\(3^a = 9^b = 27^c\) and a, b, and c don’t equal 0, what is \(\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\)

Answers

Answer 1

To solve the expression \(\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\\\) given the conditions \(\large\sf\:3^a = 9^b = 27^c\\\), we can use logarithmic properties and the fact that \(\large\sf\:3^2 = 9\\\) and \(\large\sf\:3^3 = 27\\\).

Let's start by finding the values of a, b, and c using logarithmic properties:

Taking the logarithm of both sides of \(\large\sf\:3^a = 9^b\\\), we get:

\(\large\sf\:\log_3(3^a) = \log_3(9^b)\\\)

Applying the power rule of logarithms, we can bring down the exponents:

\(\large\sf\:a\log_3(3) = b\log_3(9)\\\)

Since \(\large\sf\:\log_3(3) = 1\) and \(\large\log_3(9) = 2\\\), we simplify to:

\(\large\sf\:a = 2b\\\) ---- (1)

Similarly, taking the logarithm of both sides of \(\sf\:9^b = 27^c\\\), we get:

\(\large\sf\:b\log_3(9) = c\log_3(27)\\\)

Using the values of \(\sf\:\log_3(9)\\\) and \(\sf\:\log_3(27)\\\) as before, we have:

\(\large\sf\:b(2) = c(3)\\\)

Simplifying, we get:

\(\large\sf\:2b = 3c\\\) ---- (2)

Now, let's substitute the value of b from equation (1) into equation (2):

\(\large\sf\:2(2b) = 3c\\\)

\(\large\sf\:4b = 3c\\\)

Rearranging, we find:

\(\large\sf\:c = \frac{4b}{3}\\\) ---- (3)

We now have expressions for a, b, and c in terms of b. Let's substitute these into the expression \(\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\\\):

\(\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{2b}{b} + \frac{b}{\frac{4b}{3}} + \frac{\frac{4b}{3}}{2b}\\\)

Simplifying further, we get:

\(\large\sf\:\frac{2}{1} + \frac{3}{4} + \frac{2}{3}\\\)

Finding the common denominator and combining the fractions, we have:

\(\large\sf\:\frac{24}{12} + \frac{9}{12} + \frac{8}{12}\\\)

Adding the fractions together, we obtain:

\(\large\sf\:\frac{24 + 9 + 8}{12} = \frac{41}{12}\\\)

Therefore, \(\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{41}{12}\\\).


Related Questions

Performance
Performance Task 2
Questions
Performance Task 1
Drag the item from the item bank to its corresponding match.
This is a plane with two axes as a frame of reference. The x-axis is a
horizontal line and the y-axis is perpendicular to it i.e., the y-axis is vertical).
The intersection of the two axes is called the origin.
drag
This is a way of expressing a relationship between x and y in set notation.
ng
This is one of four sections formed by the intersection of the x-axis and y-
axis on a Cartesian coordinate plane.
49
drag

Answers

Answer:

that looks like the directions

Step-by-step explanation:

can you put a screenshot of the problem.

What’s this I don’t know

Whats this I dont know

Answers

Answer:

C.

Step-by-step explanation:

its C.

Tyler has 40 carpet squares that are 1 foot on each sides. He wants to use all of them to make a rectangled-shaped carpet for his room.
For the carpet to fit in the room, the longest side can't be more than 12 feet. What side lengths could Tyler's rectangle have?

Answers

The two possible side lengths for Tyler's rectangle are 12 feet and 3.34 feet.

A rectangle is what?

A rectangle, which is a quadrilateral, has opposite sides that are parallel and equal angles on all four sides. There are a lot of rectangular objects all around us.

A rectangle's shape is determined by its length and width. The rectangle's length is measured along the longer side and its width along the shorter side.

The rectangle-shaped carpet's longest side measures 12 feet.

Allow x feet of carpet on the opposite side.

Thus, the carpet's area is equal to (12 x) square feet.

The rectangle-shaped carpet requires a total of 40 carpet squares to be constructed.

The size of carpet squares is one foot on each side.

40 = 12x ÷ 1

⇒ 40 = 12x

Solving, we get

x = 3.34 feet

Therefore, the side lengths Tyler's rectangle could have are 12 feet and 3.34 feet.

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Angles in a triangle

Angles in a triangle

Answers

Answer

1=62

2=45

3=24

Angle 1

1 plus 118 equals 180 degrees (because both of the angles combined creates a straight angle).

1+118=180

180-118=1

1=62

Angle 2

The angles in a triangle add up to 180 degrees.

You know that angle 1 is 62 degrees.

And the other angle is 73 degrees.

You can now find angle 2.

62+73+2=180

2=180-62-73

2=45

Angle 3

Angle three is in a different triangle.

You already know that the angles in a triangle added up are 180 degrees.

The other missing angle in the triangle can be found by subtracting 73 from 180.

180-73=107

Now you know that two of the angles in the triangle are 107 and 49.

You can now find angle 3.

107+49+3=180

3=180-107-49

3=24

you should give the person above a brainliest!! :)

What is the equation of the parabola ?

What is the equation of the parabola ?

Answers

Answer:

D. y = 1/12x² + 2

Step-by-step explanation:

As per graph we observe:

The y-intercept is 2The coefficient is positive as the graph opens up

According to the observations, the equation is:

y = 1/12x² + 2

Correct choice is D

y=ax²+b

b is y intercept,a is coefficient

Here a is 1/12 as every option contains this factor so don't calculate.

As parabola is opening upwards a is positive

and

y intercept is 2

So the equation is

y=1/12x²+2

4% as a fraction or mixed number in simplest form

Answers

Answer:

1 /25

Step-by-step explanation:

percent means  

out of 100

 

4

%

=

4

100

as a fraction

To simplify the fraction we require to find a  

common factor

to both 4 and 100 and reduce the fraction by dividing. The common factors are 2 and 4 . Choose the largest, that is 4

4

100

=

4

÷

4

100

÷

4

=

1

25

This calculation is usually set out using  

cancelling

4

100

=

4

1

100

25

=

1

25

in simplest form

A fraction is in  

simplest form

when no other factor but 1 will divide into the numerator/denominator.

Dilations: Triangle RST with vertices R(-5,1), S(-3,4), and T(2,-1): k=2

Dilations: Triangle RST with vertices R(-5,1), S(-3,4), and T(2,-1): k=2

Answers

Answer:R’ (-10,2) S’(-6,8) T’(4,-2)

Step-by-step explanation:

Did it in class

After dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).

Given that, ΔRST with vertices R(-5,1), S(-3,4), and T(2,-1).

What is a dilation?

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

Given, scale factor is k=2.

So, with using scale factor

R(-5,1)→2(-5, 1)= R'(-10, 2)

S(-3,4)→2(-3,4)=S'(-6, 8)

T(2,-1)→2(2,-1)=T'(4, -2)

Therefore, after dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).

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Which graph shows the solution to the systern of linear inequalities? x+3y>6 y>2x+4

Answers

Answer: y>2x+4

Step-by-step explanation:

Find the inverse matrix or type
"none".

Find the inverse matrix or type"none".

Answers

Answer:

[-0.2  0.4]

[0.8   -0.6]

Help i need asaaaaaap °∠°

Help i need asaaaaaap

Answers

Answer:

Cube 1 = 30 cubic

Cube 2 = 48 cubic

Cube 3 = 72 cubic

Step-by-step explanation:

Cube 1 = 5x2x3

Cube 2 = 6x2x4

Cube 3 = 8x3x3

I am struggling to find domain and range please help thank you

I am struggling to find domain and range please help thank you

Answers

Answer:

Domain: 0, 1, 2, 3, 4,

Range: 1, 2, 3, 4, 5,

Step-by-step explanation:

Based on the graph the domain of the function is 0, 1, 2, 3, 4, and the range is 1, 2, 3, 4, 5,  therefore, the answer is:

Part A
Which of the following equations is an addition equation and has a solution of -8?
A) X - 2 = 6
B) 2 + 2 = 6
C).X + 2 = 6
D) X + 10 = 2

Part B
Which of the following equations is a multiplication equation and has a a solution of -4/5?

A) 4x=-5
B)4x=5
C)5x=4
D)-5x=4

Answers

Answer:

answer in part a is

c.

answer in part b is

d.

not sure

help help help
Find d
A. 74
B. 14
C. 16
D. 76

help help helpFind dA. 74B. 14C. 16D. 76

Answers

Answer:

D

Step-by-step explanation:

b/c 90 - 14 = 76 .........

What is the intermediate step in the form (x+a)^2=b as a result of complementing the square for the following equations

Answers

The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Solve for x. 6x-10≤8 or 1/3x+6>12 PLEASE HELP and show work

Answers

The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

Given two equations  1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12

Solving the above equations

1) 6x-10≤8

⇒6x ≤ 18

⇒X≤ 3

⇒x ≤ 3 i.e.  x ∈ (-infinity,3]

2)\(\frac{x}{3}\)+6 > 12

⇒\(\frac{x}{3}\) > 6

⇒x>18

⇒ x > 18 i.e.  x ∈ (18,infinity)

Therefore,The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

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Please explain how to do it too ill give brainliest

Please explain how to do it too ill give brainliest

Answers

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

\(m\overset\frown{JM}=30^{\circ}\)\(m\overset\frown{LK}=(2x - 30)^{\circ}\)

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

Please explain how to do it too ill give brainliest

what is the measure of EFD?​

what is the measure of EFD?

Answers

The measure 108 degrees.

I got my answer by dividing 540 by 5. This gave me the measure of EFD

Answer:

its a 90% angle for this question

I need help!!!! pleaseee​

I need help!!!! pleaseee

Answers

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

What is Genotypic and Phenotypic ratio?

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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Smallest successive composites with gap
17, 73, 2, 19

Answers

Answer:

Well, the smallest successive composites with gap 17, 73, 2, and 19 would have to be:

1. $341 = 11 \times 31$

2. $458 = 2 \times 299$

3. $460 = 2^2 \times 5 \times 23$

4. $479 = 13 \times 37$

Solve 10x+16 ≥ 6x+ 20.
A. xz1
B. x < 1
C. x > 9
D. x≤9

Answers

Answer:

x ≥ 1

Step-by-step explanation:

Solving inequalities are essentially like solving equations where the main focus is getting the variable, x in this case, on one side and a constant on the other using inverse operations.

10x+16 ≥ 6x+20

==> subtract 16 from both sides

10x ≥ 6x + 4

==> subtract 6x from both sides

4x ≥ 4

==> divide both sides by 4

x ≥ 1

So the answer would be A

Also an important note for future references is when you divide one of the sides by a negative number you must flip the inequality sign.

E.g. -4x>8

We would divide both sides by -4 and because we divide by a negative number we must flip the inequality signs

This would result to x<-2

If Danny earned $1,000 on a 4 year investment at a rate of 6%, how much was his original investment?

Answers

Answer:

$4,166,67

Step-by-step explanation:

Here are a few pairs of positive numbers whose sum is 34. (3 pts)
a. Find the product of each pair of numbers.
First
Number
1
4
8
14
Second
Number
33
30
26
20
b. Which pair of numbers that have a sum of 34 will produce the largest possible
product? What is that product?

Answers

Answer: 280

Step-by-step explanation:

The products of each pair of numbers are:

1 x 33 = 33

4 x 30 = 120

8 x 26 = 208

14 x 20 = 280

b. To find the pair of numbers that will produce the largest possible product, we need to look for the pair with the closest product to 340 (the square of 17, which is the average of the two numbers).

The pair of numbers with the closest product to 340 is 14 and 20, whose product is 280. Therefore, the pair of numbers that will produce the largest possible product is 14 and 20, and the product is 280.

How is mulhplying intergers
Similar to multiplying whole
numbers?

Answers

Answer:

Multiplying integers is similar to multiplying whole numbers because integers are whole numbers. An integer is a whole number that is not a fraction.

Hope This Helps :)

What is the perimeter of the garden will be the circumference of the four semi-circles with a diameter equal to 14 m.

Answers

Do you have an image of the question for me to refer to?

When I make two batches of cookies I need 4 cupsOf chocolate chips. How many chocolate chips would I need if I made 3 batches of cookies?

Answers

Answer:

it would be 6 cups I don't know  how to explain though

Step-by-step explanation:

It would be 6 cups because if you divide 4 by 2 to get the amount needed for one batch you would get 2. Then you would multiply 2(amount needed for one batch) by 3( amount of batches) you get your answer 6.

10.) Find values of x and y for which ABCD must
be a parallelogram.
A x=2 y=4
B x=2 y=6
C x=2 y=16
D x=6 y=2

10.) Find values of x and y for which ABCD mustbe a parallelogram. A x=2 y=4B x=2 y=6C x=2 y=16D x=6

Answers

Answer:

B x=2 y=6

Step-by-step explanation:

For ABCD to be parallelogram, following conditions should be satisfied:

2x - 0 = x + 2 & 4y - 8 = y + 10

2x - 0 = x + 2

2x - x = 2

x = 2

4y - 8 = y + 10

4y - y = 10 + 8

3y = 18

y = 18/3

y = 6

The relation R is shown below as a list of ordered pairs:
Which ordered pairs prevent this relation from being a function?

The relation R is shown below as a list of ordered pairs:Which ordered pairs prevent this relation from

Answers

The ordered pairings that cause the relation not to have a function are as follows: (1, 4) and (1, 3) are equivalent since they share the same x-value.

What is a relation, and how does it become a function?

If the x-values map to only one y-value, the connection is a function. In other words, a function exists whether the relationship is one-to-one or many-to-one.

A function is a relation that states that there should be only one output for each input (or) that a function is a special form of connection (a set of ordered pairs) that follows a rule, i.e., every X-value should be coupled with only one y-value.

Briefing:

There must be no more than two y-values assigned to an x-value for a relation to be considered a function. Two separate x-values can, nevertheless, have the same y-values.

Because two y-values was assigned to the same x-value in the relation presented in the equation, the ordered pairings (1,4) and (1,3) prevent the relation from being a function. x = 1 has y = 4 and y = 3 correspondingly.

So,

When both ordered pairs are also included, the relation is no longer a function.

The ordered pairings that cause the relation not to have a function are as follows: (1, 4) and (1, 3) are equivalent since they share the same x-value.

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Andre wants to buy a new car. Gas is so expensive; Andre wants to purchase a
car that has the best gas millage rate.

Car 1 has gas mileage that can be described as y = 25x, where x is the
number of gallon of gas used and y is the total miles driven.
Car 2 has he gas mileage rate displayed in the table below.
Number of
Gallons of
Gas
2
5
7
8
11
60
150
210
240
330
Which car should Andre buy? How many more miles per gallon can he
drive in this car than the other car?

Answers

Answer: Andre should buy Car 2. Brainliest?

Step-by-step explanation:

To compare the gas mileage of the two cars, we need to find out how many miles each car can travel per gallon of gas.

For Car 1: y = 25x

This means that for every gallon of gas used (x), the car can travel 25 times that amount in miles (y). So, the gas mileage for Car 1 is 25 miles per gallon (mpg).

For Car 2: we can calculate the miles per gallon by dividing the total miles traveled by the number of gallons of gas used:

For 2 gallons of gas, the car can travel 60 miles. So, the gas mileage is 30 mpg (60 miles ÷ 2 gallons).

For 5 gallons of gas, the car can travel 150 miles. So, the gas mileage is 30 mpg (150 miles ÷ 5 gallons).

For 7 gallons of gas, the car can travel 210 miles. So, the gas mileage is 30 mpg (210 miles ÷ 7 gallons).

For 8 gallons of gas, the car can travel 240 miles. So, the gas mileage is 30 mpg (240 miles ÷ 8 gallons).

For 11 gallons of gas, the car can travel 330 miles. So, the gas mileage is 30 mpg (330 miles ÷ 11 gallons).

Therefore, Car 2 has a consistent gas mileage of 30 mpg.

From the above calculations, we can see that Car 2 has a better gas mileage compared to Car 1. Car 2 can travel 30 miles on a gallon of gas, while Car 1 can only travel 25 miles on a gallon of gas.

Therefore, Andre should buy Car 2 if he wants to get the best gas mileage. Car 2 can travel 5 more miles per gallon than Car 1.

If a card is chosen from a standard
deck of cards, what is the probability
of getting a five or a seven?

Answers

Answer:

5/52 for getting a 5

7/52 for getting a 7

Answer:

Step-by-step explanation:

52 cards in a standard deck. Four 5's and four 7's.

4/52 = 5

4/52 = 7

4/52+4/52= 2/13

2/13 as a percent is 15.384615384615%

that simplified is 15.4%

or just 15%

:) Hope that helped.

What is 3/8 x 3/8 x 3/8 written as a power

Answers

Answer:

3/8^3

Step-by-step explanation:

its like 1/2 x 1/2 x1/2 its 1/2^3

or  7x7x7x7x7=7^5 its the same concept....

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