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Discontinuities are points where the function is undefined. Holes are points where the graph has a break in it. Vertical asymptotes are lines on a graph where the function approaches infinity and horizontal asymptotes are lines on a graph where the function approaches a limit.

The theory used in this question is the theory of rational functions. This theory is used to identify points of discontinuity, holes, vertical asymptotes, and horizontal asymptotes in rational functions.

In the given question,

2. f(x) = x-2/x-4

Points of discontinuity: x = 4

Holes: None

Vertical Asymptote: x = 4

Horizontal Asymptote: None

3. f(x)= 3x-3/x2-1

Points of discontinuity: x = 1

Holes: None

Vertical Asymptote: x = 1

Horizontal Asymptote: y = 0

4. f(x)  = x²+5x+6/x²+6x+9

Points of discontinuity: None

Holes: None

Vertical Asymptote: None

Horizontal Asymptote: y = 1

5. f(x) = (x+3)(x-2)/(x-2)(x+1)

Points of discontinuity: None

Holes: x = -1, x = 2

Vertical Asymptote: x = -1, x = 2

Horizontal Asymptote: y = 1

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Answer:

[tex]\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]2 \frac{5}{8} = \frac{21}{8}[/tex]

Divide [tex]\frac{21}{8}[/tex] by [tex]\frac{3}{4}[/tex]

[tex]\frac{21}{8}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{7}{2}[/tex]

The required simplified value of the given expression is given as 62.96.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression
= 3.04 × 21.5 - 9.12 / 3.8
= 65.36 - 2.4
= 62.96

Thus, the required simplified value of the given expression is given as 62.96.

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Answer: [tex]x=0, -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}[/tex]

The average cost of your item, based on a gross margin of 3%, is $108.20.

The average cost is the cost per unit.

It can be computed as the quotient of the total cost and the number of units.

The gross margin is the percentage difference between the cost of goods sold and the sales revenue.

The gross margin percentage is expressed as a quotient of the sales revenue multiplied by 100.

Selling price = $111.55

Gross margin = 3%

Selling price = 100%

Cost of goods sold = 97% (100 - 3)

Average cost (cost per unit) = Selling Price x Percentage Cost/Selling Price Percentage

$108.20 ($111.55 x 97/100)

Thus, the average cost of the product is $108.20.

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Answer:

Not rounded:

1.62 increased by 8% of the value = 1.7496

The actual change:

1.7496 - 1.62 = 0.1296

Rounded off to max. 2 decimal places:

1.62 increased by 8% of the value ≈ 1.75

The actual change:

1.75 - 1.62 ≈ 0.13

Step-by-step explanation:

'Percent (%)' means 'out of one hundred':

8% = 8 'out of one hundred',

p% is read p 'percent',

p% = p/100 = p ÷ 100

8% = 8/100 = 8 ÷ 100 = 0.08

100% = 100/100 = 100 ÷ 100 = 1

The value of the percentage increase = 8% × 1.62

The new value = 1.62 + The value of the percentage increase

The new value =

1.62 + The value of the percentage increase =

1.62 + (8% × 1.62) =

1.62 + 8% × 1.62 =

(1 + 8%) × 1.62 =

(100% + 8%) × 1.62 =

108% × 1.62 =

108 ÷ 100 × 1.62 =

108 × 1.62 ÷ 100 =

174.96 ÷ 100 =

1.7496 ≈

1.75

The actual change =

The new value - 1.62 =

1.7496 - 1.62 =

0.1296 ≈

0.13

The value of the percentage increase =

8% × 1.62 =

8 ÷ 100 × 1.62 =

8 × 1.62 ÷ 100 =

12.96 ÷ 100 =

0.1296 ≈

0.13

Answer:2200 seats per minute

Step-by-step explanation:

draw a line from 6 minutes upwards till your line and the line on the graph meet then where the line meets draw another line going across(left)

Read across (left side) and the number will be your answer

Answer:

795

Step-by-step explanation:

you mutiply 53 x 15 which gives you 795

Answer:

You have to take the 53 and divide it by 15 which gives you 3.53 repeating so than take 3.53 and multiply by 100 and that gives you 353 minutes as you answer

Step-by-step explanation:

Answer: The unit cost for a pound of sugar is $0.75. This means that for every pound of sugar, it costs $0.75.

Step-by-step explanation:

To find the unit cost for a pound of sugar, we need to divide the total cost of the 4 lb bag of sugar by the weight of the bag.

Unit cost = Total cost / Weight

Total cost = $2.99

Weight = 4 lbs

Unit cost = $2.99 / 4 lbs = $0.75 per pound

So, the unit cost for a pound of sugar is $0.75. This means that for every pound of sugar, it costs $0.75.

It's worth noting that this calculation gives us the unit price of the sugar, which is the price per pound of sugar, and not the unit cost which is the total cost of production divided by the total number of units produced.

It's also worth noting that some sellers may use different units of measurement, and you should always check that you are comparing the same units when comparing prices.

Answer:

The unit cost for a pound of sugar would be $0.75.

To find the unit cost, divide the total cost by the number of pounds: $2.99 / 4 lbs = $0.75/lb.

Step-by-step explanation:

Answer: 157.5

Step-by-step explanation:

The table is not linear.

The probability that people aged between 34 to 65 have a certain disease is 0.95.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, A stem-leaf diagram of people of different ages having a certain disease.

The probability that people have a certain disease between 35 and 64 years of age is,

= P(35 - 44) + P(45 - 54) + P(55 - 64).

= 0.14 = 0.39 + 0.42.

= 0.95.

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Answer:

A is an Irregular Polygon

B is Neither a Polygon

C is an Irregular Polygon

D is a Regular Polygon

E is a Regular Polygon

The equation for Khloe's distance from her car in miles, y, as a function of the time in hours, x, is y = -3x + 11.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.

We have the two points of x and y.

After 1 hour, Khloe is 8 miles from her car.

When x = 1, y = 8

After 3 hours, Khloe is 2 miles from the car.

When x = 3, y = 2

Points of the linear function are (1, 8) and (3, 2)

Slope of the line = (2 - 8) / (3 - 1) = -6/2 = -3

Take a point (1, 8).

Equation of the linear function in point slope form can be written as,

y - 8 = -3(x - 1)

y - 8 = -3x + 3

y = -3x + 3 + 8

y = -3x + 11

Hence the linear function representing the situation is y = -3x + 11.

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Answer:

Step-by-step explanation:

Given the histogram provided, it is not possible to draw a conclusion as it doesn't show any data.

A histogram is a graphical representation of a dataset, showing the frequency of each data point in a specific range. The x-axis shows the range of data points, and the y-axis shows the frequency of each data point. Without the data, it's impossible to draw any conclusion.

In order to draw a conclusion, we need to know the data that the histogram represents, such as the range of temperatures, the frequency of each temperature, and the number of days in the month. Based on that information, we can draw conclusions about the data provided.

The profit from Lube for Store A would be = $8.31.

Unit profit can be obtained by subtracting the cost of the product from the selling price.

Data and calculations:

Selling price for oil change = $275

Percentage of total oil revenue = 39.1%

Cost of oil per gallon = $21.25

Selling price per gallon = $29.56 ($21.25 x $1,391)

Total income = $8.31 ($29.56 - $21.25)

Therefore, the profit from Lube for Shop A would be= $8.31.

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Complete question:

Shop A charges $275.00 for an oil change and has a gross oil profit percent of 39.1% for its total oil gross profit %. Shop B charges $275.00 for an oil change and has a gross oil profit percent of 28.4% for its total oil gross profit %. Both shops pay $21.25 per gallon of oil. What is the Profit per Lube for Shop A?

Answer:

P = 5c + 11 , c = 3

Step-by-step explanation:

(a)

the perimeter P) is the sum of the sides.

Note that the 2 sides with a ' dash' through them are congruent

summing the 4 sides

P = c + 5 + 3c - 2 + 10 - 2c + 3c - 2 ( collect like terms )

  = 5c + 11

(b)

equate the expression for P from (a) to 26

5c + 11 = 26 ( subtract 11 from both sides )

5c = 15 ( divide both sides by 5 )

c = 3

The ordered pair which represents the point of intersection of the system of equations, y = 2x - 5 and y = -2/3x + 3 is: (3, 1).

The solution to a system of equations can be determined by graphing both equations that represent the lines on a coordinate plane. Search for the point where both lines intersect each other.

The point where they intersect each other is the ordered pair that represents the solution of the system of equations.

Given the following system:

y = 2x - 5

y = -2/3x + 3

y = 2x - 5 is the red line in the graph while y = -2/3x + 3 is the blue line.

Both lines intersect at (3, 1). Therefore, the solution to the system is: (3, 1).

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The two triangles below show the property of similarity.

The first property is the Side.

The side PN is similar to the side DG.

The second property his angle.

∠PNK = ∠DGK = 90°

The third property would be side as well.

Side NK is similar to the side GK.

Thus, the two triangles are similar.

Similarity is the mathematical property of triangles, wherein two triangles are called similar if they have either two congruent angles and one similar side, or two similar sides in ratio with one another and a congruent angle.

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The measure of m<1 is 108 degrees from the provided figure.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Lines are therefore one-dimensional objects, even if they can exist in spaces with two, three, or more dimensions.

From the diagram, we have the following parameters

m<2 = 72 degrees

Required parameters

The measure of angle m<1

From the figure, the sum of the interior angle is equivalent to 180 degrees, that is:

m<1 + m<2 = 180

m<1 = 180 - m<2

m<1 = 180 - 72

m<1 = 108 degrees

Hence the measure of m<1 from the given figure is 108 degrees.

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Step-by-step explanation:

[tex]p(x) = 3 {(x + 1)}^{2} - 3[/tex]

Answer:

x∈(-∞,-0.854)⋃(5.854,∞) or x<-0.854 or x>5.854

Step-by-step explanation:

depends on what u want

Answer:

93

Step-by-step explanation:

the mode is the value in the data set that occurs most often.

in this case that is 93 , so

mode = 93

Answer:

93

Step-by-step explanation:

the number which has higher frequency is the mode. here 93 comes 2 times. thus, 93 is the mode.

The expression 8h + (-7.7d) -14 +5d - 3.3h can be simplified as

4.7h - 2.7d - 14

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power (1). In other words, none of the exponents can be greater than 1.

For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

5 is an example of a constant.

8h + (-7.7d) -14 +5d - 3.3h

Taking like terms

8h - 3.3h + 5d - 7.7d - 14

4.7h - 2.7d - 14

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The constant interest rate of the Jordan's investment is 3.8%

The amount in 2017 is calculated to be $578.86

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,   f(x) = a(b)ˣ

the starting, a = 370

the base = ?

the exponents = year periods

the base is calculated below

form 2012 to 2005 is 7 years hence x = 7

amount inn 2012 = amount in 2005 (b)ˣ

480 = 370 * b⁷

48/27 = b⁷

b = 1.038

this is same as 3.8% increment

The amount in 2017

from 2017 to 2005 is 12

= 370 * 1.038¹²

= 578.86

The amount in 2017 is $578.86

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Answer: y = x/4 -7

Step-by-step explanation: hope this is right i was always good at math

Answer:

1 cm - 25 miles

4 cm - 25 x 4 = 100 miles

The required distance is 100 miles.

Answer:

Step-by-step explanation:

Ad and BC because they are 2 lines going in the same place , they are the same

The fraction will change by 200%.

Let the fraction is = x/y.

If its numerator is decreased by 10% then the new numerator is:

x - 10% of x

= x - 0.10x

= 0.90x

If its denominator is decreased by 70% then the new denominator is:

y - 70% of y

= y - 0.70y

= 0.30y

So the new fraction is = .

So the change in fraction is in percentage is:

So the fraction will change by 200%.

Answer:

Just find the LCM of all the days.

LCM of 4,5 and 12 is 60

Therefore, u will have to do all the activities again after 60 days.