x/x-2 + x-1/x+1= -1
Can someone walk me through the steps of this problem? Much appreciated. :)
Answers
[tex]\large{\boxed{ \sf x = 1, \ x = 0 }[/tex]
Explanation:[tex]\sf \Rightarrow \dfrac{x}{x-2\:}+\:\dfrac{x-1}{x+1}=\:-1[/tex]
[tex]\sf \Rightarrow \dfrac{x(x+1)+(x-1)(x-2)}{(x-2)(x+1)}=\:-1[/tex]
[tex]\sf \Rightarrow \dfrac{x^2+x+x^2-2x-x + 2}{x^2 - 2x + x - 2}=\:-1[/tex]
[tex]\sf \Rightarrow 2x^2-2x+ 2=\:-1(x^2 - 2x + x - 2)[/tex]
[tex]\sf \Rightarrow 2x^2-2x+ 2=\:-x^2 + 2x - x + 2[/tex]
[tex]\sf \Rightarrow 2x^2+x^2 -2x - x+ 2-2=0[/tex]
[tex]\sf \Rightarrow 3x^2 - 3x = 0[/tex]
[tex]\sf \Rightarrow 3x(x - 1) = 0[/tex]
[tex]\sf \Rightarrow 3x = 0 , \ x - 1 = 0[/tex]
[tex]\sf \Rightarrow x = 0 , \ x =1[/tex]
Answer:
x = 0 or x = 1
Step-by-step explanation:
Given equation:
[tex]\dfrac{x}{x-2}+\dfrac{x-1}{x+1}=-1[/tex]
Multiply the two denominators to get the same denominator:
Multiply the numerator of the first fraction by the denominator of the second fraction to get the new numerator of the first fraction.
Multiply the numerator of the second fraction by the denominator of the first fraction to get the new numerator of the second fraction.
[tex]\implies \dfrac{x(x+1)}{(x-2)(x+1)}+\dfrac{(x-2)(x-1)}{(x-2)(x+1)}=-1[/tex]
Add the numerators and keep the denominator so that there is now one fraction:
[tex]\implies \dfrac{x(x+1)+(x-2)(x-1)}{(x-2)(x+1)}=-1[/tex]
Simplify the numerator by expanding the brackets:
[tex]\implies \dfrac{x^2+x+x^2-3x+2}{(x-2)(x+1)}=-1[/tex]
[tex]\implies \dfrac{2x^2-2x+2}{(x-2)(x+1)}=-1[/tex]
Simplify the denominator by expanding the brackets:
[tex]\implies \dfrac{2x^2-2x+2}{x^2-x-2}=-1[/tex]
Multiply both sides by the denominator of the left side:
[tex]\implies 2x^2-2x+2=-1(x^2-x-2)[/tex]
Simplify and move everything to the left side:
[tex]\implies 2x^2-2x+2=-x^2+x+2[/tex]
[tex]\implies 3x^2-3x=0[/tex]
Factor:
[tex]\implies 3x(x-1)=0[/tex]
Therefore:
[tex]\implies 3x=0 \implies x=0[/tex]
[tex]\implies x-1=0 \implies x=1[/tex]
Therefore, x = 0 or x = 1
Related Questions
Which inequality symbol do I use? -3.5 ___ 1.5 and |-3.5| __ |1.5|
Answers
Answer:
-3.5 < 1.5 and |-3.5| > |1.5|
There are about 30.5 centimeters in a foot. There are 3 feet in a yard. About how many centimeters in a yard? Please explain how you got your answer
Answers
Because there is 30.5 centimeters in one foot, and 3 feet in a yard, you need to multiply 30.5 by 3 for each foot, or 30.5*3=91.5!
Answer:
[tex]10\frac{1}{6}[/tex]
Translate the following phrase to a mathematical expression.
a number times fifteen
(A) 15 n
(B) 15 + n
(D) 15 ÷ n
(C) n15
Answers
Answer:
I think C
Step-by-step explanation:
A number times fifteen would be n • 15 or just n15.
The reason it is not 15n is because it asks a "number" which in this case is represented by the letter n. That letter is now multiplied (times) by 15. So therefore the number "n" times 15 is n15.
Please hit brainliest or thanks, it would help me out.
#Learnwithbrainly
10 Points!!!
A cheese is in the shape of right prism with a triangular base and its dimensions are as shown. What is the approximate surface area of this prism?
A. 72 cm ²
B. 79.8 cm ²
C. 82 cm ²
D.87.4 cm ²
Answers
Answer:
79.8 cm²
Explanation:
surface area of triangular prism: (a + b + c) × length + base × height
Here given:
a = 3 cm, b = 3 cm, c = 3 cm, length = 8 cm, base = 3 cm, height = 2.6 cm
Inserting the values:
(a + b + c) × length + base × height
(3 + 3 + 3) × 8 + 3 × 2.6
79.8 cm²
More on surface area of triangular prism: https://brainly.com/question/27970162
A rectangular-shaped dining room table is modeled by the figure given below. A) Write an equation to represent the area of the dining room table. B) If the the area of the table is 112 ft2, what are the dimensions of the dining room table?
Answers
Answer:
A) (x+10)(x+4) = ?
B) (x+10)(x+4) = 112, solve for x
Step-by-step explanation: you multiply the two equations to get the area.
Answer:
a)[tex](x^{2} +14x+40)ft^{2}[/tex]
b)14ft, 8ft
Step-by-step explanation:
a) Area of Rectangle = Length x Breadth
= [tex](x+10)(x+4)\\=x^{2} +4x+10x+40\\=(x^{2} +14x+40) ft^{2}[/tex]
b) Given Area of rectangle = [tex]112ft^{2}[/tex]
[tex]x^{2} +14x+40=112\\x^{2} +14x-72=0 (Quadratic Equation)\\\\[/tex]
Quadratic Equations: [tex]ax^{2} +bx+c = 0\\[/tex]
In this case, a = 1, b = 14, c = -72
[tex]\frac{-b+/-\sqrt{b^{2}-4ac } }{2a} \\= \frac{-14+/-\sqrt{14^{2} 4(1)(-72)} }{2(1)} \\= 4 or - 18 (reject)[/tex]
We reject negative values.
so x = 4,
The length of table = (x+10) ft = 4+10 = 14ft
The breadth of the table = (x+4) ft = 4 + 4 = 8ft
Taxable Income, Investments and Capital Gains Calculation
Will give brainliest to the person with the best answer and explanation
Answers
Answer:
Capital Gains
Capital gain calculation in four steps
Determine your basis.
Determine your realized amount.
Subtract your basis (what you paid) from the realized amount (how much you sold it for) to determine the difference.
Review the descriptions in the section below to know which tax rate may apply to your capital gains
TaxTo calculate the taxable gain on the sale of an asset, an individual takes the difference between the original purchase price and the sale price of the investment.
Daniel is a piano instructor who gives lessons on weekends. The cost of one lesson is $30. Daniel is offering a 5-lesson package with a 25% discount off the total price.
How much would a student save by buying a multi-pack compared to 5 separate lessons?
Why would Daniel offer a discount when he knows he could earn more money selling the lessons separately?
Answers
Answer:
150 is if you buy them separately but 150-25%=112 so 150-112=38 so students would save $38
Step-by-step explanation:
he made that package so that more people would go to his lessons know that there was a discount going on and more people would choose his lessons over people who don't have discounts.
Answer:
1- Separately - 150
2- students would save 38
What is the smallest prime divisor of 5^23+7^17?
Answers
Answer:
well, both numbers are odd, so their sum will be even.
2 is the smallest prime divisor.
Mary's desk was 67.94 inches long, Joe's desk was 78.26 inches long and Troy's desk was x inches long. If the length of all the desks combined was 214.62 inches, how long was Troy's desk?
Answers
Answer:
68.42
Step-by-step explanation:
We know that when we add the lengths of all of the desks together, the total is 214.62. Based on that information, we can set up the following equation: 67.94 + 78.26 + x = 214.62. From there, all you have to do is add 67.94 + 78.26 to get 146.2. Lastly, you simply do 214.62 - 146.2 to get 68.42. Hope this helps!
Answer:
68.42
Step-by-step explanation:
We know that when we add the lengths of all of the desks together, the total is 214.62. Based on that information, we can set up the following equation: 67.94 + 78.26 + x = 214.62. From there, all you have to do is add 67.94 + 78.26 to get 146.2. Lastly, you simply do 214.62 - 146.2 to get 68.42. Hope this helps!
What is the greatest common factor of 253 and 345?
Answers
Answer:
23
Step-by-step explanation:
To find the Greatest Common Factor, or GCF, we need to factor the first 2 numbers and then find the greatest number that is both present in the prime factorization of both numbers.
253 = 1 * 11 * 23
345 = 3 * 5 * 23
Since 23 is both present in both numbers and is the greatest, the GCF of 253 and 345 is 23.
Estimate the difference by rounding each mixed number to the nearest half or whole number. 8 4/10 - 2 1/7
Answers
Answer:
6 1/2
Step-by-step explanation:
8 4/10 is rounded to 8 1/2 and 2 1/7 is rounded to just 2
8 1/2 - 2 = 6 1/2
8th grade word problem!! 100 POINTS+BRAINLIEST: just write out the steps and explain in simple language :)) Answers for the sake of points will be reported
Answers
(i) Equation : y = 6.25x + 65
(ii) Price of each ticket : $6.25
(iii) Money originally in the box : $65
Explanation:
Here from table, identify the coordinates given.
Coordinates:
(7, 108.75)(13, 146.25)(18, 177.50)Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{146.25-108.75}{13-7} = 6.25[/tex]
Slope is also the price of each ticket which is $6.25
Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\rightarrow \sf y - 108.75 = 6.25(x - 7)[/tex]
[tex]\rightarrow \sf y - 108.75 = 6.25x - 43.75[/tex]
[tex]\rightarrow \sf y = 6.25x - 43.75 + 108.75[/tex]
[tex]\rightarrow \sf y = 6.25x +65[/tex]
To find the amount of money in the box originally, insert x which represents number of tickets sold as 0.
Originally amount of money:
[tex]\rightarrow \sf y = 6.25(0) +65[/tex]
[tex]\rightarrow \sf y = 65[/tex]
Hence, there were $65 in the box before any tickets were sold.
whoever can answer all of these will get brainless
1. 121/2 - 9 1/4 =
2. 5 1/2 - 2 5/12 =
3. 7 1/5 - 3 7/10 =
4. 11 2/3 - 8 1/2 =
fractions by the way
answer that goes with each question
3 1/2) 3 1/3) 3 1/4) 3 1/6) 3 2/3) 3 3/4)
which ones do they go with?
4
Answers
Firstly, brainly allows 1 question per question. So do not try this again.
Lets make the fractions all like terms.
242/4 - 37/4=205/4. Lets now make this a mixed fraction.
By doing 205/4, we find out that 4 goes in less than 51 times.
1. 51 1/4.
2. 11/2 = 66/12.....so 66/12 - 29/12= 37/12. Make it mixed fraction: 3 1/12.
3. 36/5=72/10. 72/10 - 37/10 = 35/10. As a mixed it is 3 1/2
4. 35/3 - 17/2 can be rewritten by finding their GCM (Greatest Common Multiple). In this case it is 6.
70/6 - 51/6 = 19/6. 3 1/6.
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Part B: Starting from the origin, explain how to plot the following three points accurately:
(1, −1)
(−1, 1.25)
(−2, fraction 3 over 4)
Answers
Answer:
refer to the above attachment !
Step-by-step explanation:
Mark as brainlest answer to This answer!
50 POINTS+BRAINLIEST:8th grade systems of equations word problem-explain steps with simple language, answers for the sake of points will get reported :))
Answers
Answer:
one paperback = 0.6 pounds
one textbook = 3.6 pounds
Explanation:
Let the mass of one paperback be 'p' and one textbook be 't'.
Equation one:
sum of mass = total mass in box
20p + 9t = 44.4Equation two:
20p + 5p + 9t + 1t = 5125p + 10t = 51make 't' subject
10t = 51 - 25pt = 5.1 - 2.5pInsert this into equation one:
20p + 9(5.1 - 2.5p) = 44.4
20p + 45.9 - 22.5p = 44.4
20p - 22.5p = 44.4 - 45.9
-2.5p = -1.5
p = 0.6
The weight of 1 paperback is 0.6 pounds.
The weight of 1 textbook:
t = 5.1 - 2.5p
t = 5.1 - 2.5(0.6)
t = 3.6
The weight of 1 textbook is 3.6 pounds.
Repost 8th grade 50 POINTS+BRAINLIEST: How do you graph a quadratic equation in vertex form when the equation is a perfect square? Use x² -4x+4 as an example
Answers
Answer: Vertex : Maximum (2, 0)
Rules:
(x + d)² = x² + 2dx + d² and (x - d)² = x² - 2dx + d²x² + 2dx = (x + d)² - d² and x² - 2dx = (x - d)² - d²Solve:
x² - 4x + 4
x² - 2(2x) + 2²
(x - 2)²
Into vertex form: a(x - h)² + k
1(x - 2)² + 0
Identify:
vertex : (h, k) = (2, 0)
Find additional things, to graph the equation:
(i) x-intercept: (2, 0)
(ii) y-intercept: (0, 4)
Graph shown:
A box has the shape of a rectangle or prism with height 28 cm. If the height is increased by 0.3 cm, by how much does the surface area of the box increase?
Answers
Answer:
4.5cm
Step-by-step explanation:
28cm+0.3cm=28.3cm
surface area=28.3cm×15cm=424.5cm
original surface area=28cm×15cm=420cm
different=424.5cm-420cm=4.5cm
CORRecT ANSWERS ONLY. What is the value of x?
Answers
Answer:
x =5.25
Step-by-step explanation:
Comment
So you want to find x? If the scale factor is 1.75 it means that you multiply whatever dimension on Figure A by 1.75 to get the corresponding dimension on B.
Formula
x = 1.75 * 3
Solution
x = 1.75 * 3
x = 5.25
Trust me I did this problem and I got it correct
In Jason's class, 1/2 of the boys have brown eyes, 1/5 of the boys have blue eyes, and 3/10 of the boys have hazel eyes. How many more of the boys have brown eyes than hazel eyes?
Answers
Answer:
2
Step-by-step explanation:
ist you have to lind the lcd of each fraction. that would be 10.
1/2x5/5=5/10 of the boys have brown eyes
1/5x2/2=2/10 of the boys have blue eyes
3/10=3/10 of the boys have hazel eyes
The question is asking to see how many more boys have brown eyes than hazel eyes.
Subtract 3/10 from 5/10
and that gives you 2/10
The answer is 1/5.
We know that half of the boys in Jason's class has brown eyes, while three-tenths of the boys in his class have hazel eyes. Therefore, if we subtract the two values, you should get your answer.
[tex]\frac{1}{2} -\frac{3}{10} =\frac{2}{10}[/tex]
1/5 is the simplified version of 2/10. Therefore, 1/5 is your answer.
how do i find the LCD? ( Lowest Common Denominator )
Answers
Answer:
First for example let's say
3 and 15your going to doing what you do normally for gcf but then make an l and times it if that makes sense
Step-by-step explanation:
Multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
The two numbers common in the multiples seen above are 10 and 20, because they are multiples of both 2 and 5. However, 10 is less than 20, which would render it to be the lowest common denominator. In cases like this, the lowest integer (the number closest to 0) will always be the LCD.
If you have any further questions, I am open for discussion. Have a nice day!
Solve 2x2 + 5x = 12
Here are the answers provided
\/
x = three over two and x = −4
x = 2 and x = −3
x = −6 and x = 5
x = one half and x = one over three
Answers
Answer:
A
Step-by-step explanation:
2x² + 5x = 12
2x² + 5x - 12 = 0
x² + 5x - 24 = 0
factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. the only pair that adds to 5 is 8 and 3
2x² - 3x + 8x - 12 = 0
split the equation and factor
2x² - 3x = 0 ||| 8x - 12 = 0
x(2x - 3) ||| 4(2x - 3)
therefore the pair is (2x - 3)(x + 4)
2x - 3 = 0
2x = 3
x = 3/2
or
x + 4 = 0
x = -4
how do i turn a fraction into its simplest form?
Answers
Answer:
You divide both the numerator and the denominator by the same number until they can't be reduced any further.
Answer:
Make sure to divide the upper number and the lower number (in position) to a number which can't be futher divided. It will be of numbers which are really small numbers. like 4/2 will be divided by 2 to get the simplified answer of 1/2
Step-by-step explanation:
please help!!!!!!!!!!!!!!!!!!!!!!
Answers
the last option.
Hope this helped :)
How many solutions does the system have?
y = − 7 x + 8
y = −7x - 8
A one
B none
C Infinite
Answers
Answer: B. None
Step-by-step explanation:
The best way to figure this out is by graphing it. I used Desmos graphing calculator. The red line is the first equation, and the blue line is the second one. As you see, they do not intersect anywhere, therefore will not have any solutions.
I hope this helps!! Pls mark brainliest!! :)
Answer:
B
Step-by-step explanation:
These are PARALLEL lines....they both have the same slope -7
so there are no solutions
Find the end time in the event and enter them into table
Answers
Answer:
Movie: 1:35pm
Soccer Game: 1:05pm
Concert: 1:50pm
Step-by-step explanation:
Movie:
Starting at 11:20am and ends in 2 hours and 15 minutes
hours : minutes
2 hours after 11am is 1pm
15 minutes after 20 is 35
so the movie will end at 1:35pm
Soccer Game:
Starting at 11:35am and ends in 1 hour and 30 minutes
hours : minutes
1 hour after 11am is 12pm
30 minutes after 35 is (65) 5 minute of the next hour (1 hour and 5 mins total)
so the soccer game will end at 1:05pm
Concert:
Starting at 12:15pm and ends in 1 hour and 35 minutes
hours : minutes
1 hour after 12pm is 1pm
35 minutes after 15 is 50
so the concert will end at 1:50pm
Answer:
1:35pm
Soccer Game: 1:05pm
Concert: 1:50pm
Step-by-step explanation:
Movie:
Starting at 11:20am and ends in 2 hours and 15 minutes
hours : minutes
2 hours after 11am is 1pm
15 minutes after 20 is 35
so the movie will end at 1:35pm
Soccer Game:
Starting at 11:35am and ends in 1 hour and 30 minutes
hours : minutes
1 hour after 11am is 12pm
30 minutes after 35 is (65) 5 minute of the next hour (1 hour and 5 mins total)
so the soccer game will end at 1:05pm
Concert:
Starting at 12:15pm and ends in 1 hour and 35 minutes
hours : minutes
1 hour after 12pm is 1pm
35 minutes after 15 is 50
so the concert will end at 1:50pm
Step-by-step explanation:
Show all work to identify the asymptotes and zero of the function f of x equals 4 x over quantity x squared minus 16.
Please explain with simple words! :)
Answers
Answer:
The zeros of a rational expression are the places where the numerator is zero:
4x = 0
x = 0
divide by 4
Mr Brown has to pay a $670 power bill by the end of the month. He has 12 days to go before the end of the month. He has already set aside $152 for the bill. He plans to save an equal amount per day for each of the 12 days.
a) what is the minimum amount he should save per day to be able to pay the bill?
b) Convert your answer to a certain currency. $1 in the current currency = $1.35 to the new currency.
Answers
I need help with this topic, an explanation of how you got the answer would be very much appreciated, Thanks :)
( I attached pictures )
Answers
Answer:
No Solutions
Step-by-step explanation:
Hello!
We can approach this system using the Elimination method. Since the coefficients of the the x terms are the same, we should vertically subtract the two equations.
Subtract[tex]\left \{ {{y=9x - 5} \atop {y = 9x + 6}} \right.[/tex][tex]-\left \{ {{y=9x - 5} \atop {y = 9x + 6}} \right.[/tex][tex]-\left \{ {{y=9x - 5} \atop {y = 9x + 6}} \right.\\0 = 0 -1 1[/tex][tex]0 \neq -11[/tex]Since 0 does not equal to -11, there are no solutions to the system.
We can also look at this graphically. The two lines have the same slope but different y-intercepts, meaning that they would be parallel lines with no intersection. If there is no intersection, there are no solutions.
Answer this. Show your work. Worth 10 points. Under 4 hours. URGENT.
Answers
60-50= 10.
Only 10 minutes increases the second time she did it.
hello, please help me i dont know what 2 do
Answers
Answer:
Greater than
Step-by-step explanation:
you are adding exponent with the same denominator if its easier for you in this example you can set the denominator equal to 10.
Sum= adding
2/5 +4/5 =6/5 or 1 1/5
if you want to do it with the denominator equal to 10 just multiply each side by 2.
(2/5 +4/5)x 2
4/10 + 8/10 = 12/10
