075, $1,090, $1,172, $1,189, $1,215, $1,288, $1,322, and $ 1,465

Analyzing the above using Microsoft Excel, we see that;

Dallas Mean = $1180.5

Dallas Interquartile range = $213

Standard Deviation = $159.9597

The given data for the cost of renting a one-bedroom apartment in Austin in ascending order using is;

$900, $950, $1,100, $1,250, $1,296, $1,375, $1,389, $1,400, $1,450, $1,495

Analyzing the above using Microsoft Excel, we see that;

The mean = $1335.5

The interquartile range = $300

The standard deviation of the sample = $209.0945

The difference in the median cost of the two cities is $1,335.5 - $1,180.5 = $155

Therefore, the Austin's city data has the higher median monthly apartment cost of the two cities by $155

The difference in the sample standard deviation of the two cities is $209.0945 - $159.9597 = $49.13476

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Answer:

See below.

Step-by-step explanation:

(a) y=x²-5  NO - the x term is squared.

(b) y=x³     NO - the x term is cubed

(c) y=-9x    YES

(d) y=-x+3  YES

See attached graph.

Answer:

A = NO

B = NO

C = YES

D = YES

Step-by-step explanation:

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables.

For A: The degree of variable y is 1 and the degree of variable x is 2.

So it is not linear.

For C: The degree of variable y is 1 and the degree of variable x is 1.

So it is linear.

Answer:

After Rajesh took 493 stones, you would have 471 stones left.

Step-by-step explanation:

If you started with 964 stones and Rajesh took 493 stones, then you would have 964 - 493 = 471 stones left.

The total area of the two lawns is 30000m²

james mows two lawns

.the first lawn is 1000 meters long and 100 meters wide

Area of a rectangular lawn is calculated by the formula

area = l x w

Where l stands for the length of the lawn and w stands for the width of the lawn

Here, length is 1000m and width is 100m

area = 1000 x 100 = 100000

the second lawn is thee same length, and a width that is 2 times as much as the first one.

Area = l x w

Here Here, length is 1000m and width is 2 x 100m = 200

area = 1000 x 200 = 200000

The total area of the two lawns is equal to summatiom of area of 1st lawn and 2nd lawn

total area = 100000 + 200000 = 30000m²

Therefore,  the total area of the two lawns that is of area of 1st lawn and 2nd lawn is 30000m²

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The lightbulb should be placed at the co-ordinate F(0,1)

The general equation of a parabola is as y²=4ax for a parabola opening towards the positive x-axis.

Here a represents the point on the x-axis where the focal point lies and through which the directrix passes.

For the given question,

Equation of Parabola: x²=4y

Comparing the given equation to standard parabolic equation for parabola on y-axis( x²= 4ay)

Then,  x²=4y: x²=4ay

thus value of a=1

Hence, the focal point of the parabola will be (0,1)

Since the lightbulb is to be placed on the focal point of the parabolic mirror, the lightbulb would be placed at a unit distance away from the vertex of the parabola

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Answer:

49

Step-by-step explanation:

10 weeks = 70 days

0.7 : 1 = x : 70

x = 0.7 * 70

x = 49

To be able to make predictions for future outcomes based on present data, a statistical technique called regression analysis is used .
It helps in developing prediction models.
Regression analysis is basically a tool to show a relationship between two or more variables.  Usually expressed in a graph, the method tests the relationship between a dependent variable against independent variables.

It is a quantative method wherein the basic form of regression models includes unknown parameters (β), independent variables (X), and the dependent variable (Y). Regression allows researchers to predict or explain the variation in one variable (called the dependent variable) based on another variable( known as the independent variable).
The most common and simple form of regression is the Linear Regression model.
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If the expression AXB is defined, and A is a 3X5 matrix, then the dimension of B could be 5XN.

“N” could be the any number as in order to do any multiplication, the number of columns of first matrix and the number of rows of second matrix should be same in order to perform the multiplication between those matrices.

A matrix is a collection of integers that are organized in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. If the matrix has m rows and n columns, it is referred to as a "m by n" matrix, abbreviated "mXn."

A matrix A multiplied by a matrix B yields a matrix C only when the number of columns in the first matrix A equals the number of rows in the second matrix B. To find the element cij, which is in the product's ith row and jth column, multiply the first element in the ith row of A by the first element in the jth column of B, the second element in the row by the second element in the column, and so on until the last element in the row is multiplied by the last element in the column; the sum of all these products yields the element cij.

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For the given polynomial 5a²b-13ab+7a³-4b, the descending order is 7a³+5a²b-13ab-4b.

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Polynomials are introduced. This video defines words such as degree, standard form, monomial, binomial, and trinomial. A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division (No division operation by a variable).

Here,

The given polynomial is,

=5a²b-13ab+7a³-4b

The descending order,

=7a³+5a²b-13ab-4b

The descending order of polynomial is 7a³+5a²b-13ab-4b for the given polynomial 5a²b-13ab+7a³-4b.

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Answer:

$7800

Step-by-step explanation:

1 year = 10%

3 years = 30%

30% = 0.3

6000 times 0.3 = $1800

6000 + 1800 = $7800

So, they will pay $7800

The work required to stretch the spring is 91.6 Ibs-inch

What is work?

Work is defined as force applied across a distance. Work examples include pushing an object against gravity, driving a car up a hill, and lowering a captive helium balloon. Work is the mechanical expression of energy.

Δx : displacement from equilibrium position

f = k Δ x (force due to spring = -kΔx)

where, k is the spring constant

Given,

f = 20ibs

Δx = 24 -18 Inches = 6 inches

∴ k = 20/6 ibs/inch

Now, PE stored in spring = 1/2 k (Δx)²

Δx : displacement from equilibrium position

Work done = change in PE

= 1/2K (Δx₂)² -1/2k (Δx₁)²

given,

Δx₁ = 21-18 inches = 3 inches

Δx₂ = 26-18 inches = 8 inches

∴work done = 1/2 * 20/6 (8² - 3²)Ibs-inches

=10/6 *5*11

work done = 91.6 ibs-inch

The spring must be stretched with 91.6 Ibs-inch of force.

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The amount of candle burn after 6 hours is 4.95 inches.

What is the total amount?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total.

Here, we have

Given that the 9-inch candle burns in 6 hours.

We know that we first have to calculate how 1 hour how much candles will burn.

Candle burn in 1 hour is :

= 9 / 10

= 0.9 inch

Now,

To find out how far the candle burnt after 6 hours we need to multiply the part of the candle burned by one hour by 11/2 hours.

= 11/2 × 0.9

= 4.95 inches

Hence, the amount of candle burn after 6 hours is 4.95 inches.

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Answer:

A D F

Step-by-step explanation:

The parent functions with a domain of all real values of x are the linear function, the absolute value function, the square root function, and the cube root function.

The linear function is defined by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The domain of this function is all real values of x.

The absolute value function is defined by the equation y = |x|, where |x| is the absolute value of x. The domain of this function is all real values of x.

The square root function is defined by the equation y = √x, where √x is the square root of x. The domain of this function is all nonnegative real values of x.

The cube root function is defined by the equation y = ∛x, where ∛x is the cube root of x. The domain of this function is all nonnegative real values of x.

Therefore, the correct answers are A, D, and F. The reciprocal function, the cubic function, and the quadratic function do not have a domain of all real values of x.

Answer:

153

Step-by-step explanation:

165/3 = 55 sheet of each color

55-4 = 51

51 x 3 = 153

The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.

On data that is dispersed normally, the Z test is a parametric process that is applied. The z-test can be applied to proportions, two samples, or one sample to test hypotheses. When the population variance is known, it is possible to determine whether the means of two significant groups differ.

The second is one-way analysis of variance (ANOVA), which checks if three or more samples originate from populations with the same mean using the F-distribution.

The test statistic should be compared to the crucial value. If the test statistic is more extreme in favor of the alternative than the crucial value, the alternative hypothesis should be considered instead of the null hypothesis. If the test statistic is not as extreme as the crucial value, the null hypothesis should not be disregarded.

Therefore,

The test statistics for one-way Anova follows, the comparing of the T Statistic with the T critical value.

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The scale factor required for the dilation of the living room is 1/3.

A scale factor is a multiplicative fraction that can be used to either increase or decrease (i.e resize) the shape of a given object. It is given by the expression:

scale factor = [tex]\frac{length on the drawing}{length of the original object}[/tex]

Dilation is type of transformation that can be used to resize the dimensions of a given object. So that an image of the object is formed.

Therefore, the required scale factor is;

scale factor = [tex]\frac{length on the drawing}{length of the original object}[/tex]

                   = 7/21 or 9/27

                   = 1/3

scale factor = 1/3

The scale factor of the dilation as required in the question is 1/3.

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The rationalized expression would be [tex]\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex].

What is a rationalized expression?

A rationalized expression is an expression that has been written in a simplified form which eliminates any radicals (square roots, cube roots, etc.) from the denominator. The denominator is made a rational number, meaning it can be expressed as a fraction with an integer numerator and denominator. This is done by multiplying both the numerator and the denominator by the radical of the denominator. This process is called rationalization.

The given expression is

                          [tex]=\frac{\sqrt{9}}{\sqrt{3}+ \sqrt{x} } \\\\=\frac{\sqrt{9} }{\sqrt{3} }+ \frac{\sqrt{9} }{\sqrt{x}}\\\\=\frac{3 }{\sqrt{3} }+\frac{\sqrt{9} }{\sqrt{x}}\\\\=\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex]

Hence, the rationalized expression would be [tex]\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex].

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The amount of flour that the cake recipe call for would be equal to 3.5 cups.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

Let's write the equation according to the statement,

x = 7 × 1/2

x = 3.5 cups or,

x = 3 & 1/2 cups.

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q = 40 is the value of q in quadratic equation.

What is quadratic equation explain?

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

                    The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial equation. The answer could be simple or complicated.

the roots of a quadratic expression

             ax² + bx + c = 0

Since x' and x'' are the roots of this equation, then we can write the Vieta's formula

                 x' + x'' = -b/a

               x' * x'' = c/a

let's replace the 2nd equation of the Vieta's formula by that and make it a Linear System.

                  x' + x'' =  14/1

                 x' * x'' = 6

after solve the equations

               x' = 10

Solving the  equations

       10 + x''=14

           x'' = 4

Since we have a=1

   x^2-14x + q = 0

      Then we can make q as the parameter c.

    q = x' * x'' = 4 * 10 ⇒ 40      

x2−14x+ 40 = 0

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The complete question is -

The difference between the roots of the quadratic equation x2−14x+q=0 is 6. Find q.