Which expression is equivalent to the following complex fraction?

Which Expression Is Equivalent To The Following Complex Fraction?

Answers

Answer 1

Answer:

Option B

Step-by-step explanation:

Numerator:

[tex]\dfrac{3}{x -1 }-4 =\dfrac{3}{x-1}-\dfrac{4*(x-1)}{x-1}\\\\[/tex]

                 [tex]=\dfrac{3- 4x -4*(-1)}{x-1}=\dfrac{3-4x+4}{x-1}\\\\\\=\dfrac{-4x+7}{x-1} \: \textbf{ [Combine like terms]}[/tex]

Denominator:

[tex]2-\dfrac{2}{x-1}=\dfrac{2*(x-1)}{x-1}-\dfrac{2}{x-1}\\[/tex]

                [tex]= \bf \dfrac{2x-2-2}{x-1}\\\\\\= \dfrac{2x-4}{x-1}\\\\= \dfrac{2*(x- 2)}{x-1}[/tex]

[tex]\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}=\dfrac{\dfrac{-4x+7}{x-1}}{\dfrac{2*(x-2)}{x-1}}[/tex]

                 [tex]\bf = \dfrac{-4x+7}{x-1}*\dfrac{x-1}{2(x-2)} \ \ \ \textbf{ [(x-1) in the numerator and denominator will be cancelled]}\\\\\\=\dfrac{-4x+7}{2(x-2)}[/tex]


Related Questions

There are two boys and a girl on a trivia team. Two questions remain. One team member is randomly picked to answer the first question and a different member is picked to answer the second question.

Answers

Answer:

There are two boys and a girl on a trivia team. Two questions remain. One team member is randomly picked to answer the first question and a different member is picked to answer the second question.

Step-by-step explanation:

A suit is on sale for 72% off. The sale price is $263.20.
What is the regular price?

Answers

Answer:

940

Step-by-step explanation:

To find the original price of something that been discount do the following:

Subtract the discount from 100 to get the percentage of the original price.Multiply the final price by 100.Divide by the percentage in Step One.

Or we can do the following:

We shall consider the original price as x; hence the discount can be considered as (x−263.20). We can write the equation:

x · 72/100=x - 263.20

x · 18/25 = x - 263.20

Multiply both sides by 25

18x = 25(x - 263.20)

Open the brackets.

18x = 25x-6580

Add 6580 to each side.

6580 +18x = 25x

Subtract 18x from each side.

6580 = 7x

Subtract 7x from each side.

x = 940

Check Answer:

940 * 72% = 676.80

940 - 676.80=263.20

Hence, the regular price is 940.

~lenvy~

Step-by-step explanation:

The sale price ( The marked price ) :- $263.20

Discount :- 72%

Discount :- marked 100 ,Discount 72 ,Seliing ( Regular ) 28

Regular price :- 263.20 × 28 / 100

$ 73.69

Please help solve this SAT math problem. I have 4 more like these so need help with this so that I can solve the rest by myself. Thank you.

Answers

The notation just means

(f/g)(-4) = f(-4) / g(-4)

If f(x) = x² + 2 and g(x) = 1 - 3x, then

f(-4) = (-4)² + 2 = 16 + 2 = 18

g(-4) = 1 - 3 (-4) = 1 + 12 = 13

and so

(f/g)(-4) = 18/13

Use the diagram at the right to find the trigonometric ratio​

Answers

Answer:

sin C=20/25=4/5

cos C=15/25=3/5

tan C=20/15=4/3

Step-by-step explanation:

sine is opposite/hypotenuse

cosine is adjacent/hypotenuse

tangent is opposite/adjacent

how do I do it? I didn't understand the math.

Answers

Answer:

please try do the rest by yourself..Of you didn't get the answer you can ask me through comment..

f(x)=x-5 is the function linear quadratic exponential or neither ​

Answers

Answer:

Linear

Step-by-step explanation:

It is a first-degree function, the variable "x" has power 1

when graphed, a straight line results in

Hope this helps

What is the distance
between (-6, -2) and (2, 4)?

Answers

Answer:

10

Step-by-step explanation:

distance = √(-6-2)^2+(-2-4)^2

Ans=10

[tex]\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ [/tex]

[tex] \rule{60mm}{2.2pt}[/tex]

[tex] \large \purple{ \rm{Given ↦}} \\ [/tex]

A ( -6 , -2 ) ( x1 , y1 )B ( 2 , 4 ) ( x2 , y2 )

[tex] \rule{60mm}{2.2pt}[/tex]

[tex] \large \purple{ \rm{By \: DISTANCE \: FORMULA ↦}} \\ \\ \rm{AB =\sqrt{( x2-x1)^{2} +(y2-y1) ^{2} }}[/tex]

[tex] \rule{60mm}{2.2pt}[/tex]

Substituting values

[tex] \bold {AB= \sqrt{( - 6 - 2 )^{2} + ( - 2 - 4) ^{2}} } \\ \\ \bold {AB= \sqrt{( - 8) ^{2} + ( - 6) ^{2} }} \\ \\ \bold {AB= \sqrt {(64) + (36)} } \\ \\ \bold {AB= \sqrt{(100)}} \\ \\ \bold {AB= 10 \: units.}[/tex]

[tex]\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}} \orange{ \rule18mm{2.5pt}}[/tex]

[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]

What is the equation of the axis of symmetry?

Answers

Answer: x=7
Explanation: graph :)

prism x is showen below. the volume of prism y is 10 cubic cm greater than the volume of prism x. what is the volume of prism y.

Answers

Answer:

it’s 3 x 2x 5 = 30

Then use that product and times it by 10. ( 10 x 30 )

Ans = 300 cubic centimeters

Step-by-step explanation:

3 x 5 x 2 = 30


30 x 10 = 300

Ans = 300 cubic centimeters

The second term of a geometric progression is -576 and the fifth term is 243. Find:

a) the common ratio
b) the first term
c) the sum to infinity.​

Answers

The answor is C because the sun the infinity is infatuated

(11x-5) degrees + (6x+5) degrees

Answers

Answer:

Answer: x = 10 degrees.

Step-by-step explanation:

What is the value of x? 1/6 (3 - 2x) < 1/3 x

Answers

Step-by-step explanation:

1/6 (3 - 2x) < 1/3 x

let's multiply everything by 6

3 - 2x < 6/3 x

3 - 2x < 2x

3 < 4x

3/4 < x

so, x > 3/4

since 3/4 is never equal to x but is purely smaller than x, the interval of valid x values starts right after 3/4 and goes to infinity.

x = 3/4 is not valid, because 3/4 is not smaller than 3/4 (it is equal to) ...

[tex] \rm \int_{0}^ \infty \frac{ \sqrt[ \scriptsize\phi]{x} \tan^{- 1} (x)}{(1 + {x}^{ \phi} {)}^{2} } {}^{} {} \: dx\\ [/tex]​

Answers

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

[tex]I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx[/tex]

Replace [tex]x \to x^{\frac1\phi} = x^{\phi-1}[/tex] :

[tex]I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]

Split the integral at x = 1. For the integral over [1, ∞), substitute [tex]x \to \frac1x[/tex] :

[tex]\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]

The integrals involving tan⁻¹ disappear, and we're left with

[tex]I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}[/tex]

Ms.Wiz spent 58 dollars on a pair of jeans at old navy.A week later,the store ran a sale and all jeans were 35% off.if she had waited a week,how much would she had paid for the jeans

Answers

Answer:

$37.70

Step-by-step explanation:

56*.65

pls mark brainliest

1. (07.01 LC)
What is the value of x in the equation -6 + x = -1? (5 points)
-5
-7
7
5

Answers

Answer: the value of x = 5

please help
The radius of the base of a right circular cone is 5 times greater than the radius of a second right circular cone. If the heights of both cones are the same, what is the volume of the larger cone divided by the volume of the smaller cone?
A. 5
B. 10
C. 15
D. 25

Answers

Answer: its A or B I think its more of B than A

A store gives away gift bags during a sale. Of these gift bags, 50% are green, 20% are yellow, and 30% are blue. The average number of items in each green bag is 8. The average number of items in each yellow bag is 5. The average number of items in each blue bag is 8. What is the average number of items in all the gift bags? Enter your answer as a decimal in the box.

Answers

Answer:
7
Step-by-step add upexplanation
Add average of each bag. 21
Then divide by 3. 21÷3=7

Please help me the grading period ends in an hour

Answers

1 72
2 60
3 32.7
(The equation for this is 360 / # of angles)
4 140
5 108

6 Trapezoid or quadrilateral
7 not sure sorry
8 square
9 not sure man

evaluate the expression 2b^3+5 (BTW I did the first part it's 3 but I need the second part)​

Answers

To find the exact answer based on the last step, "[tex]2(3)^3+5[/tex]", you must use PEMDAS (attached image below)

 

          [tex]2(3)^3+5=2*27+5=54+5=59[/tex]

Thus the answer is 59.

Hope that helps!

         

Answer:

2b³ + 5 = 59

Step-by-step explanation:

Given information,

→ 2b³ + 5

→ b = 3

Let's solve the expression,

→ 2b³ + 5

→ 2(3)³ + 5

→ 2(27) + 5

→ 54 + 5 = 59

Hence, the answer is 59.

Solve the following equation:

3 x seven tenths

Answers

hello!

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

Here, we have to multiply fractions.

How to Multiply Fractions?

Here are the steps:-

Turn any whole numbers into fractions (example:- 3 = 3/1)Multiply the numerator of the first fraction times the numerator of the 2nd fraction; same with the denominator.Simplify if necessary.

So let's do it.

Step 1:-

[tex]\longmapsto\sf{3=\displaystyle\frac{3}{1}[/tex]

Step 2:-

[tex]\longmapsto\sf{\displaystyle\frac{3}{1} *\frac{7}{10}}[/tex]

[tex]\longmapsto\sf{\displaystyle\frac{21}{10} }[/tex]

We can't simplify this fraction, but there's something else we can do:-

Convert this improper fraction into a mixed number

Here's the answer:-

[tex]\boxed{\sf{2\displaystyle\frac{1}{10} }}[/tex]

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

note:-

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

After hearing about her employer’s health FSA, Yin has decided to enroll in an account. While trying to plan the amount of money to put into her FSA, Yin has made a list of items that she’d like to purchase during the plan year with FSA funds. Using the FSA Eligibility List, select all of the expenses on Yin’s list that she can pay for through money in her FSA.

hypoallergenic earrings
prescription sunglasses
makeup
medical equipment
prescription medications
shampoo
soap
sunscreen

Answers

Answer:

Prescription sunglasses

Medical equipment

Prescription medications

Sunscreen

Step-by-step explanation:

Trust me I just did this assignment

A population P is initially 3000. Find an exponential model (growth or decay) for the population after t years if the population P decreases by 0.36 every 7 years. (Round your terms to three decimal places.)

Answers

The population model is an exponential decay because it decreases

The exponential model of the population is P = 3000(0.64^1/7)^t

How to determine the function?

The population decreases by 0.36 every 7 years.

This means that the function is an exponential decay.

An exponential decay function is represented as:

P = a((1 - r)^1/n)^t

Where:

a represents the initial value (3000)r represents the rate (0.36)n represents the number of years the population decreases (7)P and t are the variables

So, we have:

P = 3000((1 - 0.36)^1/7)^t

Evaluate the difference

P = 3000(0.64^1/7)^t

Hence, the exponential model of the population is P = 3000(0.64^1/7)^t

Read more about exponential functions at:

https://brainly.com/question/11464095

A study population includes 320 freshmen 300 sophomoras, 500 juniors, and 510 seniors,
Which sample best represents the population
O 18 freshmen, 18 sophomores, 30 juniors, 30 seniors
O 18 freshmen, 18 sophomores, 18 juniors, 18 seniors
O 18 freshmen 30 sophomores, 18 juniors, 30 seniors
30 freshmen, 30 sophomores, 18 juniors 18 seniors

Answers

Answer:

18 freshmen, 18 sophomores, 30 juniors, 30 seniors

Step-by-step explanation:

Given ratio

  freshman : sophomores : juniors : seniors

= 320 : 300 : 500 : 510

320 ≈ 300  and  500 ≈ 510

Therefore, 300 : 300 : 500 : 500

Ratio of 300 : 500 = 18 : 30

So  18 : 18 : 30 : 30 best represents the population

Given nos

320300500510

Ratio:-

320:300:500:510

Round out

300:300:500:50018:18:30:30

Option A

Help help help math math

Answers

Answer:

(-16, -4)

Step-by-step explanation:

4x - 13y = -12

x = 2y - 8

Substitute for x:

4(2y - 8) - 13y = -12

8y - 32 - 13y = -12

-5y - 32 = -12

-5y = 20

y = -4

Solve for x:

4x - 13(-4) = -12

4x + 52 = -12

4x = -64

x = -16

Solution to this system: (-16, -4)

I hope this helps!

Answer:

there are two methods

1. graphical method

2. elimination method

3. substitution method


A quadrilateral has angles
measuring 105°, 80°, and 80°.
What is the measure of the fourth
angle?

Answers

Answer:

95 degrees

Step-by-step explanation:

The sum of the measures of a quadrilateral is 360 degrees.  360-105-80-80 = 95 degrees

105+80+80=265
360-265=95

Hope this helps:)

An insurance policy sells for ​$800. Based on past​ data, an average of 1 in 50 policyholders will file a ​$15,000 ​claim, an average of 1 in 100 policyholders will file a
​$30,000 ​claim, and an average of 1 in 400 policyholders will file ​a $70,000 claim. Find the expected value​ (to the​ company) per policy sold. If the company sells 20,000​policies, what is the expected profit or​ loss?

The expected value is ​$____
The profit is $_____

Answers

Answer:

The expected value is $375

The profit is $6,500,000

Step-by-step explanation:

Amount of claim:

15000, 30000, 70000

Probability:

1/100, 1/200, 1/400

So the expected value of the claim is:

15000 × (1/100) + 30000 × (1/200) + 70000 × (1/400) = 475

Given that an insurance policy sells for $800 and the expected value of the claim is $475.

So, the expected value of the companies profit is = $(800 – 475) = $325.

If the company sells 20,000 policies then the expected profit is = $(20000 × 325) = $6,500,000

Thus, The expected value (to the company) per policy sold is $375 and the expected profit is $6,500,000.

-TheUnknownScientist 72

Justin's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make lead balls that have a radius of 7.5in . If lead costs $0.36 per in3 , how much will the lead cost to make one ball?

Answers

Answer:

$636.17

Step-by-step explanation:

       First, we need to find the volume of the ball. Then, we will solve for the cost of it.

       Volume of a sphere and solving for the area:

V = [tex]\frac{4}{3}[/tex]πr³

V = [tex]\frac{4}{3}[/tex]π(7.5)³

V ≈ 1767.15 in³

       Now that we have the volume, next we need to find the cost. Since the lead costs $0.36 per in³, and our volume is in in³, we can multiply the volume by the cost.

1767.15 in³ * $0.36 = 636.174

       Money rounds to the hundredth place,

636.174 -> $636.17

          It will cost $636.17 to make one ball.

Answer:

Volume of a sphere = 4/3 Pi r³

if r = 7.5

= 4/3 pi 7.5³

= 4/3 pi 421.87

= 1687.5/3 pi

= 562.5 Pi

= 1767.15 in³

then

1767.15 x 0.36 = 636.17

if 1 in³ costs 0.36$

then 1767.15 in³ costs 636.17$

write balanced chemical equation for the process of photosynthesis giving the physical state of all the substances involved in the conditions of the reaction​

Answers

Answer:

The process of photosynthesis is commonly written as: 6CO2 + 6H2O → C6H12O6 + 6O2.

Step-by-step explanation:

Marketing analysis determined 55% of females between the ages of 25 to 34 years old search for green technology and practice being green, as compared to 33% of men in the same age group. What is the probability that a randomly selected man between the age of 25 and 34 does not search for green technology

Answers

According to the given percentages, it is found that there is a 67% probability that a randomly selected man between the age of 25 and 34 does not search for green technology.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

We have that 33% of men search for green technology, hence, there is a 100 - 33 = 67% probability that a randomly selected man between the age of 25 and 34 does not search for green technology.

More can be learned about probabilities at https://brainly.com/question/14398287

Simplify cos^4x+2cos^2xsin^2x+sin^4x

Answers

Answer: 1

Step-by-step explanation:

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