[tex] \text{Given Equation is } \frac{x}{1} = \frac{ \sqrt[3]{m + 1{ }} + \sqrt[3]{m - 1} }{ \sqrt[3]{m + 1} + \sqrt[3]{m - 1} }[/tex]
[tex]\text{On Applying componendo and dividendo, we get:-}[/tex]
[tex] \frac{x + 1}{x - 1} = \frac{( \sqrt[3]{m + 1} + \sqrt[3]{m - 1} )+ ( \sqrt[3]{m + 1}) - \sqrt[3]{m - 1} }{ (\sqrt[3]{m + 1} + \sqrt[3]{m - 1}) - ( \sqrt[3]{m + 1}) - \sqrt[3]{m - 1} } [/tex]
[tex] \implies \: \frac{x + 1}{x - 1} = \frac{2( \sqrt[3]{m + 1)} }{2( \sqrt[3]{m - 1)} } \\ \\ \implies \frac{ x + 1}{x - 1} = \frac{ \sqrt[3]{m + 1} }{ \sqrt[3]{m - 1} } [/tex]
[tex] \text{On Cubing both sides, we get} \\ \frac{(x + 1) {}^{3} }{(x - 1) {}^{3} } = \frac{m + 1}{m - 1} [/tex]
[tex]\text{Again, Applying componendo and dividendo, we get:-}[/tex]
[tex] \frac{(x + 1) {}^{3} + (x - 1) {}^{3} }{(x + 1) {}^{3} - (x - 1) {}^{3} } = \frac{m + 1 + m - 1}{m + 1 - (m - 1)} [/tex]
[tex] \implies \frac{ {x}^{3} + 1 {}^{3} + 3 {x}^{2} \times 1 + 3x \times {1}^{2} + ( {x}^{3} - 1 {}^{3} - 3x {}^{2} \times 1 + 3x \times 1 {}^{2} ) }{x {}^{3} + 1 {}^{3} + 3 {x}^{2} \times 1 + 3x \times {1}^{2} - (x {}^{3} - 1 {}^{3} - 3 {x}^{2} \times 1 + 3x \times {1}^{2}) } = \frac{2m}{2} [/tex]
[tex] \implies \frac{2x {}^{3} + 6x}{ {6x}^{2} + 2 } = \frac{m}{1} [/tex]
[tex] \implies \frac{2(x {}^{3 } + 3x) }{2(3 {x}^{2} + 1) } = \frac{m}{1} [/tex]
[tex] \implies \: x {}^{3} + 3x = 3m {x}^{2} + m \\ \\ \implies {x}^{3} - 3mx {}^{2} + 3x \\ = m[/tex]
Hope This Helps!!
Based on the calculations, the value of [tex]x^3-3mx^2+3x[/tex] is equal to m.
Given the following data:
[tex]x=\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}}{\sqrt[3]{m+1} +\sqrt[3]{m-1}}[/tex]
How to evaluate the fraction.In order to simplify the given mathematical expression, we would apply the componendo and dividendo rule because it would the number of expansions as follows:
[tex]\frac{x}{1} =\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}}{\sqrt[3]{m+1} -\sqrt[3]{m-1}}\\\\\frac{x+1}{x-1} =\frac{(\sqrt[3]{m+1} +\sqrt[3]{m-1})+(\sqrt[3]{m+1} -\sqrt[3]{m-1})}{(\sqrt[3]{m+1} +\sqrt[3]{m-1})-(\sqrt[3]{m+1} -\sqrt[3]{m-1})}\\\\\frac{x+1}{x-1} =\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}+\sqrt[3]{m+1} -\sqrt[3]{m-1}}{\sqrt[3]{m+1} +\sqrt[3]{m-1}-\sqrt[3]{m+1} +\sqrt[3]{m-1}}\\\\\frac{x+1}{x-1} =\frac{2(\sqrt[3]{m+1})}{2(\sqrt[3]{m-1})} \\\\\frac{x+1}{x-1} =\frac{\sqrt[3]{m+1}}{\sqrt[3]{m-1}}[/tex]
Taking the cube of both sides, we have:
[tex](\frac{x+1}{x-1})^3 =(\frac{\sqrt[3]{m+1}}{\sqrt[3]{m-1}})^3\\\\\frac{(x+1)^3}{(x-1)^3}=\frac{m+1}{m-1}[/tex]
Applying the componendo and dividendo rule, we have:
[tex]\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=\frac{m+1+(m-1)}{m-1-(m-1)}\\\\\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=\frac{2m}{2} \\\\\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=m\\\\\frac{2x^3+6x}{6x^2+2} =m\\\\\frac{2(x^3+3x)}{2(3x^2+1)} =m\\\\\frac{x^3+3x}{3x^2+1} =m\\\\x^3+3x=m(3x^2+1)\\\\x^3+3x=3mx^2+m\\\\x^3-3mx^2+3x=m[/tex]
Read more on componendo and dividendo here: https://brainly.com/question/134857
3,108 + 5,468 6987 +907
Answer:16470
Step-by-step explanation: I don’t know if there all adding together cause there’s not much information
Answer:
54,691,002
Step-by-step explanation:
Which list of points are solutions to the graph of y = 1/2x - 2
Answer:
B) (20,8) , (30,13) , (40,18)
Step-by-step explanation:
To check: (20,8)
y = 1/2x - 2
8 = 1/2(20) - 2
8 = 10 - 2
8 = 8
This is true, which makes our point true.
To check: (30,13)
y = 1/2x - 2
13 = 1/2(30) - 2
13 = 15 - 2
13 = 13
This is true, which makes our point true.
To check: (40,18)
y = 1/2x - 2
18 = 1/2(40) - 2
18 = 20 - 2
18 = 18
This is true, which makes our point true.
Hope that helps!
Help please how do i do this problem
Answer:
Choose any number to be the variable x, then multiply it by 13.2 for your answer.
Step-by-step explanation:
Choose a number for the variable x, and put it in the box with parentheses.
Then, multiply it by 13.2 for your final answer, and put it in the open box.
Hope this helps. Btw, can I have Brainliest? PLEASE PLEASE PLEASE?!
There are three different companies that are willing to provide the hot dogs.
• Company A charges $15 toevery 25 hot dogs, plus a cooking fee of $65.
• Company B charges $7 for every 14 hot dogs, plus a cooking fee of $62.
• Company C charges $22 for every 50 hot dogs, plus a cooking fee of $57.
Based on the number of hot dogs needed in question 5, what company will charge you the least amount of money? How do you know?
Answer:
Company A makes more for one purchase, and Company B makes more for ten purchases. Company C makes less for one purchase and Company A makes less for ten purchases.
Step-by-step explanation:
Company A: y = -3/5x + 65
Company B: y=1/2x + 62
Company C: 11/25x + 57
Make sure x is 1 then do all the equations, then x is 10 and do all the equations to see which has more amount of money and which has less.
Company A: 64.4 (if x = 1)
Company B: 62.5 (if x = 1)
Company C: 57.44 (if x = 1)
if x = 10
Company A: 59
Company B: 67
Company C: 61.4
(I might be wrong since I'm 14)
Company A makes more for one purchase, and Company B makes more for ten purchases. Company C makes less for one purchase and Company A makes less for ten purchases.
Joe used a total of 4 and 3/4 gallons of gas while driving his car. Each hour he was driving, he used 5/6 gallons of gas. What was the total number of hours he was driving?
Write your answer as a mixed number in simplest form.
Answer: 5 & 7/10 hours
Work Shown:
4 & 3/4 = 4 + 3/4 = 4 + 0.75 = 4.75
total gas used = (gas used per hour)*(number of hours)
4.75 = (5/6)x
(5/6)*x = 4.75
x = (6/5)*4.75
x = 5.7
x = 57/10
x = (50+7)/10
x = 50/10 + 7/10
x = 5 + 7/10
x = 5 & 7/10
You rent an apartment that costs $1200 per month during the first year, but
the rent is set to go up $90 per year. What would be the monthly rent during
the 6th year of living in the apartment?
Answer:
In year 6 monthly rent would cost you $1650 and it would cost $19,800 for the whole year of year 6
Step-by-step explanation:
1200x12=14,400 = year 1
1290x12=15,480=year 2
1380x12=16,560=year 3
1470x12=17,640=year 4
1560x12=18,720=year 5
1650x12=19,800=year 6
The monthly rent during the 6th year of apartment is A = $ 1,650
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
After each year, the rent goes up by $90, so in the second year the rent would be $1200 + $90 = $1290 per month, in the third year it would be $1290 + $90 = $1380 per month, and so on
On simplifying the equation , we get
Therefore, during the 6th year of living in the apartment, the monthly rent would be:
A = $1200 + ($90 x 5)
A = $1200 + $450
A = $ 1,650
Hence , the monthly rent is A = $ 1,650
To learn more about equations click :
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can someone step by step explain the answer to me please and thank u
First
angle in front of c is 30°, so hypotenuse is equal to 2c
it's right triangle, so let's use Pythagorean theorem\
[tex](2c)^2=c^2+4^2\\4c^2=c^2+16\\3c^2=16\\\\c^2=\dfrac{16}{3} \\\\c=\dfrac{4}{\sqrt{3} } =\dfrac{4\sqrt{3} }{3 }[/tex]
Second
b - the base of the triangle, angles at the base are equal ⇒ cathets are equal
it's right triangle, so let's use Pythagorean theorem
[tex]b^2=7^2+7^2\\b^2=49+49\\b=\sqrt{2\times49} =7\sqrt{2}[/tex]
In triangle ABC, EP=4. What is PC?
Answer:
PC = 8
Step-by-step explanation:
BF and CE are medians of the triangle.
On each median the distance from the vertex to the centroid P is twice as long as the distance from the centroid to the midpoint, then
PC = 2 × EP = 2 × 4 = 8
Piper invested $4,700 in an account paying an interest rate of 4.8% compounded continuously. Assuming no deposits or withdrawals are made, how much money, , would be in the account after 19 years?
Answer:
$ 11699.69
Step-by-step explanation:
The sum of the measures of three adjacent angles is 150∘. The measures of the angles are in the ratio of 1:2:3. What is the measure, in degrees, of the largest angle?
Answer:
75°
Step-by-step explanation:
1:2:3
so there are a total of 6 parts. Then, each part would be:
=) 150÷6= 25
The largest angle is 3 parts. so, if 1 part is 25, 3 parts is 25×3= 75
The largest angle is is 75°
Hope this helps!
Rewrite x1/2 in radical form.
A. √x
B. √x2
C. 1/√x
D. -√x
Answer:
we can write [tex]x^{\frac{1}{2} }[/tex] as [tex]\sqrt{x}[/tex] in radical form. { fact }
QUICK!! I need help on this Equation. I will make you Brainlist!!!
12. Arithmetic
xn = a + (n-1) d
n = 5 (three aritmetic, 4 and 12)
Input the value:
12 = 4 + 4d
8 = 4d
d = 2
the value: 4, 6 , 8 , 10 , 12
13. Arithmetic
xn = a + (n-1) d
n = 4 (two aritmetic, 4 and 19)
Input the value:
19 = 4 + 3d
15 = 3d
d = 5
the value: 4, 9 , 14 , 19
14. geometric
[tex]\tt a_n=ar^{n-1}[/tex]
n = 4 (two geometric, 2 and 54)
input the value:
52 = 2r³
r = 3
the value: 2, 6, 18, 54
15. geometric
[tex]\tt a_n=ar^{n-1}[/tex]
n = 4 (two geometric, 5 and 40)
input the value:
40 = 5r³
r = 2
the value: 5, 10, 20, 40
What is the length of the midsegment of this trapezoid?
Answer:
7 units
Step-by-step explanation:
the distance between -2 and 4 on the x axis is 7
and then i found the middle point and tried to find the length of it on the y axis
Help! Please answer quickly and accurately or I'll report your answer.
Nora rings up an item that costs $86.25. After sales tax, the total is $91.08. What is the sales tax percentage?
Write your answer as a decimal using a percent sign (%). For example, 0.5% or 12.7%
Answer:
The sales tax is equal to 5.6%
Step-by-step explanation:
To solve first we have to subtract the item's cost before sales tax from the total due. 91.08 - 86.25 = 4.83.
Next we take the amount we payed as tax and divide it by the pre-tax price. 4.83/86.25 = 0.056
Lastly we take 0.056 and convert it to a percentage. This can be accomplished by moving the decimal sign to 2 times to the left or multiplying the tax rate by 100.
The sales tax percentage is equal to 5.6%
Hope this helps you out :)
A rectangle 9cm long is equal in area to a square which has a perimeter of 24cm. Find the width of the rectangle
Answer:
4cm
Step-by-step explanation:
:)
96 stickers on 8 pages = _____ stickers per page.
[tex] \tt \to \dfrac{96}{8} [/tex]
[tex] \\ \\ [/tex]
[tex] \tt \to \: 12 \: stickers[/tex]
Verify:-
12 × 8 = 96
hope it helped u!
Answer:
96/8
I promise you that it os
In an arithmetic sequence, the first term,
a1, is equal to 9, and the sixth term, a6, is
equal to 34. Which number represents the
common difference of the arithmetic
sequence?
Answer:
See below
Step-by-step explanation:
Add 5 to each preceding number
[tex]a_{n}[/tex] = ([tex]a_{n-1}[/tex])+5
1 9 9
2 14 [9+5]
3 19 [14+5]
4 24 [19+5]
5 29 [24+5]
6 34 34 [29+5]
HELP ME what is the slope of a line y=20x
Answer:
20
Step-by-step explanation:
This equation is in slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept. Therefore, the slope is 20
Can someone help solve this equation?
Answer:
(3x+2) + (2x-2) = 2*15
....
When A is -3, is b or c greater
Answer:
c letter is correct I think....
Gwen measured a kitchen and made a scale drawing. The scale she used was 11 inches : 5 feet. If a countertop in the kitchen is 22 inches long in the drawing, how long is the actual counter?
24 as the product of 2 factors
Answer:
1 × 24 = 24 1, 24
2 × 12 = 24 2, 12
3 × 8 = 24 3, 8
4 × 6 = 24 4, 6
6 × 4 = 24 6, 4
8 × 3 = 24 8, 3
12 × 2 = 24 12, 2
24 × 1 = 24 24,1
Step-by-step explanation:
Hi!
I can help you with joy!
Remember, the product of means we multiply 2 numbers.
There are lots of ways we can write 24 as a product of 2 factors:
1×24
2×12
3×8
4×6
And the other way around as well:
6×4
8×3
12×2
24×1
Hope it helps!
Enjoy your day!
~Misty~
The values StartRoot 12 EndRoot and StartRoot 15 EndRoot are plotted on the number line. A number line going from 0 to 4. StartRoot 12 EndRoot is to the right of 3, and StartRoot 15 EndRoot is to the right of StartRoot 12 EndRoot. What is the approximate difference in tenths between StartRoot 12 EndRoot and StartRoot 15 EndRoot? 0. 2 0. 4 1. 5 1. 7.
Approximate difference between √12 and √15 on plotted number line is 0.4. Option B is the correct option.
What is the number line?The number line is the way of representation of number and digits in an arranged form to understand the data batter.
The number line going from 0 to 4. √12 is to the right of 3, and √15 is to the right of √12. Therefore, the arranged value on the number line appears as,
3, √12, √15
In the number line given, the value of √12 is near 3.4 and the value of √15 is near 3.8. The difference between both the values is,
[tex]d=3.8-3.4\\d=0.4[/tex]
The approximate difference in tenths between √12 and √15 on the plotted number line is 0.4. Option B is the correct option.
Learn more about the number line here;
https://brainly.com/question/24644930
Answer:
its c 28
Step-by-step explanation:
The cylinder below has a volume of 2,5 12 cm3
and a height of 2 centimeters. What is the
diameter of the cylinder? Use 3.14 for pi.
Answer:
Radius=10cm
Diameter=20cm
Hope this helps :))))
Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What percent of students scored above 75 points?.
Using the normal distribution, it is found that 59.09% of students scored above 75 points.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is [tex]\mu = 76.4[/tex].The standard deviation is [tex]\sigma = 6.1[/tex].The proportion of students who scored above 75 points is 1 subtracted by the p-value of Z when X = 75, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 76.4}{6.1}[/tex]
[tex]Z = -0.23[/tex]
[tex]Z = -0.23[/tex] has a p-value of 0.4091.
1 - 0.4091 = 0.5909
0.5909 = 59.09% of students scored above 75 points.
You can learn more about the normal distribution at https://brainly.com/question/24663213
pls help me on this question people are just putting the answer as I don't know plsssss help me
Answer:
322 ft²
Step-by-step explanation:
Trapezoid area formula:
[tex]A=\frac{a+b}{2} *h[/tex]
Given:
a = 11
b = 35
h = 14
Work:
[tex]A=\frac{a+b}{2} *h\\\\A=\frac{11+35}{2} *14\\\\A=\frac{46}{2} *14\\\\A=23*14\\A=322[/tex]
Answer:
322 ft^2
Step-by-step explanation:
for a trapezoid A= base 1+ base 2 divided by 2, multiplied by the height
(35+11/2)*14= 322
Reginald and his friends are going on a road trip that is 32.75 miles long. If they have 12.5 miles until their destination, how far have they already traveled? Answer in decimal form.
Answer:
They have already traveled 20.25 miles.
Step-by-step explanation:
To find out how far they've already traveled, we need to subtract the length of the road trip and the distance until their final destination.
32.75-12.5=20.25
Answer:20.25
Step-by-step explanation:
just subtract the length of the road trip and the distance to their final destination.
1. Which of the following is NOT a possibility
for a system of two linear equations?
a. having no solution
b. having one solution
c. having two solutions
d. having infinitely many solutions
Answer:
c. having two solutions
Answer:
C because for there to be two solutions, one or more of the lines graphed would have to be curved, meaning having two solutions is not possible for two linear equations
how do you find a scale factor of 15 inches /20 ft.?
Answer:
x^2 - 1 = 0
3x^2 - 15x = 0
x^2 - 3x = 0
Step-by-step explanation:
Sorry if I am wrong.
I really need some help
Answer:
CEFA
Step-by-step explanation:
1. [tex]p=2(2x)+2(3x+2)=4x+6x+4=10x+4[/tex]
2. [tex]p=2(x)+2(4x+1)=2x+8x+2=10x+2[/tex]
3. [tex]p=2(7)+2(x+5)=14+2x+10=2x+24[/tex]
4. [tex]p=2(5)+2(4x-3)=10+8x-6=8x+4[/tex]
Hope this helps