4
Write as a single fraction in its simplest form.
5/x-3+3/x-7+1/2

Answers

Answer 1

Answer:

[tex]\dfrac{x^2+6x+-67}{2x^2-20x+42} = \dfrac{x^2+6x+-67}{2(x^2-10x+21)}[/tex]

Step-by-step explanation:

[tex]\dfrac{5}{x-3} + \dfrac{3}{x-7} +\dfrac{1}{2}[/tex]

In order to perform the sum, the denominator of the fraction must be the same.

So, it will be [tex]2(x-3)(x-7)[/tex]

Therefore,

[tex]\dfrac{5\cdot2(x-7)}{2(x-3)(x-7)} + \dfrac{3\cdot2(x-3)}{2(x-3)(x-7)} +\dfrac{(x-3)(x-7)}{2(x-3)(x-7)}[/tex]

[tex]\dfrac{10(x-7)}{2(x-3)(x-7)} + \dfrac{6(x-3)}{2(x-3)(x-7)} +\dfrac{(x-3)(x-7)}{2(x-3)(x-7)}[/tex]

[tex]\dfrac{10(x-7)+6(x -3)+(x-3)(x-7)}{2(x-3)(x-7)}[/tex]

[tex]\dfrac{10x-70+6x -18+x^2-10x+21}{2(x-3)(x-7)}[/tex]

[tex]\dfrac{-67+6x+x^2}{2(x-3)(x-7)}[/tex]

[tex]2(x-3)(x-7)= 2x^2-20x+42[/tex]

So,

[tex]\dfrac{x^2+6x+-67}{2x^2-20x+42} = \dfrac{x^2+6x+-67}{2(x^2-10x+21)}[/tex]


Related Questions

1. What is the distance between -12 and 6 on the number
line?

Answers

would the answer be +18??????????

order the numbers from least to greatest 7,-2.5,4/6​

Answers

Answer:

-2.5, 4/6, 7

Step-by-step explanation:

We know this because -2.5 is the only negative number within the sequence, 4/6 is just a fraction so it's not a full number of 6, making 7 the greatest number.

Answer:

-2.5, 4/6, 7

Step-by-Step:

Use the divisibility rules to determine which of the following numbers 330 is divisible by. (Check all that apply.)

2
3
5
7
11

Answers

7 and 11 are not the answer

The numbers that divide 330 are 2, 3, 5 and 11.

How to find the divisibility for a given number?

In order to find divisibility, there are certain rules for different numbers. If a number is divisible by two numbers then it is also divisible by their product.

The given number is 330.

The divisibility rules for the number given can be applied one by one as follows,

Divisibility for 2,

For a number to be divisible by 2 its unit digit must be 0, 2, 4, 6 or 8.

Thus, 330 is divisible by 2.

Divisibility for 3,

For a number to be divisible by 3 sum of the digits of the number must be divisible by 3.

Since sum of the digits of 330 is 6 which is divisible by 3, 330 is also divisible by 3.

Divisibility for 5,

A number should either end with 0 or 5 in order to be divisible by 5.

Thus, 330 is divisible by 5 as it ends with 0.

Divisibility for 7,

For a number to be divisible by 7, the digit at ones place multiplied by 2 and then subtracted from the remaining digits must be divisible by 7.

Here, in 330 this rule is applied as,

33 - 2 × 0 = 33

Since 33 is not divisible by 7, 330 is also not divisible.

Divisibility for 11,

The difference of the sum of the digits at even place to the odd place must either be zero or divisible by 11.

In 330, 3 + 0 - 3 = 0.

Thus, 330 is divisible by 11.

Hence, the given number 330 is divisible by 2, 3, 5 and 11.

To know more about divisibility click on,

https://brainly.com/question/21416852

#SPJ2

Latrell and his cousin, Tisha, met at a state park to go for an all-day hike. Latrell drove 122 miles to get to the park, and it took him 2 hours. Tisha drove 96 miles to get to the park, and it took her 1.5 hours. On average, how much faster did Tisha drive than Latrell?

Answers

Answer:

3 miles

Step-by-step explanation:

122/2 is 61

64 plus 32 is 96. 96/1.5 is 64 meaning that she goes 64 miles an hour.

so she goes 3 miles faster on average than latrell, with latrell going 61 an hour average and her going 64 an hour average

Answer:

Tisha is faster than Latrell by 3 miles/hour

just did the math

What is the product of -4 1/2 and 2 1/2 enter your answer as a mixed number

Answers

Answer:

-1

Step-by-step explanation:

Simplify the following:

-2 + 1

Hint: | Divide 4 by 2.

4/2 = (2 (-2))/2 = 2:

-2 + 1

Hint: | Divide 2 by 2.

2/2 = (2×1)/2 = 1:

-2 + 1

Hint: | Subtract 2 from 1.

-2 + 1 = -1:

Answer:  -1

Solve for v.
v+1≤2
HELP I WILL MARK BRAINLIEST

Answers

Step-by-step explanation:

V is less or equal to 2-1

V is therefore less or equal to 1

-2-(x-3)=-4
What does x equal?

Answers

Answer:

x = 5

Step-by-step explanation:

-2 -(x-3) = -4  

 You have to switch the signs into their opposites when you have -(?)

-2 - x + 3 = -4              Add liked terms

-x + 1 = -4              

    - 1   - 1                     Subtract 1 from both sides

-x = -5                         Get rid of the negative in the x

/-1   /-1                          Divide -1 from each sides

x = 5

-2(x-3)=-4
Y-3=2
x=2+3
x=5

¿A cuál ecuación corresponde la expresión x=3?

Answers

Answer:

(8x − 2x ) + (−x − 2) = (5x − 3) − (4 −x ) a) Ecuación de Primer Grado. b)

Step-by-step explanation:

Answer:

Estas hablando espanol? Perdon, mio es muy malo. Piensa que la responder correcta es -x=-3.

Step-by-step explanation:

which rule describes the transformation? picture below​

Answers

Answer:

B) rotation 180 degrees about the origin

Step-by-step explanation:

Also, what do the words underneath D) say? I think the answer could also be a reflection across y = x.

What is the solution to the system of equations graphed below?


(2, 4)
(4,2)
(0.6)
(6.0)

Answers

Answer:

(4,2)

Step-by-step explanation:

You can see the point where lines crossed.

Hope this helps you.

4,2 of B Hope you get good grades

Prove that ✓-36 does not exist in the Real
Numbers

Answers

Answer:

undefined

Step-by-step explanation:

Becouse any number under a root sign that is negative does not give any answer.Therefore it doesn't exist in real number system.

a circle has a radius of 3.7ft what is the area of the circle 100 points

Answers

Answer:

A = 43.01

Step-by-step explanation:

To find the area of a circle use this formula

A=πr2

"r" representing the radius

Plug in . .

A = π × 3.7² = 43.0084A = 3.14 × 13.69 = 43.0084

Round

A = 43.01

Answer:

43.0 ft² (nearest tenth)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{3.9 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where $r$ is the radius.\\\end{minipage}}[/tex]

Given:

r = 3.7 ft

Substitute the given radius into the formula for area:

[tex]\implies A= \pi (3.7)^2[/tex]

[tex]\implies A = 13.69\pi[/tex]

[tex]\implies A = 43.008403427644...[/tex]

Therefore, the area of the circle is 43.0 ft² (nearest tenth).

Find two numbers whose sum is 39 and the greater number exceeds the smaller one by 5​

Answers

x : smaller no.
x + 5 : larger no.

x+x+5 = 39
2x+5 = 39
2x = 34
x = 17

Help I’m dumb and it’s the end of the quarter

Answers

Answer:its ok me too :(

Step-by-step explanation:hope you get smart soon have a nice day:)

What is the inverse of the function f(x) = x - 9?

Answers

Answer:

F^-1(x) = x+9

Step-by-step explanation:

Hope this helps!  Stay Safe!\

The inverse of the given function is f⁻¹(x) = x + 9. The correct option is a   f⁻¹(x) = x + 9

From the question, the given function is

f(x) = x - 9

To determine the inverse of this function,

First, let y = f(x)

That is,

y = x - 9

Now, make x the subject of the equation

To do that, add 9 to both sides

We get

y +9 = x - 9 +9

y + 9 = x

∴ x = y + 9

Now, rewrite as f⁻¹(x) by replacing y by x

That is,

f⁻¹(x) = x + 9

Hence, the inverse of the given function is f⁻¹(x) = x + 9. The correct option is a   f⁻¹(x) = x + 9

Learn more here: https://brainly.com/question/16149814

Quinton typically walks 28 yards south on Pine Street and 45 yards east on Maple Avenue in order to get to school. How much shorter would his walk be if he took the shortcut shown below? (50PTS)

Answers

Answer:

B- 20 yards

Step-by-step explanation:

First you have to find the hypotenuse by finding the square root of 28 squares plus 45 squared which equals 53 yards. Next you have to add the two legs of the right triangle so we can subtract the shortcut length from that. So you have to do 28 plus 45 which equals 73 yards. 73 minus 53 is 20. So the answer is 20 yards.

Answer:

20

you have to find the hypotenuse by finding the square root of 28 squares plus 45 squared which equals 53 yards.  you have to add the two legs of the right triangle so we can subtract the shortcut length from that. So you have to do 28 plus 45 which equals 73 yards. 73 minus 53 is 20. So the answer is 20 yards.

This diagram represents a function named h. Which of the choices also represents the function, h?

Answers

Answer:

if this is on Imagine Math then its the first answer

Step-by-step explanation:    got it right!

The correct choices to represents the function, h is shown in figure.

⇒ h (x) = 4x - 2

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

This diagram represents a function named h.

Now, We have;

The correct equation to represent the equation is,

h (x) = x × 4 + 9- 2)

h (x) = 4x - 2

Hence, We can draw the equation of line and find that the correct choices to represents the function, h

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ3

If vector u= (-4,8) and vector (5,-18), which vector can be added to 2u-4v to give the unit vector in the direction of the y-axis as the resultant vector?
A. w = (12, -87)
B. w = (28, -55)
C. w = (28, -87)
D. w = (12, -55)

Answers

Answer:

hey buddy im gona help you!

Step-by-step explanation:

solve the following equation algebraically:
2 x squared = 98
a.
x = 7
b.
x = plus-or-minus 49
c.
x = plus-or-minus 7
d.
x = 49

Answers

Answer:

c.  [tex] x = \pm 7 [/tex]

Step-by-step explanation:

[tex] 2x^2 = 98 [/tex]

[tex] x^2 = 49 [/tex]

[tex] x = \pm\sqrt{49} [/tex]

[tex] x = \pm 7 [/tex]

Is y=(x/3) an inverse or direct variation

Answers

Answer: y=x3 is a direct variation.

Step-by-step explanation:

) If a deposit or withdrawal will change an account balance by more
than $1,000, a manager must approve it. Which of these deposits and
withdrawals need manager approval? Choose ALL the correct answers.
-$875
-$1,600
$1,304
-$2,505
$1,001
$451
DONE
ID

Answers

The deposits and withdrawals that require manager approval are:

-$1,600 (since it changes the balance by more than $1,000)

-$2,505 (since it changes the balance by more than $1,000)

What are the deposits and withdrawals?

A deposit is a money put into a bank account for safekeeping until you need it. A withdrawal is a money that's taken out of your account.

The deposits and withdrawals that require manager approval are:

-$1,600 (since it changes the balance by more than $1,000)

-$2,505 (since it changes the balance by more than $1,000)

The deposits and withdrawals that do not require manager approval are:

-$875 (since it changes the balance by less than $1,000)

$1,304 (since it changes the balance by less than $1,000)

$1,001 (since it changes the balance by less than $1,000)

$451 (since it changes the balance by less than $1,000)

Therefore, The deposits and withdrawals that require manager approval are:

-$1,600 (since it changes the balance by more than $1,000)

-$2,505 (since it changes the balance by more than $1,000)

To learn more about deposits and withdrawals visit,

https://brainly.com/question/25920201

#SPJ1

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 17 Date Name Lesson 17 Solutions Eric's father works two part-time jobs, onc in the morning and one in the afternoon, and works a total of 40 hours each 5-day workweek. If his schedule is the same each day, and he works 3 hours each morning, how many hours does Eric's father work each afternoon?

Answers

Answer:

Eric's father work 5 hours each afternoon

Step-by-step explanation:

Let x be the no. of hours Eric's father work each afternoon

He works for hours in morning each day = 3

He works for total hours in morning in 5 days=[tex]3 \times 5 = 15[/tex]

He works for total hours in afternoon in 5 days=5x

We are given that he works a total of 40 hours each 5-day workweek.

ATQ

15+5x=40

5x=25

x=5

Hence Eric's father work 5 hours each afternoon

A cyclist travels 12 km from home to the park.
She leaves home at 13:00 and arrives at the park at 13:30.
What is her average speed in km/h?

Answers

Answer:

Speed = 24 km/h

Step-by-step explanation:

Speed =  Distance / Time

A cyclist travels 12 km from home to the park.

She leaves home at 13:00 and arrives at the park at 13:30.

Distance = 12 km

Time = 0.5 Hours

Speed =  12 / 0.5

Speed = 24 km/h

Answer:

Step-by-step explanation:

12 km to the park in 30 mins so multiply the 12 km by 2 to make a whole hour.

12*2= 24 km/h

Given f(x) = -3x - 2, find the following:
a. f(3)
b. f(-1)
c. f(-2)

Answers

Answer:

Answer is f(3)

Step-by-step explanation:

i did test

Please show your work for points

Answers

Answer:

try your best

Step-by-step explanation:

Answer is c explanation

If f(x) = 8 -3x and g(x) = 4x, solve gf(x) = 80

Answers

Answer:

(f-g)(x)= f (x)- g (x) =4^x -1 +6 -(2x-5)

=4^x +5 -2x +5

=4^x -2x +10

Step-by-step explanation:

When the quotient property of exponents is applied, which operation is used to simplify the exponents? (1 point)
A. Adding
B. Subtracting
C. Multiplying
D. Dividing

Answers

C-Multiplying
Because whatever the number is for the exponent you’re going to multiply the whole number by that much :)
Hope this helped

If y varies directly as x, and x = 13 when y = 6, what is y when x = 65?

Answers

Answer:

y=30

Step-by-step explanation:

Brian notices that a 25-meter flagpole casts a 30 meter shadow. If a nearby telephone pole casts a 40-meter shadow, how tall is the telephone pole?​

Answers

Answer:its a 35 meter

What value of x will make the equation true?
(square root of 5) (square root of 5)=x

please help me :)

Answers

The answer will be 5
The answer is 5 because the square root of 5 is approximately 2.4 so the square root of 5 plus the square root of 5 equals 5
Other Questions
Easy!!! How many lines of symmetry does the figure have? 8670 Plzzz helppppp!!! I need answers A, B, C & D PLEASE HELPStudy the map and map key. Use the information in the map to answer the questions.A map titled Egyptian Trade Routes About 1450 B C shows the Egyptian Empire extending from Nubia in central Africa through upper and lower Egypt, with the following cities located on the Nile River: Nubata in Nubia, Aswan and Thebes in Upper Egypt, and Giza and Sais in Lower Egypt. The empire also extends along the eastern shores of the Mediterranean to Syria and the city of Kadesh in the north. A network of Egyptian trade routes, shown as solid black lines, connects the empire with other regions, including the city of Knossos on the island of Crete, the city of Assur on the Tigris River and the Sumer region. Trade routes also lead into Central Africa and Western Africa.What island city did Egyptians travel to in the Mediterranean Sea? 10. Which political philosopher believed that government, school, artand newspapers naturally corrupts otherwise good people? Zn + ()HCl ()ZnCl2 + ()H2 What is the value of (-8)(45)(1/8)7th grade math How were the Hohokam of North America and the ancient Mesopotamians alike? Both used irrigation. Both existed at the same time. Both lived in grasslands. Both had a written language. #: Why do you think egg cells are large and sperm cells are small?HELP!!! ASAP if 196 soldiers are arranged in a square field how many soldiers are there in the first row? Divide 3/5 by 1/2 as a reduced fraction. Question 6 of 10Which scenario shows a division of labor?A. At the museum, there are always several people available toprovide guided tours for people who are interested in learningmore about the museum's collections.B. On an assembly line at a car factory, some workers attachwindows to cars while others paint the cars.C. At the toll stops on a major road, one worker collects money inone toll booth while another worker collects money in a differenttoll booth.D. In the lunchroom line in the school cafeteria, two workersthe food to all the students.servering GIVING BRAINLIEST!!! DUE IN 30 MINUTES!Please answer the following with 5-7 sentences.What happens to temperature as energy is added to a substance that is changing state? Which of the following was NOT mentioned as commonly cited by historians as relevant context to the War for Independence?a. A population boom and dispersion in England and especially in the North American colonies, arguably necessitating better royal control.b. Political ambiguity regarding the legal status of English colonial men.c. British plans to placate colonial tensions in granting Native American lands to the coloniesd. Historic events that put stress on the British Empire, like gaining territory and losing money amidst the Seven Years/French & Indian War. What are the responsibilities of the department of transportation? Check all that apply. maintaining Georgias ports providing drivers license applicationsmapping out routes for new highwaysmaintaining and improving Georgias roads providing routes for tourists to visit scenic sites hiring construction companies to build new roads Which statement accurately describes the relationship between cash crops and enslaved workers?Cash crops provided many enslaved workers with money to purchase their freedom. In order to make cash crops profitable, farmers sought to reduce the number of enslaved workers.Cash crops were labor intensive, so they were grown on large plantations that used many enslaved workers.In general, cash crops were grown on small family farms with only a few enslaved workers. What is the definition of a gerund? FUN RIDDLESWhat has wheels and flies, but is not an aircraft)? graph the following equation:y = -x -6 You have gone out to eat with a couple of friends. One is your date, and the other is your good friend Bill. At the end, you get the check, and you decide to split it in two parts. You will pay for yourself and your date, while Bill will pay for 1/3 of(*) the total amount. You end up paying $16.00 for your part of the meal. Later, you cant remember how much the total bill was, but you are sure you can figure it out.1. Write a system of equations to represent this situation, and solve the system to find out how much the total cost of the meal was (including your part as well as Bills part). Show all of your work. 2. How much did Bill pay for his part of the meal? Again, show all of your work. 120 passengers in 4 buses = passengers per bus