Identify the excluded values of the rational expression x^2+x/x^2-x-2

Answer:

Step-by-step explanation:

(0, -9) and (3,3)

(3+9)/(3-0) = 12/3 = 4

y + 9 = 4(x - 0)

y + 9 = 4x - 0

y = 4x - 9

The point p(x, y) lies on the terminal side of an angle theta = startfraction 3 pi over 4 endfraction in standard position. Then x values are negative and the y values are positive.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. When the two rays are creating an exact 180-degree angle, an angle is considered to be straight. It gets its name from the fact that two lines at an angle of 180 degrees resemble one single straight line. Angles, whose measure is always non-negative, have some standard language.

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Answer:

55 degrees is the measure of the unknown angle

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Answer:

no property

Step-by-step explanation:

Name the property used: no property

In 39,916,800 different strings can be made from the letters in abracadabra, using all the letters.

To find the number of different strings that can be made from the letters in abracadabra, using all the letters, we need to use the permutation formula:

$$n!/(n-r)!$$

where n is the number of items in the set and r is the number of items selected.

We know that the set of letters in abracadabra has 11 letters. So, n = 11.

To find the number of different strings using all 11 letters, we need to select all 11 letters. Hence, r = 11.

Substituting the values into the formula, we get:$$11!/(11-11)!$$$$11!$$

Since the value of 0! is defined as 1, we can write :$$11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1$$

Calculating this, we get:$$39,916,800$$

Therefore, there are 39,916,800 different strings that can be made from the letters in abracadabra, using all the letters.

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Answer: 1/5

Step-by-step explanation:

Answer:

\({ \sf{ \frac{1}{5} }} \\ \)

Step-by-step explanation:

\({ \sf{ \frac{2 \div 2}{10 \div 2} \equiv \frac{1}{5} }} \\ \)

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations, either the disk method or the shell method can be used.

When finding the volume of a solid generated by revolving a region around a line, we have two methods at our disposal: the disk method and the shell method.

1. Disk Method:

The disk method involves dividing the region into infinitesimally thin disks perpendicular to the axis of rotation. The volume of each disk can be calculated using the formula for the volume of a cylinder (V = πr^2h), where r represents the radius of the disk and h represents its height. By summing up the volumes of all the disks, we obtain the total volume of the solid.

2. Shell Method:

The shell method, on the other hand, involves dividing the region into infinitesimally thin cylindrical shells parallel to the axis of rotation. Each shell has a thickness of Δx, where x is the variable that defines the boundaries of the region. The volume of each shell is calculated by multiplying the height of the shell (given by the difference in the y-values of the two bounding curves) by the circumference of the shell (given by 2πx). By summing up the volumes of all the shells, we obtain the total volume of the solid.

Both methods yield the same result for the volume of the solid. The choice between the two methods depends on the shape of the region and the convenience of integrating with respect to either x or y.

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Answers:

======================================================

Explanation:

Skip to the "Work Shown" section below to see the steps for each part.

Each variable is a place holder for some unknown number. We can think of it like a box that holds a number. Luckily the letter x is found in the word "box" to help cement this line of thinking.

1x = 1 box

2x = 2 boxes

3x = 3 boxes

and so on

This shorthand notation allows us to quickly add boxes

2 boxes + 3 boxes = 5 boxes

So 2x+3x = 5x

And we can subtract boxes as well

7 boxes - 3 boxes = 7x - 3x = 4x = 4 boxes

The same number must go in box x for this to work out.

When it comes to dealing with negative numbers, it might help to use a vertical number line. I like to think of it like going up and down an elevator on a skyscraper. Negative integers represent basement levels.

It's possible to have boxes within boxes. The box A has the three boxes x-y+z inside it. So wherever we see an "A", replace it with x-y+z. Unfortunately we don't know what numbers go in the boxes for x, -y and z. Use the same type of thinking for B and C.

Don't forget to use the distributive property to distribute the negative through to each term.

Example: (x+y)-(w+z) = x+y-w-z

Many students make the mistake in saying that (x+y)-(w+z) = x+y-w+z which is not true. The +z should be -z at the very end.

Let me know if you have any other questions.

The next section below shows the steps needed to get the three answers.

----------------

Work Shown:

Part (I)

A+B+C = (x-y+z)+(2x-3y+4z)+(4x-5y-6z)

A+B+C = (x+2x+4x)+(-y-3y-5y)+(z+4z-6z)

A+B+C = 7x - 9y - z

Part (II)

A-B+C = (x-y+z)-(2x-3y+4z)+(4x-5y-6z)

A-B+C = x-y+z-2x+3y-4z+4x-5y-6z

A-B+C = (x-2x+4x)+(-y+3y-5y)+(z-4z-6z)

A-B+C = 3x - 3y - 9z

Part (III)

A+B-C =  (x-y+z)+(2x-3y+4z)-(4x-5y-6z)

A+B-C =  x-y+z+2x-3y+4z-4x+5y+6z

A+B-C = (x+2x-4x)+(-y-3y+5y)+(z+4z+6z)

A+B-C = -x + y + 11z

Answer:

110

Step-by-step explanation:

Rate or proportion shows the relationship between the variation in the  number of two variables.

Given that the ratio of alternative songs to total songs is 9:14.

Total songs = 308

Since the to every 14 total songs, there is 9 alternative songs.

Thus,

Number of alternative songs = \(\frac{9}{14}\) x 308

                                                = 198

There are 198 alternative songs in the music library.

The number of songs that are NOT alternative songs = 308 - 198

                                                                                         = 110

Thus, there are 110 songs that are NOT alternative songs.

The volume of the figures are;

6. Volume of the cylinder is approximately  11259 in³

7. Volume of cylinder is approximately 14476 mm³

8. Volume of box is 2808 ft³

From the question, we are to calculate the volume of the given figures

6.

The volume of a cylinder can be calculated by using the formula,

Volume = πr²h

Where r is the radius

and h is the height

In the diagram,

Diameter = 32 in

Therefore,

Radius = 16 in

Height = 14 in

Thus,

Volume of the cylinder = π × 16² × 14

Volume of the cylinder = 11259 in³

7.

First we will determine the diameter of the cylinder and then the radius

Let the diameter be d

by using the Pythagorean theorem,

40² = d² + 32²

d² = 40² - 32²

d² = 576

d = √576

d = 24

Therefore,

Radius = 12 mm

Height = 32mm

Then,

Volume of cylinder = π × 12² × 32

Volume of cylinder ≈ 14476 mm³

8.

Volume of box = Length × Width × Height

Volume of box = 39 ft × 12 ft × 6 ft

Volume of box = 2808 ft³

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The rate of change of the annual u.s. factory sales in 2000 is 7.7 billion dollars per year

From the question, we have the following parameters that can be used in our computation:

s(t) = 0.12t² − t + 5.7

In 2000, we have the value of t to be

t = 2000 - 1990

Evaluate

t = 10

So, we have

s(10) = 0.12 * 10² − 10 + 5.7

Evaluate

s(10) = 7.7

Hence, the rate in 2000 is 7.7 billion dollars per year

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Question

the rate of change of annual u.s. factory sales (in billions of dollars per year) of consumer electronic goods to dealers from 1990 through 2001 can be modeled as s(t) = 0.12t2 − t + 5.7 billion dollars per year

Calculate the rate of change in 2000

Answer:

(x,y)=(5,-2)

Step-by-step explanation:

photomath

Answer:

1.  There are 609 more fiction books than non-fiction books in the library

2. Cheryl had $900 initially

Answer:

12 peanuts

Step-by-step explanation:

use algebra using the given ratios...and use trial and error to find the total number of peanuts.

multiply that by the final ratio.

Answer:

x = - \(\frac{4}{5}\)

Step-by-step explanation:

Given

5x - 2 = 25x + 14 ( subtract 25x from both sides )

- 20x - 2 = 14 ( add 2 to both sides )

- 20x = 16 ( divide both sides by - 20 )

x = \(\frac{16}{-20}\) = - \(\frac{4}{5}\)

Answer:

x=8 and QNR= 63°

Step-by-step explanation:

90+8x-1+27=180

116+8x=180

8x=64

x=8

Answer:

8, m<QNR=63 degrees

Step-by-step explanation:

So, lets go over what we know:

The angle that makes up (8x-1) and 27 degrees is a right angle.

A right angle is 90 degrees.

So, to solve for angle m<QNR and for x, we must subtract and solve using 27 degrees, and (8x-1).

Lets put this into equation form:

(8x-1)+27=90

Lets subtract 27 from both sides to get the (8x-1) alone:

(8x-1)=63.

So lets stop here real quick.

We need to find angle M<QNR. This is (8x-1)

So looking at what we have solved so far, angle M<QNR must be 63 degrees.

Now, lets solve further to find out what x is:

(8x-1)=63

Lets add x to both sides to get 8x alone:

(8x)=64

We dont need the parethese, for they do not have a function, so:

8x=64

Finally, lets divide 8 from both sides so we can make 8x into just x:

x=8

So x is equal to 8.

Overall:

x = 8

Angle m<QNR = 63

Hope this helps! :)

Answer:

a = 92° , b = c = 143°

Step-by-step explanation:

a and 88° are same- side interior angles and sum to 180° , that is

a + 88° = 180° ( subtract 88° from both sides )

a = 92°

b and 37° are same- side interior angles and sum to 180° , then

b + 37° = 180° ( subtract 37° from both sides )

b = 143°

b and c are corresponding angles and are congruent , then

c = b = 143°

Answer:

Step-by-step explanation:

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Answer:

1) 1 m² = 10.75 tiles

2) 10 m² = 107.5 tiles

3) 9.3 m² of tiles = 100 tiles

4) a m² = 10.5a tiles

Step-by-step explanation:

The table is missing and so i have attached it.

From the question, we are told that each square meter of ceiling requires 10.75 tiles. Thus on the first row;

1 m² = 10.75 tiles

The second row of the table shows 10 m² of tiles.

Thus, by proportion, 10 m² of tiles will require; 10 × 10.75 tiles = 107.5 tiles

The third row shows us 100 tiles required.

Since 10.75 tiles is for 1  m² , then by proportion, we can find the square meters of tiling of 100 tiles. Thus;

100 tiles will use; 100 × 1/10.75 = 9.3 m² of tiles

The fourth row shows us square meter of tiles to be a.

Thus by proportion, number of tiles required for this square meter of tile is;

a × 10.75/1 = 10.75a tiles

Answer: The choice that best introduces the passage is B) In the middle of the San Francisco Bay sits a 400-acre island that, 80 years ago, did not exist.

Step-by-step explanation:

This sentence provides context for the location and history of Treasure Island and sets up the information presented in the passage.

The best introduction to the passage is option B, as it directly introduces the main subject, Treasure Island, and its historical context relating to the impact of the Great Depression and the World's Fair.

The introduction that best suits the passage given is option B) 'In the middle of the San Francisco Bay sits a 400-acre island that, 80 years ago, did not exist.' This option provides a tangible connection to the main subject of the passage, which is Treasure Island and its historical context. Notably, it introduces Treasure Island and its timeline, which directly ties into the World's Fair and the impact of the Great Depression as discussed in the passage. Options A, C, and D do not sufficiently provide a specific introduction to the unique context of Treasure Island.

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(a) The expected number of times the frisbee is thrown through the course of the game is n-1. (b) The expected number of people that never got the frisbee during the game is 1.

(a) In this game, each time the frisbee is thrown, it moves to a different person in the circle, excluding Ben. Since there are n-1 people in the circle other than Ben, the frisbee is expected to be thrown n-1 times before it reaches Ben again. (b) Since the game ends when someone throws the frisbee back to Ben, there will always be one person who never gets the frisbee throughout the game. Therefore, the expected number of people that never got the frisbee during the game is 1.

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Answer:

Step-by-step explanation:

The rate column will be:

A= 30

B= 20

C= x miles

D= x miles

It should be noted that rate simply means the measure, quantity, or frequency that one measure against another quantity or measure.

In this case, Jorden drives to the store at 30 miles per hour and on her way home she averages only 20 miles per hour.

Therefore, the rate column will be:

A= 30

B= 20

C= x miles

D= x miles

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Fill out the Rate column in the table below. Jorden drives to the store at 30 miles per hour. On her way home she averages only 20 miles per hour. If the total driving time takes half an hour, how far does she live from the store? Fill out the Rate column in the table below. a = b =

Answer:

D.

Step-by-step explanation:

C and D are our only 2 options left bc in the equation there are no negatives, so D. is the best choice, hence the equation matches the answer!!! Hope this helps! :)

Answer:

\(\sf y =\dfrac{-1}{3}x + 7\)

Step-by-step explanation:

Equation of line: y =mx +b

 Here, m is the slope and b is the y-intercept.

Parallel lines have same slope.

            \(\sf y =\dfrac{-1}{3}x + 4\)

     So, the slope of the required line = -1/3

Equation of the required line:  

                \(\sf y =\dfrac{-1}{3}x + b\)

Point(6,5) goes through the line. substitute x = 6 and y =5 in the above equation and then we can find the value of y-intercept 'b'

    \(\sf 5 =\dfrac{-1}{3}*6 +b\\\\ 5 = -2 + b\\\\5+2 = b\\\\\boxed{b = 7}\)

Equation of the require line:

           \(\sf \boxed{\bf y =\dfrac{-1}{3}x+7}\)

The rate of change of the length of the man's shadow when he is 60 feet away from the lamppost is approximately 1.11 ft/sec.

To solve this problem, we can use similar triangles and the chain rule of differentiation. Let y be the length of the man's shadow and x be his distance from the lamppost. Then we have the following ratio of corresponding sides: (6 ft)/(y ft) = (60 ft + x ft)/(22 ft). Solving for y, we get y = (22/6)(60 + x). To find the rate of change of y with respect to time, we differentiate both sides with respect to time and apply the chain rule: dy/dt = (22/6) d/dt (60 + x) = (22/6)(dx/dt). Plugging in the given values, we get dy/dt = (22/6)(5/12) = 1.11 ft/sec. Therefore, the rate of change of the length of the man's shadow when he is 60 feet away from the lamppost is approximately 1.11 ft/sec.

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