What is the product of the rational expressions below? (x - 8)/(x + 11) * (x + 8)/(x - 11) A (x ^ 2 - 121)/(x ^ 2 - 64) . B. (x ^ 2 - 64)/(x ^ 2) c (x ^ 2 - 64)/(x ^ 2 - 121) D. 64/121 .
Answers
The product of the given expression is (x²- 64)/(x² +121)
Hence,
Option C is correct.
The given expression is,
[(x - 8)/(x + 11)][(x + 8)/(x - 11)]
Now we can write the expression as,
⇒ (x-8)(x+8)/(x+11)(x-11)
Since we know the product formula
(a-b)(a+b) = a² - b²
Therefore,
The expression be,
⇒ (x²- 8²)/(x² +11²)
⇒ (x²- 64)/(x² +121)
Hence the rational expression is,
⇒ [(x - 8)/(x + 11)][(x + 8)/(x - 11)] = (x²- 64)/(x² +121)
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Related Questions
2. Write the algebraic phrases that correspond to the following word phrases: (a) The sum of four times the opposite of a number and - 5 (b) The product of 5 and the sum of 3 times a number and 4
Answers
Answer:
would not be helpful to anser nowww... sory!
Step-by-step explanation:
A 50-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 pounds/gallon is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt (in pounds) in the barrel at time t (in minutes) is given by Q(t) = 15(1 - e^-kt) where k > 0. (a) Find k if there are 5.5 pounds of salt in the barrel alter 10 minutes. Round your answer to 4 decimal places.(b) What happens to the amount of salt in the barrel as t infinity?
Answers
a) To find the value of k, we use the given information that there are 5.5 pounds of salt in the barrel after 10 minutes.
By substituting these values into the equation Q(t) = 15(1 - e^(-kt)), we can solve for k. The rounded value of k is provided as the answer.
b) As t approaches infinity, the amount of salt in the barrel will reach a maximum value and stabilize. This is because the exponential function e^(-kt) approaches zero as t increases without bound. Therefore, the amount of salt in the barrel will approach a constant value over time.
a) We are given the equation Q(t) = 15(1 - e^(-kt)) to represent the amount of salt in the barrel at time t. By substituting t = 10 and Q(t) = 5.5 into the equation, we get 5.5 = 15(1 - e^(-10k)). Solving this equation for k will give us the desired value. The calculation for k will result in a decimal value, which should be rounded to four decimal places.
b) As t approaches infinity, the term e^(-kt) approaches zero. This means that the exponential function becomes negligible compared to the constant term 15. Therefore, the equation Q(t) ≈ 15 holds as t approaches infinity, indicating that the amount of salt in the barrel will stabilize at 15 pounds. In other words, the concentration of salt in the barrel will reach a constant value, and no further change will occur.
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Eliana drove her car 81 \text{ km}81 km81, start text, space, k, m, end text and used 999 liters of fuel. She wants to know how many kilometres (x)(x)left parenthesis, x, right parenthesis she can drive on 22 litres of fuel. She assumes her car will continue consuming fuel at the same rate.
How far can Eliana drive on 22 litres of fuel?
Answers
Answer:
Eliana can travel distance of 18018 km in 222222 liters of fuel . Assumption by Eliana =rate of consuming fuel at the same rate. Therefore Eliana can travel distance of 18018 km in 222222 liters of fuel .
Step-by-step explanation:
Can someone help, please?!
Answers
Answer:
one solution
Step-by-step explanation:
Find the surface area.
1 m
10 m
Answers
Answer:
\(A=69.11\ m^2\)
Step-by-step explanation:
Given that,
The radius of cylinder, r = 1m
Height of the cylinder, h = 10 m
We need to find the surface area of the cylinder. The total surface area of a cylinder is given by :
\(A=2\pi r^2+2\pi rh\\\\A=2\pi r(r+h)\)
Put all the values,
\(A=2\pi \times 1(1+10)\\\\=69.11\ m^2\)
So, the surface area of the cylinder is equal to \(69.11\ m^2\).
Find the linear approximation of the f(x,y)=x+yx at the point (1,6)
Answers
\(L(x,y)=f(a,b)+f_x'(a,b)(x-a)+f_y'(a,b)(y-b)\\\\f(x,y)=x+yx\\(a,b)=(1,6)\\\\f(1,6)=1+6\cdot1=7\\f'_x(x,y)=1+y\\f'_x(1,6)=1+6=7\\f'_y(x,y)=x\\f'_y(1,6)=1\\\\L(1,6)=7+7\cdot(x-1)+1\cdot(y-6)\\L(1,6)=7+7x-7+y-6\\L(1,6)=7x+y-6\)
if there are 21 students in class today how much would it cost for the class and your teacher to ride the sandia aerial tram? rates $25 adults $20 seniors 62+ & teens 13-20 yrs $15 youth 5-12 yrs
Please help due soon :(
Answers
Answer:
a. f(x) = 21 (20) +1 (25) = 445
b. The scenario is a function because each student just have to pay once.
Find the total amount in an account after 8 years if the
deposit was $20,000 and the simple interest rate was
2%.
Answers
Answer:
Step-by-step explanation:
The value of a simple interest account is
A=P(1+rt), A=present amount, P=principle, r=rate, t=time
A=20000(1+0.02(8))
A=20000(1.16)
A=$23200.00
provide general rule to describe the relationship between 10 100 1000
Answers
Specifically:
100 is obtained by multiplying 10 by 10.
1000 is obtained by multiplying 100 by 10.
Therefore, the general rule is that each subsequent number is obtained by multiplying the previous number by 10.
Which is the graph of the function f() = x2 + 2x - 6?
Answers
The x-intercepts from the graph are -3.646 and 1.646 with the parabolic curve facing upwards
Quadratic graphQuadratic functions are functions that has a leading coefficient of 2.
According to the question, we are to graph the quadratic function f(x) = x^2 + 2x - 6. The curve will be parabolic in nature and facing upwards since it is a quadratic function.
The x-intercepts from the graph are -3.646 and 1.646 as shown in the attached graph.
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please help with this problem.
Answers
Perimeter=40
(I’m not too sure though I haven’t done perimeter in ages)
Is the number 123 a
prime number?
Yes
No
Answers
Answer:
\(\Huge \boxed{\mathrm{No }}\)
\(\rule[225]{225}{2}\)
Step-by-step explanation:
Prime numbers have two factors, 1 and the number itself.
Factors of 123 are 1, 3, 41, 123.
123 has 4 factors, it is not a prime number.
\(\rule[225]{225}{2}\)
Answer:
No
Step-by-step explanation:
This is because it has factors other than 1. The factors of 123 are 1, 3, 41, and 123.
Which of the decibes a unique polygon?
Answers
Answer:
In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape with straight sides. It does not have curved sides.
Step-by-step explanation:
Plssss helppp if m<6=83° m<5?
Answers
Answer:
83 degrees
Step-by-step explanation:
These 2 angles are vertical angles. This means that they are congruent to each other.
<6=<5
<83=<5
Hope this helps! :)
Answer: 83
Step-by-step explanation:
Angle and 5 and 6 are equal. Vertical angle theorem says that opposite angles of 2 intersecting lines are equal.
<5 = <6= 83
the ratio of area of two circles were the first circle's circumference is double the circumference of the second circle
Answers
The ratio of the area of the first circle to the second circle is 4:1.
To find the ratio of the areas of two circles, where the circumference of the first circle is double the circumference of the second circle, we can use the formula for the circumference of a circle:
Circumference = 2 * π * radius
Let's assume that the radius of the second circle is 'r'. Since the circumference of the second circle is half of the first circle, we can write:
C2 = 2 * C1
2 * π * r = 2 * π * (2 * r)
2 * π * r = 4 * π * r
Now, let's find the ratio of the areas. The formula for the area of a circle is:
\(Area = π * radius^2\)
For the first circle, with radius '2r', the area is:
\(A1 = π * (2r)^2\)
\(A1 = π * (4r^2)\)
For the second circle, with radius 'r', the area is:
\(A2 = π * r^2\)
Now, let's find the ratio of the areas:
Ratio of areas = A1 / A2
\(Ratio of areas = (π * (4r^2)) / (π * r^2)\)
\(Ratio of areas = 4r^2 / r^2\)
Ratio of areas = 4
Therefore, the ratio of the area of the first circle to the second circle is 4:1.
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f the quadratic function f(x) = x2^2 is graphed below along with the quadratic function g(x) which of the following could
be a correct equation for g(x)?
Answers
Answer: g(x)= -1/2x^2
Step-by-step explanation: since the parabola is opening downwards it would have to be a negative so all we are left with is g(x)=-2x^2 and g(x)-1/2x^2 and if we go in the calculator and type up each equations you would see our answers is g(x)=-1/2x^2
Perform the following area application.
Compute the number of vinyl tiles, measuring 8 in. each side, needed to tile a kitchen measuring 24 ft. by 18 ft.
__________tiles
Answers
To find the number of vinyl tiles needed to tile a kitchen measuring 24 ft. by 18 ft. with tiles measuring 8 in. each side, we need to convert all measurements to the same units.
First, we need to convert the kitchen measurements from feet to inches:
- 24 ft. = 24 x 12 = 288 in.
- 18 ft. = 18 x 12 = 216 in.
Next, we need to divide the length and width of the kitchen by the length of each tile to find the number of tiles needed in each direction:
- Length: 288 in. ÷ 8 in. = 36 tiles
- Width: 216 in. ÷ 8 in. = 27 tiles
Finally, we multiply the number of tiles needed in each direction to find the total number of tiles needed:
- Total tiles: 36 tiles x 27 tiles = 972 tiles
To tile a kitchen, it is important to accurately calculate the number of tiles needed to ensure that there is enough material to complete the job. In this case, we converted all measurements to the same units and then used division and multiplication to find the total number of tiles needed.
To tile a kitchen measuring 24 ft. by 18 ft. with vinyl tiles measuring 8 in. each side, we need a total of 972 tiles.
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Solve for x. Show work.
The teacher told us that the answer is 8 but I’m not sure what steps I need to take to show my work
Answers
Answer:
x= 8
Step-by-step explanation:
∠NWV +∠UVW= ∠NUV (ext. ∠ of △UWV)
70° +(3x +6)°= (11x +12)°
70° +6° -12°= (11x -3x)°
64°= (8x)°
8x= 64
x= 64 ÷8 (÷8 on both sides)
x= 8
Alternatively,
∠UVW+ ∠NWV +∠WUV= 180° (∠ sum of △UVW)
(3x +6)° +70° +∠WUV= 180°
∠WUV= 180° -(3x +6)° -70°
∠WUV= (104 -3x)°
∠WUV +∠NUV= 180° (adj. ∠s on a str. line)
(104 -3x)° +(11x +12)°= 180°
11x -3x +104 +12= 180
8x= 180 -116
8x= 64
x= 64 ÷8
x= 8
(b) assume 90 companies were included in the sample. what is the test statistic? (round your answer to three decimal places.)
Answers
A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years.
a) The hypotheses that can be used to challenge the validity of the claim made by the shareholders' group.
H₀ : u ≤ 9
Hₐ : u > 9
So, the correct option is option (A).
b) T- statistic value is -2.571 for a sample of 90 companies.
c) The critical value for t i.e P-value is 0.0059
d) P-value < α = 0.01, implies reject the null hypothesis. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid. So, the correct option is option(D).
We have given that,
x-bar= 7.27 , σ = 6.38, n = 90
a) Test that the mean tenure for a chief executive officer (CEO) was atleast nine years .
Null and alternative hypothesis is
H₀ : u <= 9
Hₐ : u > 9
b) test statistic:
t =( x-bar - μ ) /σ/√n
=> t = (7.27 - 9 )/6.38/90
=> t = - 1.73/0.67251
=> t = -2.571
c) P-value :
P-value = P( tₙ₋₁ < t) = P(t₉₀₋₁ < t )
=> P-value = P( t₈₉< - 2.571)
=>P-value = P( t₈₉ >2.571)
=> P-value = 1 - P( t₈₉< 2.571)
P-value = 1 - 0.9941 = 0.0059
d) Significance level, = 0.01
we see that p-value= 0.0059 < 0.01
Decision : Reject the null hypothesis H₀
We have no evidence to support the claim.
Hence, we calculate all the required result.
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Complete Question :
A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.27 yearsfor CEOs with a standard deviation of
s = 6.38 years.
(a)Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group. multiple choice:
i)H0: μ ≤ 9
Ha: μ > 9
ii)H0: μ ≥ 9
Ha: μ < 9
iii) H0: μ > 9
Ha: μ ≤ 9
iv)H0: μ < 9
Ha: μ ≥ 9
v) H0: μ = 9
Ha: μ ≠ 9
(b)Assume 90 companies were included in the sample. What is the test statistic? (Round your answer to three decimal places.)
c)What is the p-value for your hypothesis test? (Round your answer to four decimal places.)
p-value =
(d) At = 0.01,what is your conclusion? MULTIPLE CHOICE:
Do not reject H0. We cannot conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is valid.Reject H0. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid.Sam runs 6 miles in 45 minutes. At the same rate, how many minutes would he take to run 4 miles?
Answers
Answer:
It would be 30 mph
Step-by-step explanation:
45/6=7.5
7.5*4=30
Answer:
30 minutes
Step-by-step explanation:
Each mile takes him 7 minutes 30 seconds. So you will do 7.5 x 4 to get 30 minutes
-1/2 multiplied by 1/5
Answers
Answer:
-1/10 or -0.1
Hope this helps!
Three-fifths of seventh graders have a cell phone. in a seventh grade class of 450, how many students would you predict to have a cell phone
Answers
270 students in a seventh-grade class of 450 would have a cell phone which denotes three-fifths of seventh graders using fractions.
Total number of students = 450
Percent of students who have cell phones = 3/5 th
In a class, if there are three-fifths of students have cell phones, that means we need to calculate the remaining percent of students who did not have cell phones.
Students without cell phones = 1 - 3/5 = 2/5
The total number of students with cell phones = (3/5) x 450
The total number of students with cell phones = 270
Therefore, we can conlcude that 270 students in a seventh-grade class of 450 would have a cell phone.
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3.
Mr. Arnie bought 3 lbs. of apples for $1.29 for each pound. He paid $0.32 in taxes. If he paid with a ten-dollar bill, how much did he receive in change?
Answers
Answer:
5.81$
Step-by-step explanation:
A model boat i 15 inche long if the boat i bulit to a cale of 1 : 250 inche how long i the real boat
define a variable
write a porortion
olve the porportion
anwer with word
Answers
If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.
What does a scale look like in math?The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.
Briefing:The scale of drawing the horse = 1 inch :
Therefore in scale
Horse height in drawing equals one inch
The height of the horse = 250 inche
The original height of the horse = 15 inche
The height in the picture = x inches
To find the height the horse in the picture, we have to use proportion
1 inch : 250 inche = x inches : 15 inche
1 / 250 = x / 15
1 × 15= 250x
250x = 15
x = 15/250
x = 0.06 inches
Therefore, the height of the horse in drawing is 0.06 inches
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Fiona rolls a fair dice 144 times.
How many times would Fiona expect to roll a number greater than 2?
Answers
Answer:
34
Step-by-step explanation:
A city has 12,575 residents the number of residents grows by 1.6% every year to the nearest whole resident what will the city's population be in 2 years
Answers
Answer:
12981
Step-by-step explanation:
Given that :
Initial number of residents = 12575
Yearly growth rate (r) = 1.6%
Population in 2 years :
Using the relation :
Population in t years P(t) :
P(t) = initial population * (1 + growth rate)^t
t = time
Population in 2 years :
P(2) = 12575 * (1 + 0.016)^2
P(2) = 12575(1.016)^2
= 12575 * 1.032256
= 12980.6192
= 12981
Can anyone help me with 6? Please
Answers
Answer: (2)
Step-by-step explanation: y=18(0.75) 0.75 as a percent is 75%, kind of like what would happen in the graph with the mathematical term Pneumonoultramicroscopicsilicovolcanoconiosis.
the population of weights for men attending a local health club is normally distributed with a mean of 166-lbs and a standard deviation of 26-lbs. an elevator in the health club is limited to 33 occupants, but it will be overloaded if the total weight is in excess of 5940-lbs. assume that there are 33 men in the elevator. what is the average weight beyond which the elevator would be considered overloaded? average weight
Answers
This means that if the average weight of the men in the elevator is more than 180 lbs, the elevator would be overloaded.
To determine the average weight beyond which the elevator would be considered overloaded, we can follow these steps:
Find the total weight limit for 33 occupants: 5940 lbs.
Divide the total weight limit by the number of occupants to find the average weight per person: 5940 / 33 = 180 lbs.
Now, we need to find the difference between the average weight per person (180 lbs) and the mean weight of the population (166 lbs): 180 - 166 = 14 lbs.
Since we have the difference and the standard deviation (26 lbs), we can now calculate the Z-score:
Z = (difference) / (standard deviation) = 14 / 26 ≈ 0.54.
The average weight beyond which the elevator would be considered overloaded is 180 lbs.
The corresponding Z-score for this weight is approximately 0.54.
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Show that the equation is not an identity by finding a value of x for which both sides are defines but not equal.
Answers
We are given the expression:
\(\cos (x-\pi)=\cos (x)\)We, simply replace the values of solution given and then determine in which it is not a solution, but we can see that when we replace x = 0, we will get:
\(\cos (\pi)\ne\cos (0)\)So, this proves that the function is not an identity.
Which logarithmic equation is equivalent to this exponential equation?
Answers
Answer:
im doing work to im going to fail
Step-by-step explanation: