Which of the following shows the correct simplification assuming the denominator is not equal to zero?

Which Of The Following Shows The Correct Simplification Assuming The Denominator Is Not Equal To Zero?

Answers

Answer 1

Answer:

[tex]=\frac{3x+2}{x\left(x+1\right)}[/tex]

or

[tex]\frac{(3x+2)}{x^2+x}[/tex]

Step-by-step explanation:

[tex]\frac{2}{x}+\frac{1}{x+1}\\\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x+1:\quad x\left(x+1\right)\\Adjust\:Fractions\:based\:on\:the\:LCM\\Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:x\left(x+1\right)\\\mathrm{For}\:\frac{2}{x}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:x+1\\\frac{2}{x}=\frac{2\left(x+1\right)}{x\left(x+1\right)}\\[/tex]

[tex]\mathrm{For}\:\frac{1}{x+1}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:x\\\frac{1}{x+1}=\frac{1\cdot \:x}{\left(x+1\right)x}=\frac{x}{x\left(x+1\right)}\\=\frac{2\left(x+1\right)}{x\left(x+1\right)}+\frac{x}{x\left(x+1\right)}\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{2\left(x+1\right)+x}{x\left(x+1\right)}\\[/tex]

[tex]\mathrm{Expand}\:2\left(x+1\right)+x:\quad 3x+2\\2\left(x+1\right)+x\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=2,\:b=x,\:c=1\\=2x+2\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:1=2\\=2x+2\\\mathrm{Simplify}\:2x+2+x:\quad 3x+2\\2x+2+x\\\mathrm{Group\:like\:terms}\\=2x+x+2\\\\mathrm{Add\:similar\:elements:}\:2x+x=3x\\=3x+2\\=\frac{3x+2}{x\left(x+1\right)}[/tex]


Related Questions

Solve for x: 3x − 2 > 5x + 10.

Answers

Answer: hopefully this is what you need

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality form:

X < -6

Interval Notation:

(-♾, -6)

1. Is the following quadratic equation in standard form?
y = – 3x^2+ 2x - 4
No
Yes

Answers

Answer:

Yes this equation is in standard form.

Answer:

yes this equation is in standard form

What happens if you decide to cash in your Certificate of Deposit (CD) before its maturity date?

Answers

Answer:

If you decide you need your funds before the maturity date, you'll pay an early withdrawal penalty.

Step-by-step explanation:

I have a book on this kinda stuff! :D

Answer:

If you decide you need your funds before the maturity date, you'll pay an early withdrawal penalty.

Step-by-step explanation: ED2022

What are the rules of simplifying exponents?

Answers

Answer:

To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, (23)5 = 215. For any positive number x and integers a and b: (xa)b= xa· b.

Step-by-step explanation:

Please help I don’t understand

Answers

Answer:

B

Step-by-step explanation:

Find the midpoint between the points (-6, -2) and (-3, -7)

Answers

The midpoint is (-9/2, -9/2)

Answer:

(-4.5, -4.5)

Step-by-step explanation:

To find the midpoint add the x coordinates and divide by 2

(-6+-3)/2 = -9/2 = -4.5

Then add the y coordinates and divide by 2

(-2+-7)/2 = -9/2 = -4.5

14) Simplify. 6(3x - 5) + 2(3x - 5) - 8(3x - 5)

Answers

Answer:

0

Step-by-step explanation:

To simplify you need to distribute then add like terms.

6(3x-5) + 2(3x-5) - 8(3x-5)

18x - 30 + 6x - 10 - 24x + 40

0x + 0

0

Answer:

6(3x - 5) + 2(3x - 5) - 8(3x - 5) = 0

Step-by-step explanation:

The expression is,

→ 6(3x - 5) + 2(3x - 5) - 8(3x - 5)

Now we have to,

→ Simplify the given expression.

Let's simplify the expression,

→ 6(3x - 5) + 2(3x - 5) - 8(3x - 5)

Applying Distributive property:

→ 6(3x) - 6(5) + 2(3x) - 2(5) - 8(3x) - 8(-5)

→ 18x - 30 + 6x - 10 - 24x + 40

Rearranging the expression:

→ 18x + 6x - 24x - 30 - 10 + 40

→ (18 + 6 - 24)x - (30 - 10 + 40)

→ 0x - 0

0 => {final answer}

Therefore, the answer is 0.

10. Two sides of a triangle have
the following measures. Find the
range of possible measures for
the third side.

35, 29

1) 7 2) 6 3) 08 4) 9

Answers

I think the answer is 6 from the information you provided.

HELP ASAP 30 POINTS!~!!!


You start with a penny which doubles each day for 30 days. How much money would you have after 30 days?

Answers

I got 536870912 hope this helps

josh built a circular flower bed in his backyard. the radius of the flower bed is 12 feet. he wants to find the circumference of the flower bed. he uses 3.14 for pi. what is the approximate circumference for the flower bed?

Answers

75.34

Step-by-step explanation:

1.To find the circumference, you have to multiply the diameter times pi (3.14).

2.The radius (12) is half of the diameter

3. The diameter (12x2) is 24.

4. 24x3.14 is 75.36

So, the approx. circumference is 75.36.

Answer:

Step-by-step explanation:

Answer:75ft

There were 23 students running in a race. How many different arrangements of first, second, and third place are possible?

Answers

Answer:

10626 different arrangements

Step-by-step explanation:

As we have a total of 23 students and we want to form groups of 3, where the order of the 3 students matters, we can solve this problem using a permutation of 23 choose 3.

The formula for a permutation of n choose p is:

P(n,p) = n! / (n-p)!

So, using n = 23 and p = 3, we have:

P(23,3) = 23! / (23-3)! = 23! / 20! = 23 * 22 * 21 = 10626

So we have a total of 10626 different arrangements of first, second and third place.

208 divided by 6.4
What is the quotient for the equation above?
3.25
32.5
325
3,250

Answers

Answer:

B)32.5

Step-by-step explanation:

hope this helps

Answer:

32.5 or B

Step-by-step explanation:

good luck on the rest of your quiz

evaluate the following function for x=-4 f[x]=2x+5

Answers

Answer:

-3

Step-by-step explanation:

substitute -4 into the equation f(x)

2÷9/10=
please help thanks

Answers

Answer:

0.02 repeating

Step-by-step explanation:

So first we do 2/9 since all the operations are division we solve left to right. We get 0.2 repeating. Then, after that whenever we divide by 10, we shift everything to the right so we end up with :

0.02 repeating.

SOMEONE HELP PLSSS
suppose your friends parents invest $10,000 in an account paying 5% compounded annually. what will the balance be after 5 years?

Answers

Answer:

12,762.82$

Step-by-step explanation:

10,000(1+0.05)^5

If r+s/r =3 and t+r/t =5, what is the value of s/t ? (A) 12 (B) 35 (C) 4 (D) 8 (E) 16

Answers

Answer:

The answer of this question is (D) 8

Will Give Brainliest!!!! On Time Limit Hurry Please Wrong answer will be deleted!!
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation? (negative 5 minus StartRoot 34 EndRoot comma negative 5 + Startroot 34 EndRoot) (negative 5 minus StartRoot 29 EndRoot comma negative 5 + StartRoot 29 EndRoot) {–12, 2} {–2, 12}

Answers

Answer:

x = - 12, x = 2

Step-by-step explanation:

Given

x² + 10x = 24

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = 24 + 25

(x + 5)² = 49 ( take the square root of both sides )

x + 5 = ±  = ± 7 ( subtract 5 from both sides )

HOPE THIS HELPS

Answer:

x  =  2 ,  − 12

Step-by-step explanation:

Use the formula  ( b /2 ) (^)2  in order to create a new term. Solve for  x  by using this term to complete the square.

Logan is 4 times older than his cousin Dylan .Logan is less than 12 years old.which inequality shows the possible age Dylan could be.
A. d< 3
B . d > 3
C. d < 48
D. d > 48

Answers

i think the answer is a because if logan is 4 times older than dylan and dylan is less than 12 years old then that means that logan is older than dylan. which means that since logan isn’t older than 12 dylan also can’t be older than 12 which cancels out both c and d. it can’t be b because if logan is 4 times older than dylan that would most likely mean dylan is less than 3 so the correct answer (for me i might be wrong) is a
hope this helped

What is 2.08x10^7 written in standard notation?

Answers

Answer:

D) 20,800,000

Step-by-step explanation:

What is the solution to the equation sqrt2x+6-sqrtX+4=1?

Answers

Answer:

the first answer is 5

the second answer is 23

Step-by-step explanation:

edge

Answer:

x=5 and the other one is x=23

Step-by-step explanation:

A rectangular prism has a length of 12 feet, a height of 13 feet, and a width of 8 feet. What is its volume, in cubic feet?

Answers

Answer:

1248 cubic feet

Which number in the set {6, 12, 18, 36} satisfies the equation 3x-9=27?

Answers

Answer:

12

Step-by-step explanation:

3x-9=27

3x=36

x=12

How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) = StartFraction 1 Over x EndFraction?
g(x) is shifted 4 units right and 6 units up from f(x).
g(x) is shifted 4 units right and 6 units down from f(x).
g(x) is shifted 4 units left and 6 units up from f(x).
g(x) is shifted 4 units left and 6 units down from f(x).

Answers

Answer:

Option D.

Step-by-step explanation:

The given parent function is

[tex]f(x)=\dfrac{1}{x}[/tex]

The given function is

[tex]g(x)=\dfrac{1}{x+4}-6[/tex]

Using the parent function, the given function can be written as

[tex]g(x)=f(x+4)-6[/tex]        ...(1)

The translation is defined as

[tex]g(x)=f(x+a)+b[/tex]        .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2), we get

[tex]a=4>0[/tex], it means the graph shifts 4 units left.

[tex]b=-6<0[/tex], it means the graph shifts 6 units down.

So, g(x) is shifted 4 units left and 6 units down from f(x).

Therefore, the correct option is D.

Transformation involves changing the form of a function.

The true option is (d) g(x) is shifted 4 units left and 6 units down from f(x).

The functions are given as:

[tex]g(x)= \frac{1}{x + 4} - 6[/tex]

[tex]f(x)= \frac{1}{x}[/tex]

Start by shifting the function to the left, by 4 units.

This is represented as:

[tex](x,y) \to (x + 4,y)[/tex]

So, we have:

[tex]f'(x)= \frac{1}{x + 4}[/tex]

Next, shift the function down, by 6 units.

This is represented as:

[tex](x,y) \to (x,y - 6)[/tex]

So, we have:

[tex]g(x)= \frac{1}{x + 4} - 6[/tex]

Hence, the true option is (d)

Read more about transformation at:

https://brainly.com/question/12619643

SHOW WORK: Evaluate f(-2)

f(x)= 3/2x-4​

Answers

Answer:

f(-2)=-5

Step-by-step explanation:

f(-2) = 3/2(-2) -4

f(-2)= -3-2

f(-2)= -5

Evaluation of f(-2)=-5.

What is the function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

How to solve?

f(x)=3/2(x)-4

f(-2) = 3/2(-2) -4

f(-2)= -3-2

f(-2)= -5

Learn more about Functions:

https://brainly.com/question/11624077

#SPJ2

Find the length of DF

Answers

Answer:

7x-58

just add all the terms

3x-28+3x-30+x
7x-58 =33
7x=91
X=13
Soooo df= 6x-58
6*13-58=20
20 is the correct answer

A city has an elevation of –752 feet. Which statement describes the city’s elevation?
–752 above sea level
–752 below sea level
752 above sea level
752 below sea level

Answers

Answer:

it is 752 blow sea level

Step-by-step explanation:

just now took it

Answer:

752 below sea level

is the correct answer the other person was right

Step-by-step explanation:

just answered the question

Help Resources
Find the maximum value of
C = 3x + 2y
Subject to the following constraints:
x > 0
y>0
x + 3y <15
4x + y <16
Enter

Answers

Answer:

Given:

x > 0

y > 0

And,

x + 3y < 15

4x + y < 16

<=>

4x + 12y < 60

4x + y < 16

<=>

11y < 44

<=> y < 4

Otherwise

x + 3y < 15

4x + y < 16

<=>

x + 3y < 15

12x + 3y < 48

<=>

11x < 33

<=>

x < 3

=> C = 3x + 2y < 3*3 + 2*4 = 9 + 8 = 17

=>  C < 17

Hope this helps!

:)

The maximum value of  C is an illustration of objective functions

The maximum value of C is 25

The objective function is given as:

[tex]\mathbf{C = 3x + 2y}[/tex]

The constraints are:

[tex]\mathbf{x + 3y < 15}[/tex]

[tex]\mathbf{4x + y < 16}[/tex]

[tex]\mathbf{x,y > 0}[/tex]

Plot the graphs of the constraints

From the graph (see attachment), the only optimal point is (3,4)

Substitute 3 for x and 4 for y in the objective function.

So, we have:

[tex]\mathbf{C = 3x + 2y}[/tex]

[tex]\mathbf{C = 3(3) + 2(4)}[/tex]

[tex]\mathbf{C = 9 + 8}[/tex]

[tex]\mathbf{C = 17}[/tex]

Hence, the maximum value of C is 17

Read more about optimizing functions at:

https://brainly.com/question/14778650

Which shows the pre-image of triangle X'Y'Z' before the figure was rotated 90° about the origin?

On a coordinate plane, a triangle has points X prime (negative 2, 2), Y prime (0, 6), Z prime (1, 1).

On a coordinate plane, a triangle has points X (2, negative 2), Y (6, 0), Z (1, 1).
On a coordinate plane, a triangle has points X (2, 2), Y (6, 0), and Z (1, negative 1).
On a coordinate plane, a triangle has points X (negative 2, negative 2), Y (6, 0), Z (negative 1, 1).
On a coordinate plane, a triangle has points X (negative 2, 2), Y (negative 6, 0), Z (negative 1, negative 1).

Answers

A rotation of 90° about the origin includes the interchange of the position of  x, and y in the ordered pair and a change of one of the signs of the pair.

The option that shows the pre-image of triangle X'Y'Z' before the figure was rotated 90° about the origin is the option;

On a coordinate plane, a triangle has points X(2, 2), Y(6, 0), and Z(1, -1).

Reasons:

The given transformation the gives the X'Y'Z' = 90° rotation about the origin

The given coordinates of X'Y'Z' are;

X'(-2, 2), Y'(0, 6), and Z'(1, 1)

Required:

The figure that shows the preimage of X'Y'Z'

Solution:

Given that X'Y'Z' is obtained by the rotation of XYZ 90°, therefore, the

coordinates of XYZ are given by the rotation of X'Y'Z' in the reverse

direction either counterclockwise and clockwise.

(x, y) [tex]\underrightarrow {R_{90^{\circ}}}[/tex] (-y, x)

(x, y) [tex]\underrightarrow {R_{-90^{\circ}}}[/tex] (y, -x)

Therefore, we have;

X'(-2, 2) [tex]\underrightarrow {R_{90^{\circ}}}[/tex] X(-2, -2)

Y'(0, 6) [tex]\underrightarrow {R_{90^{\circ}}}[/tex] Y(-6, 0)

Z'(1, 1) [tex]\underrightarrow {R_{90^{\circ}}}[/tex] Z(-1, 1)

Similarly, we get;

X'(-2, 2) [tex]\underrightarrow {R_{-90^{\circ}}}[/tex]  X(2, 2)

Y'(0, 6) [tex]\underrightarrow {R_{-90^{\circ}}}[/tex]  Y(6, 0)

Z'(1, 1) [tex]\underrightarrow {R_{-90^{\circ}}}[/tex] Z(1, -1)

The above coordinates of XYZ; X(2, 2), Y(6, 0), and Z(1, -1), corresponds to

the option;

On a coordinate plane, a triangle has points X(2, 2), Y(6, 0), and Z(1, -1).

Therefore, XYZ was rotated 90° clockwise to form X'Y'Z'

Learn more about rotation transformation here:

https://brainly.com/question/4738741

Answer: the first box is 90 degrees and the second box is 2 :D

Step-by-step explanation: ed 2020

hope you have a goody day / night ^^

Name the values represented by the box plot.

Lower quartile:

Upper quartile:

Median:

Answers

Answer: The lower quartile is 10, the upper quartile is 21, and the median is 17.

Step-by-step explanation:

Answer:

It sould be 5,10,26

Step-by-step explanation:

Use DeMoivre’s Theorem to find (3cis(pi/6))^3.
a.) (27sqrt3)/2 +27/2 i
b.) (9sqrt3)/2 +9/2 i
c.) 27i
d.) 9i

Answers

Answer:

C. 27i

Step-by-step explanation:

Given the complex number in polar coordinate expressed as

z = r(cos∅+isin∅)

zⁿ =  {r(cos∅+isin∅)}ⁿ

According to DeMoivre’s Theorem;

zⁿ =  rⁿ(cosn∅+isinn∅)

Given the complex number;

(3cis(pi/6))^3

= {3(cosπ/6 + isinπ/6)}^3

Using  DeMoivre’s Theorem;

= 3³(cos3π/6 + isin3π/6)

=  3³(cosπ/2 + isinπ/2)

= 3³(0 + i(1))

= 27i

The right answer is 27i

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