Mathematics College

which of the following is equal to the rational expression below when x=11?
x^2-121/x+11
a. x-11
b. x+11
c. x+11/x-11
d. 1/x-11

Answers

Answer 1
Final answer:

The algebraic expression that is equivalent to the given rational expression is (x-11), but when we substitute x=11 into the expression, we receive 0. However, this leads to an indeterminate form in the original rational expression.

Explanation:

The rational expression given in the question is x^2-121/x+11. If we factorize x^2-121, we'll get (x-11)(x+11), because x^2-121 is a difference of squares. Now, the expression becomes: (x-11)(x+11)/(x+11). We see that (x+11) on numerator and denominator will cancel out each other. This leaves us with (x-11).

Now, let's substitute x=11 in (x-11). We obtain 11-11 which equals 0. So the correct answer is (x-11), but we get 0 when we substitute x=11 into the expression. This actually results in an indeterminate form because the original rational expression becomes a 0/0 form, which points to a situation of undefined or indeterminate form.

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Related Questions

Your state's bigbucks lottery prize has reached $100,000,000, and you decide to play. you have to pick ve numbers between 1 and 60, and you'll win if your numbers match those drawn by the state. you decide to pick your "lucky" numbers using a random number table. which numbers do you play, based on these random digits? 43680 98750 13092 76561 58712

Answers

Numbers 1-60 don't map nicely to numbers 0-99999, so some method needs to be devised to create that map. Perhaps the simplest is to use these digits as a decimal fraction and compute
.. 1 + floor(60*N/100000)
The possibilty of collision needs to be considered. One way to deal with that is to add or subtract a constant, using the next higher available number, for example. This would give the choices {8, 27, 36, 46, 60}.

Choose the correct simplification of (8x4y3)2. (5 points)

Answers

Not sure what your options are but if it is
(8x^4y^3)^2 the answer should be
64x^8y^6

Answer:

the person below is correct  64x8y6 is the right answer

Step-by-step explanation:

Troy is going to Spain and needs to convert his dollars to euros. He knows that when he goes, $5.00 is equivalent to about 3.45 Euros, How many will he get for $125?

Answers

125/5=25
25*3.45=86.25

86.25 euros
To solve this, you need to set up a proportion.

$5/3.45 euros = $125/x euros

then, cross multiply

5x=(3.45)(125)
5x=431.25
x=86.25

The answer is 86.25 euros

A class of 32 students shares a class set of 78 colored pencils. On a day with six students absent, which statement is true? A. For each student, there are 4 colored pencils. B. For each student, there are 3 colored pencils. C. For every 3 students, there is 1 colored pencil. D. For every 4 students, there is 1 colored pencil. I need help solving the problem

Answers

With six students absent, there are 26 students, so 78/26 = 3 colored pencils for each student.

Selection B is appropriate.

is the sample valid? what percent of students prefer caramel popcorn?

Answers

Is the sample valid?
 First you must see if the number of students in the table corresponds to the number of students surveyed that was 75.
 We have then:
 33 + 15 + 27 = 75
 We have then that:
 The sample is valid.

 what percent of students prefer caramel popcorn? 
 We can make the following rule of three to answer this question:
 75 ---> 100%
 27 ---> x
 Clearing x we have:
 x = (27/75) * (100)
 x = 36%
 36% percent of students prefer caramel popcorn

As per an axiom in Euclidean geometry, if points lie in a plane, the containing those points also lies in the same plane?


A) two/plane

B) three/plane

C)two/line

D)three/line

Answers

According to Postulate 5, otherwise known as the Plane Line Postulate, if two points lie in a plane, the line containing those points also lies in the same plane. In other words, if you have a square plane, for example, and you put two points within the plane and you draw a line that connects both of those points. The line you created using those two points, or the line that connects the points, are within the same plane. 

Your answer is C.

Answer: two, line

Step-by-step explanation:

A realtor earns a 0.8% commission on the homes sje sells. Last month, she sold a $380,000 home. How much did the realtor earn as her commission for the sale

Answers

380,000(0.008) = 3,040

Answer:

Her commission for the sale was $3,040

Step-by-step explanation:

A realtor sold a home costs = $380,000

She earns commission on the home she sells = 0.8%

Commission for the sale she earns = 0.8% of 380,000

[tex]\frac{0.8}{100}[/tex] × 380,000

0.008 × 380,000 = 3,040

Her commission for the sale was $3,040

Two buses leave the station traveling in opposite directions one going east and one going west the eastbound bus travels at 40 mph and the west bound bus travels at 65 mph if both buses leave the station at 10 AM at what time will they be 1260 miles apart

Answers

Answer:

  10 PM

Step-by-step explanation:

The combined speed of the two buses is ...

  40 mph + 65 mph = 105 mi/h

The relationship between distance, speed, and time can be written ...

  time = distance/speed

so the elapsed time until the buses cover the distance is ...

  time = (1260 mi)/(105 mi/h) = 12 h

___

12 hours after 10 AM is 10 PM.

The buses will be 1260 miles apart at 10 PM.

can u show me common core way this problem how to do 5/9 ×3 1/2

Answers

1.) you want to make 3 1/2 an improper fraction. so multiply 3 times 2 (your denominator) then add 1 (numerator). 
3x2= 6  6+1=7, then put 7 over your denominator which would be 7/2.
2.) multiply 5/9 times 7/2
5 times 7 is 35
9 times 2 is 18
your answer is 35/18
3.) make it a proper fraction
18 times 2 is 36 so that would't work to have two!
so you only can put 18 into 32 once so subtract 32-18 so you know what is left over after you take a whole out. 32-18=14. 14 is now the numerator and so put your whole number first then put your numerator over your denominator: 1 14/18
4.) simplify
1 14/18=  1 7/9, I divided 14 and 18 by 2 to simplify


The answer is 1 7/9
first off, we change the mixed fraction to an "improper" fraction, and then multiply like we would any other fractions, so let's do so,

[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies\cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\ -------------------------------\\\\ \cfrac{5}{9}\times 3\frac{1}{2}\implies \cfrac{5}{9}\times\cfrac{7}{2}\implies \cfrac{5\times 7}{9\times 2}\implies \cfrac{35}{18}\implies 1\frac{17}{18} \\\\\\ \textit{keep in mind that }1\frac{17}{18}\implies \cfrac{1\cdot 18+17}{18}\implies \cfrac{35}{18}[/tex]

Mr. Lin baked banana bread for a bake sale to raise money for the math team. He said that he added a spoonful of walnuts for each of the students in his three classes, and that he added more than 250 walnuts. He used the inequality
16w + 24w + 10w > 250 to represent this situation, where w represents the number of walnuts in each spoonful. How many walnuts can be in a spoonful?

Answers

To answer this question you would need to solve this inequality. The first step would be to combine all three terms on the left-hand side of the greater than symbol. By doing this you would have 50w > 250. To solve this inequality divide both sides by 50. The answer is w > 5. In words, this means the number of walnuts per spoonful is greater than five.

When a grizzly bear hibernates, it’s heart rate drops to 10 beats per minute, which is 20% of its normal value. What is a grizzly bear’s normal heart rate when not hibernating?

Answers

If something 20% of its normal value, then it has been divided by 5 (using the example of 100%, if you divide this by 5 it leaves you with 20%). This means that 10 beats per minute are only a fifth of its usual heart rate. Therefore a grizzly bear's normal heart rate is 10 × 5 = 50 beats per minute. 

the hardware store sells sparklers for the 4th of july. they charge 19 cents apiece. the firework stand charges 85 cents for four. which is the better deal? how can you tell

Answers

Let’s start by finding the average for the place that charges 85 cents for 4 fireworks. You simply do 85 divided by 4 to get 21.25 cents. This means that each firework costs about 21 cents a piece. So, the first firework stand is the better deal, because 19 cents a piece is better than 21 cents a piece.

Heights of adult women in the united states are normally distributed with a population mean of μ = 63.5 inches and a population standard deviation of σ = 2.5. a medical researcher is planning to select a large random sample of adult women to participate in a future study. what is the standard value, or z-value, for an adult woman who has a height of 50.4 inches? (calculate to 1 decimal)

Answers

For an adult woman with a height of 50.4 inches in the United States, the standard value (z-value) is approximately -5.2, calculated based on a normal distribution with a mean of 63.5 inches and a standard deviation of 2.5 inches.

To find the standard value or z-value for a given height in a normal distribution, you can use the formula:

[tex]\[ Z = \frac{{X - \mu}}{{\sigma}} \][/tex]

where:

- Z is the z-value,

- X is the individual data point (height in this case),

- [tex]\( \mu \)[/tex] is the population mean,

- [tex]\( \sigma \)[/tex] is the population standard deviation.

For the given problem:

- [tex]\( \mu = 63.5 \)[/tex] inches,

- [tex]\( \sigma = 2.5 \)[/tex] inches,

- X = 50.4 inches.

[tex]\[ Z = \frac{{50.4 - 63.5}}{{2.5}} \]\[ Z \approx -5.24 \][/tex]

Rounded to one decimal place, the z-value for an adult woman with a height of 50.4 inches is approximately -5.2.

In the diagram below QRS=NMP what is length in inches of MP

Answers

mp is congruent to rs

This table shows the weekly rainfall, in inches, for two cities for ten weeks. City A 0.2 0 1.5 1.3 2.5 3 0.4 0.3 0.2 1 City B 0 0 0.4 0.2 0.3 1 1 1 0.1 0.1 Which conclusion can be drawn from the data?

WILL GIVE BRAINLISET

Answers

the choices for the question are as follows;
A. During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.
this is correct. rainfall of 1 inch was recorded on three days so it was the most often recorded rainfall. 

B. The range between the maximum and minimum values for City B is greater than the range between the maximum and minimum values for City A.
range for city A - 3 - 0 = 3
range for city B - 1- 0 = 1
this statement is incorrect as the range for city B is lesser than the range for city A.

C. For the ten weeks, City A received less rainfall, on average, than City B
the average rainfalls for;
City A - 1.04
city B - 0.41
city A received more rainfall on average than city B on average therefore this statement is incorrect.

D. The median for City A is less than the median for City B. 
city A - 0.7
city B - 0.25
median for city A is greater than median for city B therefore this statement is incorrect.

Therefore the conclusion that can be drawn from the data is During the 10 wk period, the rainfall amount recorded most often for City B was 1 in. - Statement A

Answer:

During the 10 wk period, the rainfall amount recorded most often for City B was 1 in

Step-by-step explanation:

Using the equation, y=10000(0.97)x predict the purchasing power of $10000 ten years later

Answers

 Using the equation, y= 10,000(0.97)^ , predict the purchasing power of $10,000 ten years later. 
$7374

Answer:

The purchasing power is $7374

Step-by-step explanation:

We are given an equation [tex]y=10000(0.97)^x[/tex]

where,  

y represents purchasing power.

x represents the number of years.

We need to find purchasing power of $10000 after 10 years.

Put x=10 into equation and solve for y

[tex]y=10000(0.97)^{10}[/tex]

[tex]y=7374.24\approx 7374[/tex]

After 10 years the purchasing power of $10000 becomes $7374

As we can see the value of the product decrease.

Hence, The purchasing power is $7374

You find that the going rate for a home mortgage with a term of 30 years is 5% APR. The lending agency says that based on your income, your monthly payment can be at most $750 . How much can you borrow?

Answers

Using
A=monthly payment
P=amount borrowed (present value)
i=5%/12 per month (period)
n=30*12 months (months)

Then
[tex]P=\frac{A*((1+i)^n-1)}{i*(1+i)^n}[/tex]
Substitute values
[tex]P=\frac{750*((1+.05/12)^{360}-1)}{.05/12*(1+.05/12)^{360}}[/tex]
[tex]=\frac{750*((1+.05/12)^{360}-1)}{.05/12*(1+.05/12)^{360}}[/tex]
[tex]=139711.21[/tex]  to the nearest cent

we built a fence around the back of his yard he built 7 feet of fence every day in July and was finished how long is the fence explain how you got the answer

Answers

First, it's important to remember that July has 31 days. So, if he built 7 feet of fence everyday for 31 days, thn altogether he built 7×31= 217 feet if fence in total. Therefore, the fence is 217 feet long.

Box contains 4 bolts. two of them, labeled #1 and #2 are 5 mm in diameter, and two of them, labeled #3 and #4, are 7 mm in diameter. bolts are randomly selected until a 5 mm bolt is obtained. the outcomes are the sequences of the bolts that can be selected. so one outcome is 1, and another is 342. let x represent the number of bolts selected.
a.find the probability mass function of x.

Answers

This can be solved with a tree diagram, or a table, or a simple enumeration.
The following is the last method.
1
2
31
32
341
342
41
42
431
432
So there are 10 possible outcomes, out of which 2 have a single pick, 4 have 2 picks, and 4 have 3 picks.
The pmf of x is therefore
x   p
1   1/5
2   2/5
3   2/5


Math help!! 5 questions!!! A classmate believes that a triangle can have both right angle and an obtuse angle. Which of the following statements would you use to convince him that he is incorrect. A. Its is not possible because the sum of the angles in the triangle can't exceed 180 d. B. It is not possible because if a triangle has an obtuse triangle , that means all the angles are obtuse angles. C. It is not possible because if a triangle has a right triangle, that means all the angles are right angles. Its is possible. The classmate is correct.

Answers

Final answer:

A triangle cannot have both a right angle and an obtuse angle, as the sum of its angles must always equal 180 degrees.

Explanation:

To convince your classmate that a triangle cannot have both a right angle and an obtuse angle, you should explain that according to Euclidean geometry, the sum of the angles in any triangle must equal two right angles, or 180 degrees.

If a triangle has a right angle (90 degrees), then the remaining two angles must sum up to 90 degrees as well. Introducing an obtuse angle, which is any angle greater than 90 degrees, would cause the total sum of the angles to exceed 180 degrees, which is impossible.

Therefore, the correct statement to use would be 'A. It is not possible because the sum of the angles in the triangle can't exceed 180 degrees.'

If sec(x)=13/12 what is cos(x)?

Answers

recall that cosine is the reciprocal of secant, so is the same fraction, just upside-down.

expand the equation 1/3(2/5-2/3w)

Answers

1/3(2/5-2/3w)
= 1/3 * 2/5   - 1/3 *2/3w
= 2/15 - 2/9w

How are exponential functions related to logarithmic functions?
Model that with an example.

Answers

Exponential functions are related to logarithmic functions in that they are inverse functions. Exponential functions move quickly up towards a [y] infinity, bounded by a vertical asymptote (aka limit), whereas logarithmic functions start quick but then taper out towards an [x] infinity, bounded by a horizontal asymptote (aka limit).
If we use the natural logarithm (ln) as an example, the constant "e" is the base of ln, such that:
ln(x) = y, which is really stating that the base (assumed "e" even though not shown), that:
[tex] {e}^{y} = x[/tex]
if we try to solve for y in this form it's nearly impossible, that's why we stick with ln(x) = y
but to find the inverse of the form:
[tex]{e}^{y} = x[/tex]
switch the x and y, then solve for y:
[tex] {e}^{x} = y[/tex]
So the exponential function is the inverse of the logarithmic one, f(x) = ln x

Exponential and logarithmic functions are related in that they are inverses of each other.

Logarithmic functions and exponential functions are inverses of each other.

For instance, let [tex]log a = b[/tex]

In order to eliminate the logarithmic function, we will apply an exponential function ([tex]e[/tex])to both sides.

[tex]e^{loga} = e^b[/tex]

The exponential function will cancel out the logarithmic function since they are inverses of each other to give:

[tex]a = e^b[/tex]

This example shows the inverse relationship that exists between the logarithmic and exponential functions.

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Convert a length of 25.0 m to inches.
express your answer numerically in inches.

Answers

Answer:

  98.4 inches

Step-by-step explanation:

You want the length 25.0 meters expressed in inches.

Conversion

There are 0.254 m in an inch, so the distance d can be found from the proportion ...

  d/(25 m) = (1 in)/(0.254 m)

Multiplying by 25 m, we find ...

  d = 25/0.254 in ≈ 98.4252 in

The length is about 98.4 inches.

__

Additional comment

The value to convert is given to 3 significant figures. The conversion factor is exact. The answer is appropriately expressed using 3 significant figures.

what is the solution of the equation 1.6m - 4.8 = -1.6m

Answers

Solve for m:
1.6 m - 4.8 = -1.6 m

Add 1.6 m to both sides:
1.6 m + 1.6 m - 4.8 = 1.6 m - 1.6 m

1.6 m - 1.6 m = 0:
1.6 m + 1.6 m - 4.8 = 0

1.6 m + 1.6 m = 3.2 m:
3.2 m - 4.8 = 0

Add 4.8 to both sides:
3.2 m + (-4.8 + 4.8) = 4.8

4.8 - 4.8 = 0:
3.2 m = 4.8

Divide both sides of 3.2 m = 4.8 by 3.2:
(3.2 m)/3.2 = 4.8/3.2

3.2/3.2 = 1:
m = 4.8/3.2

4.8/3.2 ≈ 1.5:
Answer:  m ≈ 1.5

Answer:

m=1.5

Step-by-step explanation:

I took the test.

Susan been a total of $26 at the State Fair she's mad she spent 9 on food in the rest of the money susan spent on games,g.

Answers

the answer for this problem would be D. g+9 = 26
The answer is D, because she spent 9 on food and subsequently 15 on games.

8.73e16 in simple form

Answers

8.73e16
= 8.73 x 10^16 ..............................scientific form 
= 87,300,000,000,000,000 ...........standard form

Solution:

we have been asked to write [tex]8.73e^{16}[/tex] in the simplest form.

This can be alternatively written as [tex]8.73*10^{16}[/tex]

And as we know that a number written in scientific notation can be re-written in the simple form by removing the "10 to the power" term by expanding the given number as below

[tex]8.73*10^{16}=8.73*1000,000,000,000,0000[/tex]

It can be further written by removing the decimal as below

[tex]8.73*10^{16}=87,300,000,000,000,000[/tex]

Hence the required simple form is 87,300,000,000,000,000


Tom spent 1/3 of his monthly salary for rent and 1/7 of his monthly salary for his credit card bill. If $1320 was left, what was his monthly salary?

Answers

assume that x = monthly salary

x -1/3x - 1/7x = 1320
11/21x =1320
x = 1320 divides by 11/21
x = $ 2520

his monthly salary was $ 2520

Abigails mom said she will be home from work in 65 minutes its 4:27 pm and abigail has dance practice at 6:00 pm. How much time will abigail have between the time that her mom gets home from work and the beginning of dance practice

Answers

she will have 28 minutes. 65 mins= 1 hour and 5 minutes. 1 he and 5 min+ 4:27= 5:32. 5:33 + 28=6:00.

The time that her mom gets home from work and the beginning of dance practice is 28 minutes.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, It is 4:27 pm and Abigail's mom said she will be home from work in 65 minutes.

Now 60 minutes from 4:27 pm is 5:27 pm and 5 minutes more is 5:32 pm.

Abigail has dance practice at 6:00 pm, So the time that her mom gets home from work and the beginning of dance practice is 28 minutes seems obvious.

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Which of the following are the correct properties of slope A.If two lines have the same slope, then they are the same line. B.The slope of a line that moves up from left to right is positive. C.A steep line has negative slope. D.Some lines have an undefined slope. E.The slope of a line is always positive.

Answers

Answer:

B.The slope of a line that moves up from left to right is positive.

Step-by-step explanation:

Slope is the ratio of vertical change to horizontal change. If a line moves up as x-values increase, then the signs of both changes are positive, and the slope is positive. This observation matches selection B.

_____

Comments on other choices

If a line is vertical, it will exhibit a vertical change with no horizontal change. The denominator of the ratio for slope will be zero. Division by zero is undefined, so we say the slope of a vertical line is "undefined."

Lines with the same slope will be parallel, if they're not the same line.

A line that moves down to the right has a negative change in its vertical coordinate for a positive change in its horizontal coordinate. The ratio of changes will have a negative sign. So, the slope of a line that moves down to the right is negative, not positive.

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