Here we need to Prove that ,
[tex]\bf\implies \sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]
Lets start with LHS , which is ,
[tex]\bf\implies LHS = \sqrt[ab]{ \dfrac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \dfrac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \dfrac{ {x}^{c} }{ {x}^{a} } } [/tex]
We know that ,
[tex]\bf\implies \sqrt[n]{k^m }= k^{\frac{m}{n}}[/tex]
• So that ,
[tex]\bf\implies \sqrt[ab]{x^{a-b}} . \sqrt[bc]{x^{b-c}} .\sqrt[ac]{x^{c-a}} \\\\\bf\implies x^{\frac{a-b}{ab}} . x ^{\frac{b-c}{bc}} .x^{\frac{c-a}{ca}} \\\\\bf\implies x^{\frac{ ac - bc + ab - ac + bc - ba }{abc } }\\\\\bf\implies x^{\frac{0}{abc}} \\\\\bf\implies x^0 \\\\\bf\implies 1 = RHS [/tex]
Hence ,
[tex]\implies \boxed{\bf \red{ LHS = RHS }} [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider LHS:
[tex]\sf= \sqrt[\sf ab]{\dfrac{\sf x^{a}}{\sf x^{b}}}\cdot \sqrt[\sf bc]{\dfrac{\sf x^{b}}{\sf x^{c}}}\cdot \sqrt[\sf ac]{\dfrac{\sf x^{c}}{\sf x^{a}}}[/tex]
As we know that:
[tex]\sf\red\leadsto\dfrac{x^{a}}{x^{b}}=x^{a-b}[/tex]
We get:
[tex]\sf= \sqrt[\sf ab]{\sf x^{a-b}}\cdot \sqrt[\sf bc]{\sf x^{b-c}}\cdot \sqrt[\sf ac]{\sf x^{c-a}}[/tex]
We can also write it as:
[tex]\sf= x^{\dfrac{a-b}{ab}}\cdot x^{\dfrac{b-c}{bc}}\cdot x^{\dfrac{c-a}{ac}}[/tex]
We know that:
[tex]\sf \red\leadsto x^{a}\cdot x^{b}=x^{a+b}[/tex]
We get:
[tex]\sf= x^{\bigg(\dfrac{a-b}{ab}+\dfrac{b-c}{bc}+\dfrac{c-a}{ac}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{c(a-b)+a(b-c)+b(c-a)}{abc}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{ac-bc+ab-ac+bc-ab}{abc}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{0}{abc}\bigg)}[/tex]
[tex]\sf= x^{0}[/tex]
[tex]\sf=1[/tex]
[tex]\textsf{= RHS}\\[/tex]
Anyone can solve this for me??
Answer:
15.25 is the better.
Step-by-step explanation:
you don't ounces divided by money.
In a project there are 560hrs
Answer:
560hrs
Step-by-step explanation:
1day=24hrs
560hrs=(560÷24)days
=23.333days
Adjoa’s gross salary for last month was Ghc4,687.24. If Ghc421.78 was deducted from Adjoa’s salary pay, how much take-home pay did Adjoa earn this past month?
Adjoa take-home pay earned for the past month is Ghc4,265.46
From the question,
We are to determine the amount of take-home pay Adjoa earn the past month
From the given information, we have that
Adjoa’s gross salary for last month was Ghc4,687.24
Also
Ghc421.78 was deducted from Adjoa’s salary pay
To determine how much take-home pay Adjoa earn the past month,
We will subtract the amount deducted from Adjoa’s salary pay from Adjoa’s gross salary for last month
That is,
Adjoa take-home pay = Ghc4,687.24 - Ghc421.78
Adjoa take-home pay = Ghc4,265.46
Hence, Adjoa take-home pay earned for the past month is Ghc4,265.46
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SOMEONE HELP ME PLEASE
Answer:
h=4
Step-by-step explanation:
the height can't be smaller than 3 and higher than 5, you're making a hypothesis.
Jaden goes to dinner with his family. Their total bill comes to $52.25. They received
great service, so they decide to leave a 20% tip. How much should they leave for a
tip?
$16.12
$1.05
$10.45
$2.61
Work Shown:
20% = 20/100 = 0.20
20% of 52.25 = 0.20*52.25 = 10.45
side note: The total cost, including the tip, is 52.25+10.45 = 62.70 dollars
how to solve 5 divided by 2545
According to a 2014 Pew Research poll, 58% of Americans believe in Hell. Suppose a random sample of 100 Americans is obtained and the number of Americans who believe in Hell is recorded. Can this binomial experiment be approximated using a normal distribution? Be sure to demonstrate your conclusion numerically.
Testing the conditions, we get that [tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.
For each person sampled, there are only two possible outcomes. Either they believe in Hell, or they do not. The probability of a person believing in hell is independent of any other person, which means that the binomial distribution is used to solve this question.
Binomial distribution:
Probability of x successes on n trials, with p probability.
If [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex], it can be approximated to the normal distribution.
In this problem:
Sample of size 100, thus [tex]n = 100[/tex].58% believe in Hell, thus [tex]p = 0.58[/tex].Then
[tex]np = 100(0.58) = 58 \geq 10[/tex]
[tex]n(1 - p) = 100(0.42) = 42 \geq 10[/tex]
[tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.
A similar problem is given at https://brainly.com/question/24261244
sin⁻¹(-[tex]-\frac{\sqrt{3} }{2}[/tex]
Answer:
240,300
[tex] \frac{4\pi}{3} . \: \: \frac{5\pi}{3} [/tex]
See attachment. Please give step by step solution. Thank you
Answer:
x=19
Step-by-step explanation:
cross multiply
(−3)(+5)(3+5)=(−3)(+5)⋅2−3
(−3)⋅3=(+5)⋅2
3(−3)=(+5)⋅2
=19
How would I find the derivative of 2^3^x^2
Answer:
d
y
d
x
=
−
4
3
x
3
Explanation:
y
=
2
3
x
2
=
2
3
x
−
2
Applying the power rule:
d
y
d
x
=
2
3
⋅
(
−
2
)
x
−
3
=
−
4
3
x
3
Step-by-step explanation:
NO LINKS!!!
Find the coordinates of point on the directed segment from (1,6) to (-2,-3) that divides it into a ratio of 5:1.
a. (-1.5,-1.5)
b. (1.5, 1.5)
c. (-1,-1)
d. (-2.5, -3.5)
Answer:
A. (-1.5, -1.5)Step-by-step explanation:
Find the coordinates:
x = 1 + 5/6(- 2 - 1) = 1 - 5/2 = -1.5y = 6 + 5/6(-3 - 6) = 6 - 15/2 = -1.5Correct choice is A
Given that the points (12, –4) and (–36, 8) lie on a line, what is the equation of the line?
The equation of the line passing through the points (12, –4) and (–36, 8) is y = -1/2 x - 1
The formula for calculating the equation of a line is expressed as:
y = mx + b
m is the slope of the line
b is the y-intercept
Given the coordinate points expressed as (12, –4) and (–36, 8)
Get the slope:
m = 8+4/-36-12
m = 12/-48
m = -1/4
Get the y-intercept "b"
Recall that y = mx + b
8 = -1/4(-36) + b
8 = 9 + b
b = 8 - 9
b = -1
Get the required equation.
Recall that y = mx + b
y = -1/2 x + (-1)
y = -1/2 x - 1
Hence the equation of the line passing through the points (12, –4) and (–36, 8) is y = -1/2 x - 1
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how to find root hair
103.468 round this to the nearest liter
Answer:
103
Step-by-step explanation:
So the .4 in the tenths place is less than 5 it is rounded down/stays the same so its 103
Hope this helps!!
Have a nice day! :D
Please help and answer both of the questionssss
Answer:
(n + 6) / -4 = 10
n + 6 = 10 × -4
n + 6 = -40
n = -40 - 6
n = -46
(n - 2) / -3 = -6
n - 2 = -6 × -3
n - 2 = 18
n = 18 + 2
n = 20
Step-by-step explanation:
brainliest plz
Help, What is the volume of the concrete piece?
Answer:
72,000
Step-by-step explanation:
multiply everything
3v + 7v + 9v =3 v+7 v+9 v=
Answer:
I cant help you
Step-bBecause i just c
y-step explanation:
The table below shows the cost for a factory to produce mid-sized cars.Based on the information in the table, how much does it cost the factory to produce each car?
A.
$10,206.00
B.
$15,309.00
C.
$5,103.00
D.
$2,552.00
Answer:
B
Step-by-step explanation:
because you are looking for the car that cost the most
What is the value sinθ?
12/13
13/5
5/12
5/13
Answer:
12/13
Step-by-step explanation:
I got a 100% on the test
The trigonometric function sin is the ratio of perpendicular to hypotenuse thus sinθ = 5/13.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
As per the given right angle triangle,
By sine function.
sinθ = perpendicular/hypotenuse
sinθ = 5/13
Hence "The trigonometric function sin is the ratio of perpendicular to hypotenuse thus sinθ = 5/13".
For more information about the trigonometric function,
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. A store is going to mark down all of their items by 33%. The cost of a computer you really want is $750. How much will the computer get marked down?
Answer:
$247.50
Step-by-step explanation:
33/100x750=247.50
Since 33% in a fraction is 33/100, use that x 750 and you will get how much the computer gets marked down.
Hope this helps! Thanks.
1. find the measure of each angle
Answer:
The equation is 3x -5 + 10x -7 = 180°
Step-by-step explanation:
These angle are a linear pair. Linear pair are two angles that are adjacent and their sides are opposite rays, or the two angles form a straight angle = 180°
The equation is 3x -5 + 10x -7 = 180°
In a school 2/3 parts of the total numbers of students. 3/10 parts are between 8 to 12 years and the remaining are above 12 years . What parts of the students are above the age of 12 years.
ans:3/10
3/10
As you know the answer already I don't think you need any further explanation :)
If there are 2,000 females and 2,000 males enrolled at a college and four different students are randomly selected to receive a book scholarship, what is the probability that at least one is female?
Calculate the probability two ways: a) treat as dependent selections and b) treat as independent selections.
Answer:
500
Step-by-step explanation:
you just divide 2000 by 4 and get 500
HELP!?!?!?! I can't figure this out
Answer:
So, I believe n/2 may be even and 3n+1 is odd. They succumb to 3n if that helps.
Step-by-step explanation:
I'm not certain on what to do but I hope this helps some what.
Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?
After dividing 25 into 105, the next step is to
25 by 4.
The next step is to
100 from 105.
The next step is to
the next number.
The first step is to Multiply The next step is to Divide.
Ok so if you were wondering what to do on the box that says this
Move Decimal
Divide
Multiply
Subtract
Bring down
On this, I agree with myself. The solution is straightforward. Simply click them in the sequence listed, beginning with the first and ending with the last. Wow, what sleuthing I did. I realize it's not much, but I was perplexed by this as well, so you could be as well. So here we go with the actual answer. To tackle these sorts of issues, you must employ a technique known as PEMDAS, which stands for.
Parenthisis
Exponent
Multiply
Divide
Add Subtract
I realize I spelt the first one incorrectly, but it's 2 a.m. and I'm doing homework for you. Now we must consider whether or not this has any parenthesis. This particular issue does not. Now we must determine whether or not this issue has exponents, which it does. As mentioned in the response box on the lesson's main page. So we have to consider that (spelled incorrectly, but who cares, it's math class)Now we multiply by a power of ten, so the divisor is a whole number. The following step is to divide by calculating how many times 25 equals 105. I realize it was stolen from the question, but whatever. So there was the explanation; I realize I didn't answer the entire problem, but I didn't have to; it wasn't in the cards.
Estimate the product 2.1 x 0.9
Answer:
2.0 estimated product
1.89 Actual product
Step-by-step explanation:
2.0*1.0=2.0
2.1*1.0=1.89
The product of 2.1 x 0.9 = 1.89
What is Product?A product is something that has been multiplied one or more times. For instance, the mathematical formula "times equals" would be written with the terms "times," "multiplicand," and "product," respectively.
Given:
2.1 x 0.9
Now, Multiplying
2 . 1
x 0 . 9
_________
1 8 9
0 0 x
__________
1 . 8 9
Hence, the product of 2.1 x 0.9 = 1.89
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the differentiation of x^4 + y^4=0 is..?
Answer:
I am doinnnnnmngggg gggg
please help me with this sum
Answers:
59 × 9 = 531
63 × 8 = 504
83 × 4 = 332
38 × 5 = 190
72 × 6 = 432
48 × 4 = 192
19 × 3 = 57
58 × 2 = 116
73 × 8 = 584
60 × 7 = 420
36 × 5 = 180
56 × 7 = 392
75 × 3 = 225
63 × 6 = 378
73 × 3 = 219
70 × 5 = 350
57 × 6 = 342
53 × 7 = 371
27 × 6 = 162
29 × 4 = 116
73 × 3 = 219
49 × 9 = 441
92 × 2 = 184
57 × 9 = 513
36 × 3 = 108
given cosec theta = 7/2 find sin theta
Answer:
Sin0=7/25
Step-by-step explanation:
The high temperature was recorded as 23 7°F The low temperature that same day was recorded as
6.9°F
What was the difference between the high and low temperatures for that day?
Enter your answer as a decimal in the box
Answer:
The high temperature was recorded as 23 7°F The low temperature that same day was recorded as
-6.9°F
What was the difference between the high and low temperatures for that day?
Enter your answer as a decimal in the box
Answer is 30.6
Step-by-step explanation:
23.7
- 6.9
______
30.6
Have a blessed day
The difference between the high and low temperatures for that day is 30.6
what is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The high temperature was recorded as 23 7°F = +23.7
the low temperature that same day was recorded as 6.9°F = -6.9 F
so, difference between the high and low temperatures for that day
= 23.7- (-6.9)
= 30.6
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