How does the volume of an oblique cylinder change if the radius is reduced to 2/9 of its original size and the height is quadrupled?

A. V=2/81pir^2h
B. V=16/81pir^2h
C. V=4/9pir^2h
D. V=16/9pir^2h

Answers

Answer 1
New volume is given by:
New volume=(old volume)×(4×2/9×2/9)
simplifying the above we get:
New volume=(old volume)×16/81
Thus the new volume is 16/81 times the old volume
old volume=πr²h
Hence:
Answer:16/81πr²h



Related Questions

The total number of points scored by each player throughout a season are listed on a roster by the player's jersey number. is this a function? explain your reasoning.

Answers

Yes, this would be a function.

Using ordered pairs to represent this, we would have (jersey #, points).  A relation is a function if no element of the domain matches more than one element of the range; in our case, the domain is the jersey number and the range is the number of points.

The jersey number will not match two numbers of points throughout the season; a player will only have one total number of points throughout the season.  Therefore no element of the domain matches more than one element of the range, and this is a function.

A)Yes, it is a function because each player's jersey number will have only one number for the points scored during the season.

Each jersey number has exactly one number for the total points scored by the player.

In a function, every input has exactly one output. In this situation, each jersey number is an input, and the total points scored for the season by the player is the output.

Sue Baker is given a prescription of MECLIZINE 25MG to be taken three times daily. She was given enough for ten days. She has been given her pills following the six "rights" (right resident, right drug, right dosage, right time, right route, right record/documentation). On the start of day four, how many pills should be in the bottle?

Answers

There should be 21 pills.

Assuming she started taking the pills the morning of the first day, 3 pills per day x 3 days = 9 pills.

She had enough for 10 days; 10 days * 3 pills per day = 30 pills

30 pills to begin with - 9 pills taken = 21 pills left

Find the base area of a rectangular pyramid whose pyramid height is 5 cm and slant height of one side of the base is 13 cm and another side of the base is 7 cm.

a. 92√6 cm^2 
b. 96√6 cm^2 
c. 180√6 cm^2
d. 100√6 cm^2
e. 198√6 cm^2

Answers

Let
x------> the larger side of the rectangular base
y-------> the smaller side of the rectangular base

we know that
Applying the Pythagoras theorem

for the larger side of the base
slant height =13 cm
h=5 cm
13²=5²+(x/2)²-----> (x/2)²=13²-5²-----> 144
(x/2)²=144------> x/2=12------> x=24 cm

for the smaller side of the base
slant height =7 cm
h=5 cm
7²=5²+(y/2)²-----> (y/2)²=7²-5²-----> 24
(y/2)²=24------> y/2=√24------> y=4√6 cm

the area of the base is
24*4√6------> 96√6 cm²

the answer is the option
b. 96√6 cm^2 


Which of the following rates is proportional to $2.50 for 5 cans?

A. $2.00 for 3 cans
B. $4.00 for 7 cans
C. $4.50 for 9 cans
D. $1.50 for 1 can

Answers

C. $4.50 for 9 cans would be the correct answer

Answer:

C. $4.50 for 9 cans

Step-by-step explanation:

Divide £770 in the ratio of 4:3 plsss

Answers

we'll simply divide the amount by 4+3, namely 770 ÷ (4+3) and split the amounts accordingly,

[tex]\bf 4:3\qquad \cfrac{4}{3}\qquad \cfrac{4\cdot \frac{770}{4+3}}{3\cdot \frac{770}{4+3}}\implies \cfrac{4\cdot 110}{3\cdot 110}\implies \cfrac{440}{330}[/tex]

One of the mutually exclusive results of an activity conditional probability 2. a combination of one or more outcomes independent events 3. a measure of likelihood of a given result event 4. compound events whose outcomes do not affect each other outcome 5. events involving two or more activities compound events 6. probability of one event given that another has occurred probability

Answers

outcome - one of the mutually exclusive results of an activity
probability - a measure of likelihood of a given result
compound events - events involving two or more activities
event - a combination of one or more outcomes
independent events - compound events whose outcomes do not affect each other
conditional probability - probability of one event given that another has occurred

From the information given about the probability, the appropriate terms that denotes them will be:

outcome - one of the mutually exclusive results of an activity.probability - a measure of the likelihood of a given result.compound events - events involving two or more activities.event - a combination of one or more outcomes.independent events - compound events whose outcomes do not affect each other.conditional probability - the probability of one event given that another has occurred,

Probability

It should be noted that probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur.

The probability of an event occuring is a number between 0 and 1. 0 indicates the impossibility of the event while 1 indicates certainty.

The outcome is one of the mutually exclusive results of an activity.

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A. 3
B. 5
C. 6
D. 10

Answers

C. 6
_________________

A family drove 2,275 miles from Los Angeles to Atlanta in a time span of 35 hours . Calculate their average speed in miles per hour .

Answers

look at my work in the picture and you’ll see the answer and how i got it

The family drove at an average speed of 65 mph from Los Angeles to Atlanta with a span length of 2275 miles

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

The equation for average speed is given as:

Average speed = Total distance / total time

Hence:

Average speed = 2275 miles / 35 hour = 65 mph

The family drove at an average speed of 65 mph from Los Angeles to Atlanta

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A notebook has a perimeter of 36 inches. It’s area is 80 square inches. What are the dimensions of the notebook

__inches by___ inches

Answers

Let's call he width of the notebook w and the length l

w*l=80

2(w+l)=36
w+l=18
w=18-l

(18-l)*l=80
-l^2+18*l-80=0
l=8 or 10

Therefore, the notebook is 8 by 10 inches


Final answer:

To solve for the dimensions of the notebook, we set up equations based on the perimeter and area, then solved the quadratic equation to find that the dimensions are 10 inches by 8 inches.

Explanation:

To find the dimensions of a notebook with a perimeter of 36 inches and an area of 80 square inches, we will use the formulas for the perimeter and area of a rectangle. The perimeter (P) of a rectangle is 2 times the length (l) plus 2 times the width (w), or P = 2l + 2w. The area (A) of a rectangle is length times width, or A = lw.

Given P = 36 and A = 80, we can set up two equations:

2l + 2w = 36l × w = 80

First, we simplify the perimeter equation to l + w = 18 by dividing everything by 2. We can then express w in terms of l: w = 18 - l. Now, we substitute w into the area equation: l(18-l) = 80. Expanding this gives us a quadratic equation: l2 - 18l + 80 = 0.

To solve the quadratic equation, we look for factors of 80 that add up to 18. The factors are 10 and 8, meaning the length is 10 inches and the width is 8 inches, since l = 10 and w = 8 satisfy both the area and perimeter equations.

Therefore, the dimensions of the notebook are 10 inches by 8 inches.

Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x3 and y = x. (10 points)

Answers

See the graph attached.

The midpoint rule states that you can calculate the area under a curve by using the formula:
[tex]M_{n} = \frac{b - a}{2} [ f(\frac{x_{0} + x_{1} }{2}) + f(\frac{x_{1} + x_{2} }{2}) + ... + f(\frac{x_{n-1} + x_{n} }{2})][/tex]

In your case:
a = 0
b = 1
n = 4
x₀ = 0
x₁ = 1/4
x₂ = 1/2
x₃ = 3/4
x₄ = 1

Therefore, you'll have:
[tex]M_{4} = \frac{1 - 0}{4} [ f(\frac{0 + \frac{1}{4} }{2}) + f(\frac{ \frac{1}{4} + \frac{1}{2} }{2}) + f(\frac{\frac{1}{2} + \frac{3}{4} }{2}) + f(\frac{\frac{3}{4} + 1} {2})][/tex]
[tex]M_{4} = \frac{1}{4} [ f(\frac{1}{8}) + f(\frac{3}{8}) + f(\frac{5}{8}) + f(\frac{7}{8})][/tex]

Now, to evaluate your f(x), you need to look at the graph and notice that:
f(x) = x - x³

Therefore:
[tex]M_{4} = \frac{1}{4} [(\frac{1}{8} - (\frac{1}{8})^{3}) + (\frac{3}{8} - (\frac{3}{8})^{3}) + (\frac{5}{8} - (\frac{5}{8})^{3}) + (\frac{7}{8} - (\frac{7}{8})^{3})][/tex]

[tex]M_{4} = \frac{1}{4} [(\frac{1}{8} - \frac{1}{512}) + (\frac{3}{8} - \frac{27}{512}) + (\frac{5}{8} - \frac{125}{512}) + (\frac{7}{8} - \frac{343}{512})][/tex]

M₄ = 1/4 · (2 - 478/512)
     = 0.2666

Hence, the area of the region bounded by y = x³ and y = x is approximately 0.267 square units.

Using the mid-point rule with n = 4, we approximate the area bounded by y = x³ and y = x b as 0.2578125.

To approximate the area of the region bounded by y = x³ and y = x using the mid-point rule with n = 4, we follow these steps:

Determine the points of intersection between y = x³ and y = x. Solving x³ = x, we get the points of intersection at x = 0 and x = 1.

Divide the interval [0, 1] into 4 subintervals, each of width Δx = (1 - 0)/4 = 0.25.

Calculate the midpoint of each subinterval: 0.125, 0.375, 0.625, and 0.875.

Evaluate the functions y = x³ and y = x at these midpoints:

At x = 0.125: y = x³ = 0.125³ = 0.001953125 and y = x = 0.125At x = 0.375: y = x³ = 0.375³ = 0.052734375 and y = x = 0.375At x = 0.625: y = x³ = 0.625³ = 0.244140625 and y = x = 0.625At x = 0.875: y = x³ = 0.875³ = 0.669921875 and y = x = 0.875

Determine the heights of the rectangles by finding the difference between the values of y:

At x = 0.125: Δy = 0.125 - 0.001953125 = 0.123046875At x = 0.375: Δy = 0.375 - 0.052734375 = 0.322265625At x = 0.625: Δy = 0.625 - 0.244140625 = 0.380859375At x = 0.875: Δy = 0.875 - 0.669921875 = 0.205078125

Compute the area of each rectangle (height × width) and then sum them up:

Area at x = 0.125: 0.123046875 × 0.25 = 0.03076171875Area at x = 0.375: 0.322265625 × 0.25 = 0.08056640625Area at x = 0.625: 0.380859375 × 0.25 = 0.09521484375Area at x = 0.875: 0.205078125 × 0.25 = 0.05126953125

Add the areas to get the total approximate area:

0.03076171875 + 0.08056640625 + 0.09521484375 + 0.05126953125 ≈ 0.2578125

Therefore, the approximate area of the region bounded by y = x³ and y = x using the mid-point rule with n = 4 is 0.2578125.

There are 100 students in a drawing contest, and 58 of them are girls. What percent of the students in the contest are girls?

Answers

You take 58/100 and you’ll get your answer and you should get 58%

There are 100 students in a drawing contest and 58 of students are girls. What percent of students in the drawing contest are girls?

The fraction [tex]\frac{58}{100}[/tex] represents the number of girls in the drawing contest out of all the students.

To find out what percent of the students are in the drawing contest, we can change [tex]\frac{58}{100}[/tex] into a percent.

We can first reduce the fraction by dividing both the numerator and denominator by the Greatest Common Factor of 58 and 100 using 2.

58 ÷ 2 = 29

100 ÷ 2 = 50

Our reduced fraction is [tex]\frac{29}{50}[/tex].

29 ÷ 50 = 0.58

0.58 × 100 = 58%

Therefore, 58% of the students in the drawing contest are girls.

Chiara pays $21 for 3 DVDs that she finds in a one-price bin. Gunther wants to know how much he would spend for 1 DVD in this bin. Chiara wants to know how many dollars she will need to purchase 9 DVDs the next time she goes.

Answers

Gunther would spend $7 for 1 DVD. Chiara would need $63 for 9 DVD's
To figure out what one DVD would cost, we take our information "$21 for 3 DVD's." All you have to do here is do $21 divided by 3 DVD's to find that one DVD is $7.

If Chiara wants to purchase 9 DVD's next time and needs to know the money, we take our previous information (1 DVD = $7) and input it into this equation.

x (unknown dollars) = 9 (DVD) * 7 ($).

Meaning that 9 * 7 = 63.

It will cost $63 for 9 DVD's, when 1 DVD is $7.

______________ is process that you can do over and over, where each result does not affect the next.
Ex. Flipping a coin, rolling dice, choosing a card, etc.

Answers

In probability, an experiment is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes. Thus, an experiment is a process that you can do over and over, where each result does not affect the next. For example: Flipping a coin, rolling dice, choosing a card, etc. are all experiments.

Suppose f(x) = x. Find the graph of f(x+1)

Answers

Given:
 
f(x) = x

Therefore, if f(x) = x, than f(x + 1) = x + 1, for with an equal sign, what you do to one side, you do to the other.

Answer:

f(x + 1) = x + 1


hope this helps

Rovide an appropriate response.4) assume that adults have iq scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the wechsler test). find the iq score separating the top 14% from the others. 4)

Answers

9484 hope i helped u

Christopher is analyzing a circle, y^2 + x^2 = 121, and a linear function g(x). Will they intersect?



A. Yes, at the positive x coordinates.


B. Yes, at negative x coordinates.


C. Yes, at the negative and positive x coordinates.


D. No, they will not intersect

Answers

Circle: x^2+y^2=121=11^2 => circle with radius 11 and centred on origin.
g(x)=-2x+12   (from given table, find slope and y-intercept)
We can see from the graphics that g(x) will be almost tangent to the circle at (0,11), and that both intersection points will be at x>=11.
To show that this is the case, 
substitute g(x) into the circle
x^2+(-2x+12)^2=121
x^2+4x^2-2*2*12x+144-121=0
5x^2-48x+23=0
Solve using the quadratic formula,
x=(48 ± √ (48^2-4*5*23) )/10
=0.5058 or 9.0942
So both solutions are real and both have positive x-values.

Yes, they will intersect at the positive x coordinates.

What is the equation of the circle?

The standard equation of a circle is: (x-h)^ 2 + (y-k) ^2 =r ^2 Where (h, k) is the coordinates of the center, and r is the radius of the circle.

Christopher is analyzing a circle, y^2 + x^2 = 121, and a linear function g(x). Will they intersect?

The given equation of the circle is;

[tex]\rm x^2+y^2=121\\\\x^2+y^2=11^2[/tex]

The circle with center at (0,0) and radius r = 11 units and g(x) points (-1,14)  (0,12)  (1,10).

The linear function is;

[tex]\rm y=mx+b[/tex]

From the graph on drawing all the co-ordinates lies in positive x and y axis.

Hence, they will intersect at the positive x coordinates.

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if 3x+2y=12 and -4x+6y=24 what is the value of -x+2y

Answers

(1) 3x+2y=12
(2) -4x+6y=24

Solving the system of equations using the method of substitution:
Isolating y in the first equation:
(1) 3x+2y=12→3x+2y-3x=12-3x→2y=12-3x→2y/2=(12-3x)/2→y=(12-3x)/2

Replacing "y" by (12-3x)/2 in the second equation:
(2) -4x+6y=24
y=(12-3x)/2→-4x+6[(12-3x)/2]=24

Solving for x:
-4x+3(12-3x)=24
-4x+36-9x=24
-13x+36=24
-13x+36-36=24-36
-13x=-12
-13x/(-13)=-12/(-13)
x=12/13

Replacing "x" by 12/13 in y=(12-3x)/2
x=12/13→y=[12-3(12/13)]/2
y=(12-36/13)/2
y={[(13)(12)-36]/13}/2
y=[(156-36)/13]/2
y=(120/13)/2
y=(120/13)(1/2)
y=60/13

x=12/13; y=60/13
-x+2y=-12/13+2(60/13)
-x+2y=-12/13+120/13
-x+2y=(-12+120)/13
-x+2y=108/13

Answer: The value of -x+2y is 108/13 

BRAINLIEST!!PLS HELP!
Question 19 Unsaved
Ann office building has the same number and size of office units per floor. If there are 21 units on the first 3 floors, then what is the total number of offices in the 10 story building?

Question 19 options:

7


24


63


70

Answers

Your answer would be 70

10 divided by 3=3.33
3.33 times 21= 70
The answer you are looking for is 70.

There are a couple ways to find this. You could...

A. Since the question states "21 units on the first 3 floors" you could multiply 21 and 10 to get 210 (number of units if there were 21 on each floor), then divide it by 3 to find the total number in the building. Dividing by 3 compensates for the 21 units on the first 3 floors. Or...

B. Divide 21 by 3 to find how many units are on each floor (7), then multiply by the number of floors in the building (10). Either way, both ways will give you 70.

I hope this helps!

Which of the following choices is the value of cscΘ?

a) 12/15

b) 9/15

c) 15/12

D) 15/9

Answers

r² = 12² + 9²

r² = 144 + 81

r² = 225

r = √225

r = 15

For Θ,

Base = 9
Perpendicular = 12
Hypotenous = 15


cscΘ = Hypotenous/Perpendicular

= 15/12

Ans:- Option c)15/12

Hope this helps!

Find the coordinate of the point (x,y) shown on the unit circle

Answers

Here the angle is

[tex]\frac{4 \pi}{3}[/tex]

And radius is 1 units .

And

[tex]x = r cos  \theta, y = r sin  \theta[/tex]

Substituting the values of theta and r, we will get

[tex]x = 1 cos(\frac{4 \pi}{3} ) = -1/2 \\ y=1 sin( \frac{4 \pi}{3} ) =\sqrt3 /2[/tex]

So we will get

[tex]x = \frac{-1}{2} , y = -\frac{ \sqrt 3}{2}[/tex]

The coordinate of the point (x,y) shown on the unit circle is therefore: (-1/2, -√3/2)

The circle given is a unit circle.

In essence, the radius as indicated by the blue line is 1.

The angle subtended by the line is; 4π/3.

Therefore, from trigonometry of right-angled triangles; we have;

x = r Cos(4π/3)

y = r Sin(4π/3)

where, r = 1

Therefore,

x = -1/2y = -√3/2

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Which compound inequality can be used to solve the inequality |3x+2|>7

Answers

Answer:

x>[tex]\frac{5}{3}[/tex].

Step-by-step explanation:

We have given an  inequality |3x+2|>7.

We need to solve this inequality |3x+2|>7, and find the compound which can solve this.

We know that,  inequality :

|3x+2|>7

Subtrating 2 from both sides,

|3x+2-2|>7-2

3x>5

Dividing by 3 both sides,

[tex]\frac{3x}{3} > \frac{5}{3}[/tex]

x>[tex]\frac{5}{3}[/tex]

Therefore, we can see that on the inequality |3x+2|>7, we find x>[tex]\frac{5}{3}[/tex] compound.

Answer:

D. 3x + 2 < –7 or 3x + 2 > 7

Step-by-step explanation:

Aaron solved an inequality and then graphed the solution as shown below. Anwser: A

A student found the solution below for the given inequality lx-9l less than 4

Anwser: D

Amber is solving the inequality lx+6l - 12 less than 13 by graphing. Which equations should Amber graph?

Anwser: A

What is the solution, if any, to the inequality l3xl greater than or equal to 0?

Anwser: A

Which compound inequality is equivalent to lax-bl greater than c  for all real numbers a, b, and c, where c is greater than or equal to 0?

Anwser: D

Which compound inequality is equivalent to the absolute value inequality lbl greater than 6?

Anwser: D

What is another way to write the absolute value inequality lpl less than or equal to 12?

Anwser: A

What is the solution to the inequality lx-4l less than 3?

Anwser: B

Which inequality is equivalent to lx-4l less than 9?

Anwser: B

Hope This Helps!

Give the dimensions of a cuboid with a volume of 18cm to the power 3.

Answers

we know that
volume of a cuboid=length*width*height

in this problem
we have 
volume=(18 cm)³
so
volume=18*18*18 cm³

the dimensions of the cuboid are
length 18 cm
width 18 cm
height 18 cm
 18 cm x 18 cm x 18 cm

Write x2 − 2x − 3 = 0 in the form (x − a)2 = b, where a and b are integers.


A.(x − 4)2 = 3

B.(x − 3)2 = 2

C.(x − 2)2 = 1

D.(x − 1)2 = 4

Answers

[tex]x^2-2x-3=0\\\\x^2-2\cdot x\cdot1+1^2-1^2-3=0\\\\(x-1)^2-4=0\ \ \ \ |+4\\\\(x-1)^2=4[/tex]


Answer: D. (x - 1)² = 4.

Used:
(a - b)² = a² - 2ab +

Ronald and Tim both did their laundry today. Ronald does laundry every 666 days and Tim does laundry every 999 days.
How many days will it be until Ronald and Tim both do laundry on the same day again?

Answers

It will be 18 days.

We want the least common multiple (LCM) of 6 and 9.  First we find the prime factorization:
6 = 2*3
9 = 3*3

They have a 3 in common; we use this first in the LCM.  Then we take the "leftover" factors, 2 and 3:
LCM = 3*2*3 = 18

Answer:

18

Step-by-step explanation:

In 2010, 100 japanese yen purchased .88 u.s. dollars and in 2013, it purchased .93 u.s. dollars. how much was 1 u.s. dollar worth in japanese yen, in 2010 and 2013?

Answers

To find how many Japanese yen $1 was worth in 2010 and 2013, you will create ratios with the information we know and then solve for the number of yen.

2010:

100 yen    x yen  (use cross products to solve for x yen)
$0.88   =   $1
100 = 0.88x
0.88   0.88

x = 113.6 yen

In 2010, $1 was worth approximately 114 yen.


2013:

100 yen    x yen
$0.93   =   $1

100 = 0.93x
0.93   0.93
x = 107.5

In 2013, $1 was worth approximately 108 yen.

Write an equation that you can use to solve for x.

Enter your answer in the box.

Answers

The given angle ( 47 degrees) and x are supplementary angles, which equal 180 degrees.
 
 So x would equal 180 degrees minus 47 degrees

This can be written as x = 180-47 

x = 133 degrees

133 degrees is your answer

Every day for two full weeks (14 days) jimmy records the number of coins in his pocket. he finds that the mean is 27. he decides to remove one sunday's total because it was an outlier. his new mean is 18 coins. how many coins did he have in his pocket on the sunday he removed?
a.18
b.27
c.126
d.144

Answers

(18+x)/2=27
18+x=54
x=36
What have I done wrong?

Answer:

It is D.)144

Step-by-step explanation:

The volume of a cylinder is given by the formula v=pi r^2h, where r is the radius of the cylinder and h is the height. Which expression represents the volume of this cylinder? h=2x+7, r=x-3.

Answers

Substituting for r and h:-

volume = pi (x - 3)^2 *  (2x + 7)

=   pi* (2x + 7)(x^2 - 6x + 9)
= pi *  (2x^3 - 12x^2 + 18x + 7x^2 - 42x + 63)
= (2x^3 - 5x^2 - 24x + 63) pi  answer

What is the equation of a circle with center (8, 4) and radius 7?

Answers

Final answer:

The standard form of the equation of a circle is given by (x-h)² + (y-k)² = r², where (h, k) are the center and r is the radius. For a circle with center at (8, 4) and radius 7, the equation of the circle becomes (x - 8)² + (y - 4)² = 49.

Explanation:

The equation of a circle in standard form is given by (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the center of the circle and r is the radius. This formula comes from Pythagorean theorem and how a circle is defined as the locus of points equidistant from a given point (the center).

By substituting the given center and radius into this formula, we can write the equation of the specific circle you're asking about. The center of this circle is (h, k) = (8, 4), and its radius is r = 7. Therefore, the equation of the circle is (x - 8)² + (y - 4)² = 7² or (x - 8)² + (y - 4)² = 49.

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Final answer:

The equation of the circle is (x-8)^2 + (y-4)^2 = 49.

Explanation:

The equation of a circle with center (h, k) and radius r is given by the formula:

(x-h)2 + (y-k)2 = r2

In this case, the center is (8, 4) and the radius is 7. So, the equation of the circle is:

(x-8)2 + (y-4)2 = 72

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Simplify the questions that aren't crossed on the attachment, thank you

Answers

(3) (x - 2 +3(x +1))/3 = (4x+1)/3

(5) (3(x +1) +4x)/(x(x +1)) = (7x+3)/(x² +x)

(7) same as (5)

(8) (a(a +4))/((a -1)(a +4)) = a/(a -1) . . . . . a ≠ -4

(11) (2a -3b)/(4a(2a -3b)) = 1/(4a)
Other Questions
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