Show that: [tex]\sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]
Brainliest! Brainliest..ans.
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]
Find cos 30 in terms of cos 0
Answer:
cos(30) = (sqrt(3)/2) * cos(0)
Step-by-step explanation:
cos(0) = 1
cos(30) = sqrt(3)/2
Thus, we can write that:
cos(30) = (sqrt(3)/2) * cos(0)
Use the substitution method to solve the system.
2x + 8y = 4
x = -4y - 2
Answer:
no solution
Step-by-step explanation:
2x + 8y = 4
x = -4y - 2
Divide both sides of the first equation by 2.
x + 4y = 2
x = -4y - 2
Substitute -4y - 2 for x in the first equation.
-4y - 2 + 4y = 2
0 - 2 = 2
0 = 4
Since after doing legal steps, we get a false statement, 0 = 4, that means there is no solution.
x cube + 1 ÷ x squared -x+1
PLEASE HELP ITS MATH THANK YOUUUU
Answer:
3 centimeters : 100 centimeters
Step-by-step explanation:
The scale is 6 centimeters = 2 meters or 6 centimeters : 2 meters
2 meters = 200 centimeters
Both of them are multiples of 2, so simplify:
6/2 centimeters = 200/2 meters
3 centimeters : 1 meter, or 3 centimeters : 100 centimeters
-Chetan K
Is this last one correct?
Answer:
yes
Step-by-step explanation:
2 1/4 is the most ofen used.
1 1/2 is the least amount of glue needed
subtract it and you get 3/4
Answer:
yes it is
Step-by-step explanation:
help me quick please --4x-7-3x+4=25
Answer:
x = 32Step-by-step explanation:
4x - 7 - 3x + 4 =25
=> 4x - 3x = 25 + 7
=> x = 32 (Ans)
The temperature at 10:00 a.m was -3 and increased 2.25 each hour for the next 5 hours.What was the temperature at 3:00pm?
9514 1404 393
Answer:
8.25°
Step-by-step explanation:
The increase over 5 hours was ...
(5 h) × (2.25 °/h) = 11.25°
When that is added to the starting value, the ending value is ...
-3° +11.25° = 8.25°
The temperature at 3:00 pm was 8.25°.
Multiply. Write your answer as a fraction in simplest form.
8
X
9
Answer:
40/54 = 20/27
Step-by-step explanation:
Scientists often write very large or very small numbers using exponents. How might a scientist write the number shown using exponents?
make it look like a seventh grader wrote it please
Look at picure please
Answer:
[tex]2 {y}^{7} x - 5 {y}^{5} {x}^{2} - 4{y}^{8} {x}^{3}[/tex]
I NEED HELP OR I WILL GET A FAT F!!! What Is 6.38 times 5.2 rounded product to the nearest whole number!!!
Answer:
33.176
Step-by-step explanation:
Brianna works for a large fast food chain recording and publishing training videos for employees. Which job title would Brianna MOST likely have?
Answer:
Multimedia Specialist
Step-by-step explanation:
Had a question like this before
[tex][ 1 1 1 -1\\ 2 0 3 1\\ 4 x 1 -1\\ 1 0 -1 2 ] = 0[/tex]
Answer:
5hg vb
Step-by-step explanation:
,hgbn
Answer:
−120314x − 11
Step-by-step explanation:
Which equation does NOT have like terms to collect?
Answer:
15t+9r=2
Step-by-step explanation:
the terms which are the variables are not the same on any part of the equation
SOMEONE HELP ME PLEASE
Step-by-step explanation:
height is find by Pythagoras theorem.
h=4 .
h²=5²-3² = 16
h=4.
area = bh = 4×10 = 40 units .
hope this helps you.
A supermarket advertises a new product by offering samples to customers. The table shows the number of samples distributed each hour. At what rate does the supermarket distributes samples?
Answer:
38 samples an hour, next time taken the first two numbers in the table and divide the one on the right by the one on the left
811570 rounded to nearest hundred thousand
Answer:
800,000
Step-by-step explanation:
8 is in the hundred thousands, 1 is in the ten thousands, 1 is in the thousands, 5 is in the hundreds, 7 is in the tens, 0 is in the ones place
It rounds down as its nowhere near 900,000 which changes all its digits.
What is the value of W?
951 4 1404 393
Answer:
w = 17
Step-by-step explanation:
Altitude SU of isosceles triangle RST bisects base RT. This means ...
UR = UT
5w = w+68
4w = 68 . . . . . subtract w
w = 17 . . . . . . divide by 4
ive been stuck for so long. pls help
Answer:
B
Step-by-step explanation:
Might be C, but I hope it helps
Hey , help maybe please thanks<3?
Answer:
48 fluid ounces= 3 pints
Answer:
3 pints
Step-by-step explanation:
[tex]48 \: fl \: oz \: \div \frac{8 \: fl \: oz}{cup} = 6 \: cups[/tex]
[tex]6 \: cups \: \div \frac{2 \: cups}{pint} = 3 \: pints[/tex]
WILL GIVE BRAINLIEST!... whats the unit rate of the equation(HAVE TO SHOW HOW YOU GOT ANSWER)
y=-4x
Answer:
-4
Step-by-step explanation:
The form of a liner equation is y=mx+b. b is 0 in this example. So we are left with y=-4x
-4 is the m, the slope. It is also called the unit rate of change. It tells us how much y changes for each 1x unit.
y x
0 0
-4 1 One unit changes y by -4 : The unit rate of change.
-8 2
What are the measurements of angles x,y,z & w?
Thank you<3
Step-by-step explanation:
z°=180°-25°
z°= 155°
z°=x°=155° (vertically opposite angle).
w°=25°(alternate angle).
y°=z°=155°(alternate angle).
hope this helps you.
Answer:
See belowStep-by-step explanation:
As AB and CD are parallel lines cut by a transversal, we have:
∠x and ∠z are congruent as vertical angles∠x and y are congruent as corresponding angles∠w is congruent with 25° as alternate interior anglesSo the measures are:
m∠x = m∠y = m∠y = 180° - 25° = 155° (supplementary angles sum to 180°)m∠w = 25°In 1995, the cost of tuition at a large Midwestern university was $146 per credit hour. In 2001, tuition had risen to $200 per credit hour.
Determine a linear equation to represent the cost, C, of tuition as a function of x, the number of years since 1990. (Assuming the cost increases by the same amount each year.)
Linear Equation:
In the year 2008, tuition will be ($ )per credit hour.
In the year( ) , tuition will be $317 per credit hour
Answer:
72 is the correct answer
Answer:
I believe 72 is the correct answer
Step-by-step explanation:
PLEASEE I NEEEDDD HELPPPPPP
Answer:
make a chart and it will be easy for you
What are the slope and y-intercept of the linear function?
2
-3 -2 -1.
2
оа
Oь
slope:-2: y-intercept: 2
1
slope: 2 :y-intercept: 1
Ос
1
slope: 2 :y-intercept: 2
slope: 2; y-intercept: 1
Od
144 = -12 (x + 5)
find x
Show work.
Answer:
-17 =x
Step-by-step explanation:
144 = -12 (x + 5)
Divide each side by -12
144/-12 = -12 (x + 5)/-12
-12 = x+5
Subtract 5 from each side
-12-5 =x+5-5
-17 =x
Answer:
[tex]144=-12x-60\\12x=-204\\x=-17[/tex]
Step-by-step explanation:
Jane went on a 50-minute bicycle ride. Choose the graph that best matches the given key features. Y-intercept: Jane starts at 0 miles from her house…… PLEASE HELP ILL MARK BRAINLIEST
Explanation: the correct answer is C.
f(x) = 3x + 6 please help quickly!!!!!!!
Given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and [tex]\frac{(f(a + h) - f(a)) }{h}[/tex] by substituting their values into f(x) = 3x + 6. We will have the following:
[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]
Given:
f(x) = 3x + 6We are told to find:
f(a)f(a + h), and[tex]\frac{(f(a + h) - f(a)) }{h}[/tex]1. Find f(a):
Substitute x = a into f(x) = 3x + 6f(a) = 3(a) + 6
f(a) = 3a + 6
2. Find f(a + h):
Substitute x = a + h into f(x) = 3x + 6f(a + h) = 3(a + h) + 6
f(a + h) = 3a + 3h + 6
3. Find [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]:
Plug in the values of f(a + h) and f(a) into [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]Thus:
[tex]\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\[/tex]
Add like terms[tex]\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}[/tex]
Therefore, given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and [tex]\frac{(f(a + h) - f(a)) }{h}[/tex] by substituting their values into f(x) = 3x + 6. We will have the following:
[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]
Learn more here:
https://brainly.com/question/8161429
PLEASE HELP WITH THIS ONE QUESTION
Answer:
11
Step-by-step explanation:
pls maerk as brainliest