What are recipicles

Step-by-step explanation:

If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

Let a = log82x, b = log4x and c = log2x

If a = log8 2x; 8^a = 2x... (1)

If b = log4 x; 4^b = x ... (2)

If c = log2 x; 2^c = x...(3)

Since a, b c are in GP, then b/a = c/b

Cross multiplying:

b² = ac ...(4)  

From eqn 1, x = 8^a/2

x = 2^3a/2

x = 2^(3a-1)

From eqn 2; x = 4^b

x = 2^2b

From eqn 3: x = 2^c

Equating all the values of x, we have;

2^(3a-1) = 2^2b = 2^c

3a-1 = 2b = c

3a-1 = c and 2b = c

a = c+1/3 and b = c/2  

Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;

(c/2)² = c+1/3×c

c²/4 = c(c+1)/3

c/4 = c+1/3

Cross multiplying;

3c = 4(c+1)

3c = 4c+4

3c-4c = 4

-c = 4

c = -4  

Substituting c = -4 into equation 3 to get the value of x we have;

2^c = x

2^-4 = x

x = 1/2^4

x = 1/16    

Since the number x can be written as m/n, then x = 1/16 = m/n

This shows that m = 1, n = 16

m+n = 1+16

m+n = 17  

The required answer is 17.  

The value of m+n in which m and n are relatively prime positive integers is 17.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,

[tex]\log_82 x,\log_4x, \log_2x[/tex]

The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,

[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]

Using the base rule of logarithmic function,

[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]

Using the Power rule of logarithmic function,

[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]

The number x can be written as

[tex]\dfrac{m}{n}[/tex]

Here, m and n are relatively prime positive integers. Thus, the value of m+n is,

[tex]m+n=1+16=17[/tex]

Hence, the value of m+n in which m and n are relatively prime positive integers is 17.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

Answer:

The change in the sea level will be by 0.2925 inches

Step-by-step explanation:

First of all , we will need to write out the rate at which the sea level is rising. This is 0.13 inches, per year. This means that every year, the sea level increases by 0.13 inches.

Since the sea level increases by 0.13 inches every year, in 2.25 years, to get the sea level, we will have to multiply the current rate at which it is rising by that duration of time.

This will be 2.25 years X 0.13 inches/ year = 0.2925 inches

Therefore, the change in the sea level will be by 0.2925 inches

Answer:

0.2925 inches

Step-by-step explanation:

Answer: x = 2

Step-by-step explanation:

[tex]10x - 15x + 5= -45 + 40[/tex]

subtract 5

[tex]10x - 15x= -45 + 40-5[/tex]

Combine like terms;

[tex]-5x=-10[/tex]

Divide by -5

[tex]x=\frac{-10}{-5}\\ x=2[/tex]

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]

Answer: [tex]96ft^2[/tex]

Step-by-step explanation:

We have a composite figure. We have a rectangle and a triangle. Calculate each of these figures' areas individually and add them together.

Rectangle:

length=10ft

width=8ft

[tex]Formula:A=l*w\\A=(10ft)(8ft)\\A=80ft^2[/tex]

----------------------------------------------------------

Triangle:

base: 4ft

height: 8ft

[tex]A=\frac{hb}{2}[/tex]

[tex]A=\frac{(8ft)(4ft)}{2}[/tex]

[tex]A=\frac{32ft^2}{2}[/tex]

[tex]A=16ft^2[/tex]

-------------------------------------------------------------

Add them:

[tex]80ft^2+16ft^2=96ft^2[/tex]

Answer:

Therefore the largest number that these fractions can be divided by to give them a whole number is

a) 8/15 = The largest number is 8/15

b) 18/35 = The largest number is 18/35

Step-by-step explanation:

A quotient is the result obtained by dividing two numbers.

So that the quotient obtained is a whole number we have to find out, what number they can be divided by to give them that.

Let's assume the whole number is 1

a. 8/15

8/15 ÷ x = 1

8/15 × 1/x = 1

8/15x = 1

We would cross multiply

8 = 15x

We would divide both sides by 15

8/ 15 = x

Hence the largest number that would divide 8/15 and give it a whole number = 8/15

b) 18/35

18/35÷ x = 1

18/35 × 1/x = 1

18/35x = 1

We would cross multiply

18 = 35x

We would divide both sides by 35

18/ 315 = x

Hence the largest number that would divide 18/35 and give it a whole number = 18/35

Answer:

The answer is 2/105

Step-by-step explanation:

first we have to find the LCM of both denominators. IN this case, the LCM of 15 and 35 is 105. Then we have to find the GCF of these numerators. IN this case, the GCF of 8 and 18 is 2.

Now, put the GCF you found over the LCM.

ANSWER: 2/105

This fraction is the largest number you can divide both numbers by to get a whole number.

Answer:

Side AB has a length of 4, and side BC has a length of 11.7

Answer:

There are a total of 2500 cups

Step-by-step explanation:

10% of the cups are green

you can set up a equation for this

x = total cups

.10x = 250

multiply both sides by 10 to make x a whole number

x = 2500

Answer:

7.35 pints

Step-by-step explanation:

If we use 1/4 of the 9.8 pints for blue, then the remaining white paint takes up 3/4 of the 9.8 pints of paint. To find how many pints of paint is equal to 3/4 of it, you must multiply that fraction by the amount (9.8).

[tex]\frac{3}{4}[/tex] * 9.8 (or 0.75 * 9.8) = 7.35

Therefore, 7.35 pints of the total paint used is white.

Hope I helped! Please give me brainliest!

Answer:

Step-by-step explanation:

In this problem, we have to find the area of an square adjacent to the third side of the right triangle.

To solve this problem, we need to use Pythagorean's Theorem, beacuse it's about a right triangle. Also, this theorem is about square areas, that's the geomtrical meaning of it.

[tex]h^{2} =32 \ u^{2} + 32 \ u^{2} = 64\ u^{2} \\h=\sqrt{64 \ u^{2} } =8u[/tex]

Therefore, the area of a square adjacent to the third side is 64 square units.

Answer:the answer is 8

Step-by-step explanation:

Answer:

14/50 or 28%

Step-by-step explanation:

THERE ARE 14 MALES WHO CHOSE INVISIBILITY AND 50 MALES IN TOTAL.

EZPZ

Answer:

equal to ab

Step-by-step explanation:

The area of a parallelogram is Area =  ab

therefore, the area is ab

Answer:

Less than ab

Step-by-step explanation:

Answer:

the formulae for the volume of a cylinder= πr²h

so we then put the figures at their respective positions. and for the pie we put either 22/7 or 3.143 or 3.14

Answer:

8

Step-by-step explanation:

7*4=28

2*4=8

Answer:

c=8

Step-by-step explanation:

Using cross. multiplication

multiply 2 by 28 2x28=56

Multiple c by 7 cx7=7c

divide both sides by 7

c=8

Answer:

3 cones

Step-by-step explanation:

This is why the formula for the volume of a cone is 1/3 (π×r^2)× h, while the volume for a cylinder is (π× r^2)× h, respectively.

Answer:

C) 3 Cones.

Explanation:

Hope this helps! :)

Answer:

C

Step-by-step explanation:

[tex]y^2+4y-32=0\\(y+8)(y-4)=0\\y=4,-8[/tex]

Therefore, the answer is C. Hope this helps!

Answer:

7 is the most common roll with two six-s

( I hope this helped <3 )

Answer:

7/8

Step-by-step explanation:

I think the most common are 7/8.

Answer:

The graph changes from the original position to right 3 units and down 1 unit.

I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!

Answer:

Find the area of the shape

First the two triangles

3 x 4 = 12 so the area of both triangles is twelve

Now it is only 1 big rectangle left

The side lengths can be added 3 + 4 + 5 = 12

12 x 11 = 132

132+12=144

144 is the surface area/area

If you have any questions please ask

Step-by-step explanation:

Answer:

no real solutions

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

hello :

Y-3 (4-2Y) = 16​

y-12+6y = 16​

7y-12=16

so :7y =12+16

7y=28

y=28/7 =4

Answer: C

Step-by-step explanation:

[tex]\frac{3a}{4}+\frac{2a}{3}-\frac{a}{12}[/tex]

Find the least common denominator of 4, 3, and 12.

4-3-12 | 3

4-1-4   | 4

1-1-1    |-------- 12

The first fractions needs to be multiplied by 3, and the second fraction, by 4

[tex](\frac{(3a)*3}{(4)*3})+(\frac{(2a)*4}{(3)*4})-\frac{a}{12}[/tex]

Solve;

[tex]\frac{9a}{12}+\frac{8a}{12}-\frac{a}{12}[/tex]

Add the fractions with positive signs and subtract the one with negative sign.

[tex]\frac{(9a+8a)-a}{12}[/tex]

Solve;

[tex]\frac{17a-a}{12}=\frac{16a}{12}[/tex]

Simplify by 4;

16/4=4

12/4=3

[tex]\frac{4a}{3}[/tex]

Answer:

(4a)/3

Step-by-step explanation:

3a/4+2a/3-a/12

find L.C.M

9a+8a-1a/12=16a/12

16a/12=(4a)/3

Answer:

x = -9

Step-by-step explanation:

-4x = -1/2(10x + 18)

Distribute

-4x= - 5x -9

Add 5x to each side

-4x+5x = -5x+5x -9

x = -9

Hey there! I'm happy to help!

To find the volume of a cone, you multiply the base by the height and then divide by three.

The base of a cone is a circle. To find the area of a circle, we square the radius and then multiply it by pi (we will use 3.14). Let's find the base below.

6²=36

36×3.14=113.04

Now, we multiply by the height.

113.04×8=904.32

Finally, we divide by three.

904.32÷3=301.44

Therefore, the volume of this cone is about 301.44 units cubed.

Now you can find the area of cones! I hope that this helps! Have a wonderful day!

Answer:

301.44

Step-by-step explanation:

Answer:

Exponential decay is the decrease in a quantity according to the law. (1) for a parameter and constant (known as the decay constant), where is the exponential function and is the initial value.

Answer:

When a population or group of something is declining, and the amount that decreases is proportional to the size of the population, it's called exponential decay. In exponential decay, the total value decreases but the proportion that leaves remains constant over time.

Step-by-step explanation:

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's no solution to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

Answer:

B. No

Step-by-step explanation:

In order to see if (4, 2) is a solution, we have to plug 4 in for x and 2 in for y in the equations. If it's a true statement, then we know that the point is a solution.

One of the equations is y = 3x + 4. Plug in 4 for x and 2 for y:

y =? 3x + 4

2 =? 3 * 4 + 4

2 =? 12 + 4

2 ≠ 16

Thus, we know that (4, 2) is not a solution and the answer is B.

~ an aesthetics lover

Answer:

C. Estimate the probability using your simulation.

Step-by-step explanation: