Determine when the function is positive, negative, increasing, or decreasing.
Then describe the end behavior of the function.

The rational function is (x + 2)/(x - 3)(x + 2) which has a vertical asymptote at X = 3, and a removable discontinuity at x = -2.

Function

The function is referred as a mathematical expression that defines a relationship between one variable and another variable.

Given,

Here we need to construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2.

Through the given question, we have been given that the rational function that has a vertical asymptote at x = 3, and a removable discontinuity at x = -2.

Here the x = 3 is a vertical asymptote.  

So the one factor in the denominator is (x - 3),

And the discontinuity at x = - 2 can be removed, so the another common factor in the numerator and denominator is x+2.

Therefore, the rational function would be :

f(x)  = (x + 2)/(x - 3)(x + 2)

So, the rational function would be (x + 2)/(x - 3)(x + 2).

To know more about Function here.

https://brainly.com/question/5975436

#SPJ1

Answer:

B. 10

Step-by-step explanation:

[tex]\rm \implies 28 \div 7 + 2 \times 3 \\ \\ \rm \implies 4 + 2 \times 3 \\ \\ \rm \implies 4 + 6 \\ \\ \rm \implies 10[/tex]

Answer:

70

Step-by-step explanation:

If lines l and m are parallel, then using the corresponding angles theorem, the angle that forms a linear pair with angle [tex]x[/tex] is [tex]110^{\circ}[/tex].

This means that [tex]x=70[/tex].

Answer:

The difference is the what the sum of 2+x is

Step-by-step explanation:

suppose x=3 2+3 = 5

the difference between 5 and 2 is 3

Answer:

D

Step-by-step explanation:

supplementary angles sum to 180° , that is

∠ 1 + ∠ 2 = 180°

67° + ∠ 2 = 180° ( subtract 67° from both sides )

∠ 2 = 113°

The value of constant C is 50.

Equations with a maximum degree of one are referred to as linear equations. According to this rule, a variable in a linear equation cannot have an exponent greater than 1.

A linear equation's graph is always depicted as a straight line. There are linear equations for one variable and two variables, respectively.

Given, the linear equation is 12.5x+5y = C

Here, constant C.

Consider one points from given table x = -2 and y = 15,

Putting the value of x and y,

C = 12.5×(-2) + 5×15

   = -25 + 75

   = 50

For point, x = 0 and y = 10,

Putting the value of x and y,

C = 12.5×0 + 5×10

   = 50

For point, x = 2 and y = 5,

Putting the value of x and y,

C = 12.5×2 + 5×5

   = 25 + 25

   = 50

Given, x = 4 and y = 0,

Putting the value of x and y,

C = 12.5×4 + 5×0

   = 50

Therefore, the value of constant C was found to be 50.

To know more about linear equations, visit:

https://brainly.com/question/11897796

#SPJ1

The  total cost for the group of ten people after discount is 10 t - 0.5 t.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Discount = 5%

Total tickets= 10

We have t represents the cost of one ticket.

So, For 10 person the cost of the ticket = 10t

Now, after discount the price of tickets

= 5% of 10t

= 0.5 t

Hence, the total cost for the group of ten people after discount is 10 t - 0.5 t.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ1

The image point of the point (-3, -2) after the transformation r x-axis R 270° is; (3, -2).

It follows from the task content that the image point of the pair of coordinates given is to be determined.

Given point is; (-3, -2).

Hence, after a reflection over the x-axis; we have; (-3, 2).

Also, after a rotation of 270°, it follows that we have; (x, y) ==> (-x, -y).

Therefore, the image point is; (-(-3), -(2)).

The image point is therefore; (3, -2).

Read more on transformations;

https://brainly.com/question/1462871

#SPJ1

Step-by-step explanation:

so there sre 104 postcards .so what we do is 104 ÷ 4 post cards on each page , it will then = to 26 pages

Based on the equation, the minimum number of years an employee would have to stay to make a salary of over $40,000 per year is B. 12 years.

An equation is a mathematical statement that defines that two or more mathematical expressions are equal or equivalent.

Equations show equality using the equation symbol (=).

When one expression is more or less than, or not equal to another expression, it is an inequality.

If S = $33,113 + $600t

Where S = the salary before taxes

t = the time since the date of hire in years.

For S ≥ $40,000:

$33,113 + $600t ≥ $40,000

$600t ≥ $40,000 - $33,113

$600t ≥ $6,887

t ≥ 11.48

t = 12 years

Thus, using the given equation, an employee needs to stay at the work for 12 years to earn more than $40,000 a year.

Learn more about equations at https://brainly.com/question/2972832

#SPJ1

The measure of ∠QTS = 58°

Given; A triangle QPR

PQ = PR

this means that ∠ Q = ∠ R

and QR = QT this means ∠ R = ∠ T

And ST ║ QR

and QT is the transversal

From the above mentioned information we can conclude that

∠QTS = ∠TQR -------------- 1

Thus since ∠ Q = ∠ R  

by using angle sum property of triangle we can conclude that

∠ Q + ∠ R = 116  [ exterior angle sum property ]

2 ∠ Q = 116

∠ Q = 58°

this means ∠ TQR = 58°

And from 1 we know that this angle is equal to angle QTS

Thus ∠QTS = ∠TQR = 58°

To know more about triangle and parallel lines you may visit the link which is mentioned below:

https://brainly.com/question/16701300

#SPJ13

The range of the given function is:

Range: {-9,-3,0,5,7}

We are given ordered pair of set (x,y)

where, first value of ordered pair shows domain of function and second value of ordered pair shows range.

Range: It is output value of function.

Ordered pair: {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}

We can write as:

f(-2)=0,     f(-4)=-3,   f(2)=-9,   f(0)=5,    f(-5)=7

The values of f(x) are the range of function.

We will make a set of second value of all ordered pair of given set.

Range: {-9,-3,0,5,7}

Hence we get the required range of the function.

Learn more about Range here:

brainly.com/question/26098895

#SPJ9

Answer:

-4 is not a solution to the following equation.

Step-by-step explanation:

It you replace x with -4 on both sides of the equation you get -2=-12 and they are not equal to each other. Therefore, -4 is not a solution to the equation.

The required sum of the first twenty terms of the series ∑n=1log 5r are in AP will be 32.37.

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

We have been given that the terms of the series ∑n=1log 5r are in AP.

As per the given question,

∑n(log(5r)) = log(5·1)+log(5·2)+log(5·3)+...+log(5·n)

n = 20

∑log(5r) = log(5·1)+log(5·2)+log(5·3)+...+log(5·20)

Using the property of logarithmic logₐ(xy) = logₐx + logₐy,

∑log(5r) = (log(5)+log(1)) + (log(5)+ log(2))+(10g(5)+Log(3))+ ...(10g(5)+Log(20))

∑log(5r) = (log(5)+log(5)+log(5)+...+log(5)

∑log(5r) = 20·1og(5)+((log(1)+log(2)+log(3)+...+log(20)

Using property of logarithmic logₐ(xy) = logₐx + logₐy,

∑log(Sr)=20·1og(5)+log(1×2×3×...20)

∑log(5r) = 20-log(5)+log(201)

∑log(5r) = 32.365524703598

Rounded to the nearest hundredth decimal,

∑log(5r) = 32.37

Thus, the required sum of the first twenty terms of the series ∑n=1log 5r in AP will be 32.37.

Learn more about the logarithmic properties here:

brainly.com/question/24211708

#SPJ1

130 units should be manufactured to minimize the cost.

Calculation

by using the quadratic formula

[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]

where, a = 0.15, b = -39 and c = 4500

x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]

Hence, 130 units should be manufactured to minimize the cost of fax machines

To learn more about quadratic equations, refer to https://brainly.com/question/1214333

#SPJ1

130 units should be manufactured to minimize the cost.

Calculation

by using the quadratic formula

[tex]x = \frac{-b\sqrt{b^{2}-4ac} }{2a}[/tex]

where, a = 0.15, b = -39 and c = 4500

x= [tex]\frac{-b}{2a} = \frac{39}{0.3} =130[/tex]

Hence, 130 units should be manufactured to minimize the cost of fax machines

To learn more about quadratic equations, refer to https://brainly.com/question/1214333

#SPJ1

Answer:

2nd

Step-by-step explanation:

The future value of the account in 3 years is $15,918.

What is a future value?

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

Here, we have

FV  =C×[ ((1+i)ⁿ −1)/i]

where:

C = cash flow per period

i = interest rate

n = number of payments

By applying the future value formula, we get

= ​$5,000×[ ((1+0.06)³ −1)/0.06 ]

= $5,000×3.1836

= $15,918

​Hence, the future value of the account in 3 years is $15,918.

To learn more about the future value from the given link

https://brainly.com/question/24703884

#SPJ9

The principal is 1900

From the question, we have

after 40 month amount of 2375 is received by 15/2% interest rate

T = 40/12 = 10/3

amount = 2375 = P+I

R = 15/2%

amount = P+I

2375 = P+(PRT)/100

2375 = P(1+(RT)/100)

substituting the value  we get

2375 = P(1+(25)/100)

2375 = P*125/100

P = 2375*100/125

P = 1900

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

To learn more about multiplication visit: https://brainly.com/question/5992872

#SPJ9

The probability of drawing two queens without replacement from ths standard deck is 1/221.

Probability is the likelihood that an event will occur.

In a standard deck of cards, the total number of cards is 52.

There are 4 queens, the probability of drawing the first queen is 4/52.

After the first draw, there'll be 3 queens left and 52 cards. Therefore, the probability will be:

= 4/52 × 3/51

= 1/13 × 1/17

= 1/221

The probability is 1/221.

Learn more about probability on;

brainly.com/question/24756209

#SPJ1

The expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7  is 7+(3-2).8

The commutative property of addition states that a change in the order of the numbers being added does not affect the sum. We can define commutative property of addition as adding the numbers in any order will give the same answer.

a + b = b + a

3(2x8) + 7 = 7 + 3(2x8)

The associative property of multiplication says that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.

a(b x c) = (a x b) c

7 + 3(2x8) = 7 + (3.2)8

Therefore, the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7  is 7+(3-2).8

To learn more about the commutative property refer here

https://brainly.com/question/778086

#SPJ9

Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives

The perimeter of a rectangle, P is given by the formula

P = 2(L + W) ≤ 57 units of wire

width, W = 2 units

length, L = 1 + W

= 1 + 2

= 3

The perimeter of the rectangle is given by

P = 2(L + W)

plugging the values of L and W

P = 2 (3 + 1)

P = 2 (4 )

P = 8 units

Learn more about inequalities here:

https://brainly.com/question/29007832

#SPJ1

The ratio of 6 cups of sugar to pie that Quinn needs to make 12 potato pies will be 6 cups.

Ratio basically compares quantities, that shows value of one quantity with respect to other quantity.

If a and b are two values, there ratio will be a:b.

Given that,

For 3 potato pies required sugar is 3/2,

For 5 potato pies required sugar is 5/2,

for 9 potato pies required sugar is 9/2,

From the given information,

For 1 potato pies required sugar is 1/2

⇒For 12 potato pies required sugar=12×1/2=6

To make 12 potato pies,  required sugar will be 6.

To learn more on Ratio :

https://brainly.com/question/13419413

#SPJ1

The mistakes that Claire made in solving the equation are;

1) She did not use distribution property correctly in step 1 as 2(8) = 16 and not 10.

2)  - (2+5x) should have been simplified to -2 - 5x and not -2 + 5x

3) 10 + 56x = 8x - 2 should have been 12 = -64x and not 12 = 64x

We want to solve the equation 8(2 + 7x) = 3x - (2 + 5x)

Step 1; Expand the bracket on the left hand side and right hand side to get; 16 + 56x = 3x - 2 - 5x

Step 2; Simplify the right hand side to get;

16 + 56x = -2x - 2

Step 3; Rearrange to get;

16 + 2 = -58x

Step 4; Add up the left hand side to get;

18 = -58x

Step 5; Divide both sides by -58 to get;

x = -9/29

Read more about Linear Equations at; https://brainly.com/question/13738662

#SPJ1

Complete question is;

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It

turns out Clare's work has three mistakes!

find all three mistakes explain the below

8(2 + 7x) = 3x - (2+5x)

10 + 56x = 3x - 2 + 5х

10 + 56x = 8x - 2

10 = 64x - 2

12 = 64x

x = 3/16

The derivative of the natural log function y = e^(-1/x^2) is

The given function is

y = e^(-1/x^2)

The given function is rearranged as

y = e^(-1/x^2) = e^u such that u = (-1/x^2)

Applying chain rule

y = e^u

y' with respect to u = e^u

u = (-1/x^2) = -x^(-2)

u' with respect to x = 2x^(-3)

(y' with respect to u) *  (u' with respect to x)

= e^u * 2x^(-3)

plugging in the value of u

=  e^(-1/x^2) * 2x^(-3)

= 2x^(-3)e^(-1/x^2)

Learn more about differentiation here:

https://brainly.com/question/25081524

#SPJ1

Answer: I believe the answer is (-7, 12)

Step-by-step explanation:

Answer:

-7,12

Step-by-step explanation:

Answer: 19.2, 1.7, 15.93, 0.0512

Step-by-step explanation:

We can multiply these straight across but the trick with decimals is that your answer needs to have the same decimal place distance as what you are multiplying. In the first question, we go one decimal place. In the second, we go two decimal places. In the fourth, we go four decimal places.