Determine the domain of the function h(x)=9x/x(x2-49).

(a) [tex]\frac{x}{x^2 + x + 3}[/tex] will be a continuous function in interval (- ∞ ,  ∞), (b)   [tex]\frac{x + 7}{\sqrt{x} }[/tex] will be a continuous function in interval (0,  ∞), and (c) [tex]x\sqrt{x + 6}[/tex] will be a continuous function in interval [-6,  ∞).

(a)  [tex]\frac{x}{x^2 + x + 3}[/tex]

x² + x + 3 will never be zero.

so it will be a continuous function all the time or in the interval (- ∞ ,  ∞).

(b)  [tex]\frac{x + 7}{\sqrt{x} }[/tex]

in this function x cannot be negative or zero.

so the function will be a continuous function for x >0

or in the interval (0,  ∞)

(c)  [tex]x\sqrt{x + 6}[/tex]

for this function, the value of  (x + 6) cannot be a negative value.

or x + 6 >=0 or x >= -6

so the function will be continuous in the interval [-6,  ∞)

Therefore, (a) [tex]\frac{x}{x^2 + x + 3}[/tex] will be a continuous function in interval (- ∞ ,  ∞), (b)   [tex]\frac{x + 7}{\sqrt{x} }[/tex] will be a continuous function in interval (0,  ∞), and (c) [tex]x\sqrt{x + 6}[/tex] will be a continuous function in interval [-6,  ∞).

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The complete question is:

describe the interval(s) on which the function is continuous. (enter your answer using interval notation.)

(a)  [tex]\frac{x}{x^2 + x + 3}[/tex]

(b)  [tex]\frac{x + 7}{\sqrt{x} }[/tex]

(c)  [tex]x\sqrt{x + 6}[/tex]

Yes, it is possible that you have to travel a greater distance to reach point b than to reach point a.

A straight line is a geometric concept that refers to a line that extends indefinitely in two directions without any curvature. It is the shortest distance between two points in Euclidean space and it is represented by an equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

As both destinations, A and B are measured as the crow flies, or in a straight line, and you are able to travel only in straight lines along the main directions (north, south, east, and west), it is possible that the path to point B includes more turns or obstacles, such as buildings or rivers, that require you to travel further in order to reach the destination.

That's why it is possible that you have to travel a greater distance to reach point B than to reach point A.

Therefore Yes, it is possible that you have to travel a greater distance to reach point b than to reach point a.

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The values of y are 0, 3 and 7/4 respectively. The solution has been obtained by using the substitution method.

What is substitution method?

The substitution approach is one of the algebraic methods for resolving simultaneous linear equations. It entails swapping any variable to change its value from one equation to another. By doing this, two linear equations are merged into one straightforward equation with one variable.

We are given a rule which is that y= x-1/4

Various values of x are given

So, in order to find the values of y, we will use the substitution method.

When x=1/4, then

⇒y=1/4-1/4

⇒y=0

When x=13/4, then

⇒y=13/4-1/4

⇒y=12/4

⇒y=3

When x=2, then

⇒y=2-1/4

⇒y=8/4-1/4

⇒y=7/4

Hence, the values of y are 0, 3 and 7/4 respectively.

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The complete question has been attached below

The difference between the number of expected outcomes and the number of actual outcomes is 1/30.

What is the difference?

The expected outcome of flipping heads and rolling a number less than 3 = probability of flipping a head x probability of rolling a number less than 3

Probability of flipping a head = number of sides that are heads / total number of sides = 1/2

Probability of rolling a number less than 3 = number of sides that are less than 3 / total number of sides = 2/6 = 1/3

The expected outcome = 1/2 x 1/3 = 1 /6

The difference =

[tex]\frac{1}{6} - \frac{2}{15}[/tex]

[tex]\frac{15 - 12}{90}[/tex] = [tex]\frac{3}{90}[/tex] = [tex]\frac{1}{30}[/tex]

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The histogram's smallest and greatest ranges, 0 to 4.9 and 45 to 49.9, respectively, represent the percentage of residents in each state and the District of Columbia who identify as Hispanic or Latino.

The histogram's smallest and greatest ranges, 0 to 4.9 and 45 to 49.9, respectively, represent the percentage of residents in each state and the District of Columbia who identify as Hispanic or Latino.

Percentage refers to quantifying anything per 100, as the word indicates.You can get the percentage, for instance, by dividing your score by 100.

Given: The histogram summarizes the proportion of persons who identify as Hispanic or Latino in each state and the District of Columbia,

The x-axis displays the population's frequency, while the y-axis displays the population's Hispanic or Latino proportion.

Consider the graph to determine the narrowest range possible,

The smallest possible range = 0 - 4.9

Calculate the broadest range feasible while keeping in mind the graph,

The largest possible range = 45 - 49.9

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Answer: x = 3

Step-by-step explanation:

Set the two equal to each other.

-5 (2x+1) = -35

-5 x 2x = -10x , -5 x 1 = -5

-10x -5 = -35

Add 5 to both sides.

-10x = -30

Divide both sides by -10.

x = 3

The charge to play two games is $19 and the charge to play six games is $49.

The question states the expression to calculate the charge. The expression has a variable x, which indicates the number of games. Thus, keeping the value of x in the formula to find the charge.

Calculating a part -

t = 7.5 × 2 + 4

Performing multiplication on Right Hand Side of the equation

t = 15 + 4

Performing addition on Right Hand Side of the equation

t = 19

Thus, the charge to play two games is $19.

Calculating b part -

t = 7.5 × 6 + 4

Performing multiplication on Right Hand Side of the equation

t = 45 + 4

Performing addition on Right Hand Side of the equation

t = 49

Thus, the charge to play six games is $49.

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This triangle is an acute triangle because all three angles measure less than 90 degrees.

It is also a scalene triangle because all three sides have different lengths. I know this because an acute triangle is defined as a triangle where all three angles measure less than 90 degrees and a scalene triangle is defined as a triangle where all three sides have different lengths.

According to the lengths of sides, triangles can be classified into :
Scalene.
Isosceles.
Equilateral.

Different Types of Triangles Based on Angles are :
Acute-angled. Obtuse-angled. Right-angled.

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By substituting the values of A, C, and D, the equation modelling the function is g(x) = 3·sin(x - π/2) - 4.

From the question, we have the following information;

The vertical distance of the sine function = 3 × The parent function

∴ A = 3

Given that the horizontal shift left = π/2 units (from an online source with a similar question)

The vertical shift down = 4 units

The given function g is g(x) = A·sin(x + C) + D

Where,

A is the amplitude = The maximum displacement from the rest or equilibrium position = 3

C is the horizontal shift = -π/2 (The negative sign is for the shifting to the left)

D is the vertical shift = -4 (The negative sign is for a shift in the downward direction)

Therefore, the equation modelling the function is g(x) = 3·sin(x - π/2) - 4.

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

"Enter the correct answer in the box. Function g is the result of these transformations on the parent sine function:

Vertical stretch by a factor of 3.

Horizontal shift left units.

vertical shift down 4 units.

Substitute the values of A, C, and D to complete the equation modelling function g. g(x) = Asin(x + C) + D."--

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Answer: x=6, y=-6

Step-by-step explanation:

-4x + -2y = -12 (a)

4x + 8y = -24 (b)

(a)+(b)= -4x+4x+8y+(-2y)=-12+(-24)

                                 6y= -36

                                   y=-6

put y=-6 into formula (a)

-4x+12=-12

-4x= -24

x=6

The value of the expression or equation is 142

An algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

The algebraic word problem says:

188 fewer than B is 330

Express in equation form to have

B-188 = 330

Making B the subject of the formula

B = 330+188

B=510

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The complete proof of the parallel lines k and l is:

The complete question is added as an attachment

With the given information and the image attached below, we can state that the two lines are parallel

Then go ahead to use the angle theorems and transitive properties to complete the proof

So, the complete proof is:

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Answer:

7/20

Step-by-step explanation:

Answer:

The shaded area is equal to [tex]\frac{7}{20}[/tex]

Step-by-step explanation:

The full circle has a value of 1.

We know that 1/4 and 2/5 of the circle are not shaded and we are asked for the shaded area.

We can use 1-(1/4)-(2/5) to find the shaded area.

1-1/4=3/4

3/4-2/5=15/20-8/20=7/20

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The measure of FD = 16.001 units

Consider following diagram.

We can observe that ΔABE and ΔACD are similar triangles.

By definition of similar triangle the sides of ΔABE and ΔACD must be in proportion.

AB/AC = AE/AD

Let us assume that AB = x

x/(x + 12) = 6/15

15x = 6(x + 12)

15x = 6x + 72

9x = 72

x = 8

So, AB = 8 units

And AC = 12 + 8

       AC = 20 units

Consider right triangle ΔACD

Here, AC = 20, AD = 15

Using Pythagoras theorem,

AC² = AD² + CD²

CD = [tex]\sqrt{AC^2 - AD^2}[/tex]

CD = [tex]\sqrt{20^2 - 15^2}[/tex]

CD = 13.23 units

For right triangle CDF,

Using Pythagoras theorem,

FD² = CD² + CF²

FD² = 13.23² + 9²

FD = 16.001

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The percentage of M.B. A's will have starting salaries of $24,000 to $46,000 is 83.09.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

[tex]$$\begin{aligned}& \mu=\$ 35,000 \\& \sigma=\$ 8,000\end{aligned}$$[/tex]

we need to calculate probability for

[tex]& P(24000 < x < 46,000)\\ \\& =P\left(\frac{24000-35,000}{8,000} < \frac{x-\mu}{\sigma} < \frac{46,000-35,000}{8000}\right)\\ \\& =P(-1.37 < z < 1.315) \\\\& =P(z < 1.37)-P(z < -1.37)[/tex]

[tex]& =0.9147-0.0853[/tex]          [tex]=0.9162-0.0838 \\[/tex]

[tex]& =0.8294[/tex]    [tex]=0.8324 \\[/tex]

[tex]& =82.94 \% \\[/tex]    [tex]& =83.09[/tex]

Therefore, the percentage of M.B. A's will have starting salaries of $24,000 to $46,000 is 83.09.

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When the figure is dilated by a scale factor of 3, the original coordinates of P are (1,2).

A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. The study of algebraic equations on graphs is known as coordinate geometry. Plotting points, lines, and curves on an x and y axis is an example of coordinate geometry. Make corrections.

Here,

scale factor=3

dilated point=(3,6)

original coordinates=(3/3,6/3)

=(1,2)

The original coordinates of P are (1,2) when figure is dilated by a scale factor of 3.

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Solution of the given inequalities based on integer 'n' is given by :

a. Value of 'n' for 15n > 12n + 18 is n > 6.

b. All the possible integer value of 'n' for -2 <n + 3 ≤ 4 are -4, -3, -2, -1, 0.

a. Solution of the expression 15n > 12n + 18 is :

15n > 12n + 18

Subtract 12n from both the sides ,

⇒ 15n - 12n >  12n - 12n + 18

⇒ 3n > 18

Divide by 3 from both the sides,

⇒ 3n/3 > 18 /3

⇒ n > 6

b.  -2 <n + 3 ≤ 4

where 'n' is an integer

⇒ -2 -3 < n + 3 -3 ≤ 4 -3

⇒ -5 < n < 1

All the possible values of 'n' smallest to largest are:

-4, -3, -2, -1, 0.

Therefore, the answer of the questions based on integers 'n' are :

a. 15n > 12n + 18 ⇒ n > 6.

b. All possible integers of 'n' are -4, -3, -2, -1, 0.

The above question is incomplete , the complete question is:

a) Solve 15n > 12n + 18

b) n is an integer and -2 <n + 3 ≤ 4

Write down the possible values of n, from smallest to largest.

All values must be separated by commas. Eg. .... , .... , .....

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Answer:

Step-by-step explanation:

well, it will be 13/20 because you can't simplify our ya

Answer:no answer

Step-by-step explanation:no explanation help

After divide, the value of quotient is 23.4.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ 159.12 divided by 6.8

Now, We can divide the numbers as;

⇒ 159.12 divided by 6.8

⇒ 159.12 ÷ 6.8

⇒ 23.4

Thus, The value of quotient = 23.4

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The formula for a cube's volume is L * W * H.But because it is a cube, its length, breadth, and height are all equal and correspond to one of the cube's edges. The answer is 2.7 equals 3 centimeters.

The formula for a cube's volume is L * W * H.But because it is a cube, its length, breadth, and height are all equal and correspond to one of the cube's edges.Finding the cube root of the volume will allow you to determine the length of a cube's edge.

A cube's edge measures 3 centimeters in length and has a volume of 27 cubic centimeters.

Six square faces make up the three-dimensional shape of a cube.

It has 12 edges and 8 vertices.

Volume of a cube is equal to the length of an edge3

In order to calculate the length of an edge, the cube root of the cube's volume must be known if the cube's volume is given.

Find the cube root of 27 to get the length of an edge.

2.7 equals 3 centimeters

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For the given situation sentence represents amount of the sparkling water bought by Layla is given by :

Option A). Layla bought 20milliliters less sparkling water than 2 liters.

Sparkling water in each pack is equal to 330 milliliters

Number of packs of sparkling water bought by Layla is equal to 6 packs

Amount of sparkling water in 6 packs = 330 milliliters

⇒ Amount of sparkling water in 6 packs = ( 330 × 6 ) milliliters

⇒ Amount of sparkling water in 6 packs = ( 1980 ) milliliters

1 liter = 1000milliliters

⇒ 2 liter = 2000milliliters

1980 is less than 2 liters

Difference between 1980milliliters and 2 liters

2000 - 1980 = 20milliliters

Therefore, sentence which represents the given situation of sparkling water bought by Layla is option A) Sparkling water bought by Layla is 20ml less than 2L.

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Answer:12 feet

Step-by-step explanation:

A constraint is a restriction or limitation on the possible solutions of a problem or system. In the context of a system of inequalities, a constraint is an inequality that must be satisfied by any solution of the system. A system of inequalities is a set of multiple inequalities that must all be satisfied simultaneously. Solving a system of inequalities involves finding the set of all possible solutions that satisfy all of the constraints. This can be done graphically by graphing the inequalities and finding the intersection of their solution sets, or algebraically by isolating the variables and solving for their values.

The length of segment PR is given by the following option:

The angle measure of the altitude is given as follows:

m < RSP = 5x + 40º.

The altitude of the triangle is always going to form a right angle, with measure of 90º, hence the value of x is obtained as follows:

5x + 40 = 90

5x = 50

x = 50/5

x = 10.

The length of segment PR is given as follows:

PR = x - 1.

As the value of x is of x = 10, the numeric length of the segment is given as follows:

PR = 10 - 1

PR = 9.

Meaning that the correct option is given by option C.

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The sum of money that can be divided between two parts = Rs 200

Adding three times the smaller part to half of the larger part then its will always be less than Rs 200

Let The smaller part = Rs S

The larger part = Rs L

The sum of parts = Rs 200

Larger + Smaller = Rs 200

L+S=200---------------(1)

And, Adding three times the smaller part to half of the larger part then the result will always be less than Rs 200

(3S+1/2× L)-200 = 0

3S+ L/2=200                    

6S+L=400 --------(2)

Solving eq 1 and eq 2

(6S+L)-(L+S)=400 - 200

(6S-S )+(L-L )=200

5S+0=200

S = 200/4

∴Smaller = S=Rs40

Now, Plug the value of S into eq 1

L+S = Rs 200

L+40 = Rs 200

L = 200 - 40

L = Rs 160

Larger = L= Rs160

Hence, the larger part is Rs 160 and the smaller part is Rs 40      

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The region is function determining the total sales and the number of boxes covered to make the desired sale. The inequality representing the function is f(b) ≤ 3.75b + 25.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the values and determine whether they are less than or higher than.

a. The region represents the function determining the total sales and the number of boxes covered in order to make the desired sale.

b. The inequality that represents the area under the graph up until the point of intersection is given by:

f(b) ≤ 3.75b + 25

The less than equal to sign is used, as the area used lies below the curve.

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17 people were fans of the Chiefs or Royals but not Sporting KC.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. The basic operations of algebra include addition, subtraction, multiplication, and division, as well as the manipulation of exponents and roots.

Have given ,

26 people were fans of the Kansas City Chiefs

36 people were fans of the Kansas City Royals

18 people were fans of both the Chiefs and the Royals

13 people were fans of the Chiefs and Sporting KC

20 people were fans of the Royals and Sporting KC

6 people were fans of none of the teams

The principle of inclusion and exclusion says that the number of people who are fans of the Chiefs or the Royals but not Sporting KC is:

(26 + 36) - (18 + 13 + 20) + 6 = 62 - 51 + 6 = 17

So, 17 people were fans of the Chiefs or Royals but not Sporting KC.

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An  inequality represents the situation is: t < 3

The correct answer is an option (a) t < 3

We know that an inequality is a mathematical statement that represents the inequalities between two algebraic expressions with two variables .

It is an unequal relation between two algebraic expressions.

The symbols used between the expression:

less than ‘<’,

greater than ‘>’,

less than or equal to ‘≤’

greater than equal to ‘≥’,

Let t represents the distance between Tori's house and the school.

Tori lives less than 3 miles from the school.

This means, the distance t is less than 3 miles

so, we get an inequality t < 3

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A)

House 1 value is an exponential function.

House 2 value is a linear function.

B)

House 1:

f(x) = 253,980 x

House 2:

f(x) = 256,000 + 7000x

C)

House 1 will have the greatest value.

The significant difference in the value of either house after 45 years is $168844

The value of house 1 after 45 years:

f(45) = $739844

The value of the house 2 after 45 years:

f(45) = $571000

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

House 1:

The value of the hours is described by an exponential function.

There is an increase of 2% per year.

f(x) = 253,980 x [tex]1.02^x[/tex]

Where x is the number of years.

House 2:

The value of the hours is described by a linear function.

There is an increase of $7000 per year.

f(x) = 256,000 + 7000x

Where x is the number of years.

Now,

For x = 45,

f(45) = 253,980 x [tex]1.02^x[/tex]

f(45) = 253,980 x [tex]1.02^{45}[/tex]

f(45) = $739843.74

f(45) = $739844 ____(1)

f(x) = 256,000 + 7000x

f(45) = 256,000 + 7000 x 45

f(45) = 256,000 + 315000

f(45) = $571000 ______(2)

From (1) and (2),

House 1 will have the greatest value.

The significant difference in the value of either house after 45 years

= $739844 - $571000

= $168844

The value of house 1 after 45 years:

f(45) = $739844

The value of the house 2 after 45 years:

f(45) = $571000

Thus,

The Part  A, Part B, and Part C are given above.

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The negation of the following statements are a. R: Ron did not go to school. b. S: A triangle does not have 3 sides. c. T: x ≠ 9 d. U: 20 is not a multiple of 3.

It's vital to know the opposite of a particular mathematical statement from time to time in mathematics. This practice is known as "negating" a claim. Remember that if a claim is true, then the negation must be false.

The negation of the following statements is:

a. R: Ron did not go to school.

b. S: A triangle does not have 3 sides.

c. T: x ≠ 9

d. U: 20 is not a multiple of 3.

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