A circle has centre (0, 0) and it passes through the point (5, -3)
Find the radius of the circle, in surd form.

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.

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Answer: The parabola is wider than the parent function

Step-by-step explanation:

If "a" is a fraction less than one, then the parabola becomes wider.

See graph (attached)

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:

[tex]6x + 42[/tex]

Step-by-step explanation:

Apply the distributive property:

[tex]6x + 6 \times 7[/tex]

Multiply 6 by 7

[tex]6x + 42[/tex]

Answer:

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

Answer:

The correct answer is 11 ft.

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.

Subtract x from each side:

x+4-x=2x-7-x

4=x-7.

Add 7 to both sides:

4+7=x-7+7

11=x

Answer:

11

Step-by-step explanation:

On edge

Answer:Perimeter, 50ft

Step-by-step explanation:since it is around the answer is 50 ft

Answer:

m = 17

Step-by-step explanation:

[tex]4(m - 13) - 8 = 8 \\ 4(m - 13) = 8 + 8 \\ 4(m - 13) = 16 \\ (m - 13) = \frac{16}{4} \\ m - 13 = 4 \\ m = 4 + 13 \\ \huge \red { \boxed{m = 17}}[/tex]

Answer:

It is A because due to the slope it is a parallelogram.

Step-by-step explanation:

Answer:

its a

Step-by-step explanation:

Answer:

A 50

B 10

C 12/5

D 5

E 21

F 100

Answer:

angle of depression = -12 degrees

Step-by-step explanation:

Sin = opposite/hypotenuse

sin = -208/1000

inv sin 0.208 = -12

To solve this problem, we just need to use trigonometric ratio and use the ratio that best fits this problem. The angle of depression is equal to 76.23 degrees.

Using SOHCAHTOA, we can easily solve this problem, but we need to first know which ratio to use

Data;

since we have the value of opposite and adjacent, we can solve this using the tangent of the angle

[tex]tan\theta = \frac{opposite}{adjacent} \\tan \theta = \frac{1000}{208} \\tan\theta = 4.807\\\theta = sin^-^1 (4.0807)\\\theta = 76.23^0[/tex]

From the calculation above, the angle of depression is equal to 76.23 degrees.

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Answer:

x=6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

x = 6

Step-by-step explanation:

In this equation, we are told to solve for the value of x. Thus, we must isolate the variable x (poor x... we're always trying to isolate it).

3 - 2x = -1.5x

(I'm going to swap sides to make it easier for me to solve. This doesn't change anything mathematically due to the associative laws. It's purely cosmetic.)

-1.5x = 3 - 2x

First, we can add 2x to both sides of the equation to get all algebraic expressions containing the variable x on one side of the equation alone.

0.5x = 3

For our next part here, let's convert 0.5 to a fraction to make life easier for us.

[tex]\frac{1}{2}[/tex]x = 3

When isolating x in this, we are trying to get rid of 1/2. How can we do this? We can multiply is by 2!

[tex]\frac{1}{2}[/tex]x · [tex]\frac{2}{1}[/tex] = 1x (or simply x)

What we do to one side we must do to another.

x = 3 · 2

x = 6

Our answer is x = 6. Woo!

Answer:

5.3

Step-by-step explanation:

Answer:

The answer is 5.3

Step-by-step explanation:

5.3x3-2= 13.9 but when you round its 14

Answer:

See explanation below.

Step-by-step explanation:

First, read this explanation of how to understand probability numbers.

A probability number is a number from 0 to 1. It can be written as a decimal, a fraction, or a percent, but it must be from 0 to 1. The numbers 0, 25%, 1/3, 0.75 are all examples of probabilities since they are all from 0 to 1. 25% is the same as 0.25; 1/3 is the same as 0.333... All probabilities are expressed as 0, 1, or a number in between 0 and 1.

A probability of 0 means the event will not happen. It is an impossibility.

A probability of 1 or 100% is a sure thing it will happen. It is certain it will happen.

A probability of 50% or 0.5 or 1/2 means it is as likely to happen as it is not to happen.

A probability of between 0 and 0.5 is more likely not to happen than to happen.

A probability of between 0.5 and 1 is more likely to happen than to not happen.

Now let's look at each one of the probabilities in your problem.

1. 1/4

1/4 is the same as 0.25 which is between 0 and 0.5. It is more likely to not happen.

1. b. Unlikely

2. 0.0

0.0 will definitely not happen.

2. e. Impossible

3. 0.50

0.50 can just as easily happen or not happen.

3. d. Equally Likely

4. 100%

100% is the same as 1. A probability of 1 means an event that is certain to happen.

4. a. Certain

5. 75/100

75/100 is the same as 3/4 and 0.75; 0.75 is between 0.5 and 1, so it is more likely to happen than to not happen.

5. c. Likely

Answer:

[tex]73\%[/tex]

Step-by-step explanation:

Given: Present weight of Caleb’s puppy = 2,250 grams

Puppy weighed 600 grams at his last visit to the veterinarian’s office.

To find: percent increase in the puppy’s weight rounded to the nearest whole number

Solution:

Increase in puppy's weight = 2250 - 600 = 1650 grams

Percent increase in the puppy’s weight =( Increase in puppy's weight/Present weight of Caleb’s puppy) × 100 = [tex]\frac{1650}{2250}(100)=73.33 \%[/tex]

[tex]73.33\%[/tex] is rounded to [tex]73\%[/tex]

Answer: 20x + 20

Step-by-step explanation: In this problem, the 5 "distributes" through the parentheses, multiplying by each of the terms inside.

So we have 5(4x) + 5(4) which simplifies to 20x + 20.

Answer:

Step-by-step explanation:

43feet

Answer:

The math function has the greater slope, which shows that the estimated time per question for math is greater than the estimated time per question for language arts.

OR B on edge

Step-by-step explanation:

The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is increasing at a faster rate than the cost per pound of broccoli.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

First, Slope for Broccoli

Slope = (3.6 - 3) / (3 - 2.5)

Slope = 0.6 / 0.5

Slope = 1.2

Second, Slope for Cauliflower

slope = (4.50 - 2.75) / (4.5 - 2.75)

= 1.75 / 1.75

= 1.000

Since the slope of the cauliflower function (1.0000) is greater than the slope of the broccoli function (0.8364), we can conclude that the cauliflower function has the greater slope.

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Answer:

2x+2(x+5)) = 24

Step-by-step explanation:

2x+ 2(x+5) = 24

x is represented by the shorter side. Multiply by 2 because of the 2 sides. For the longer side, since it is 5m longer than the shorter side, you have to write (x+5). Multiply by 2 because of the 2 sides. Finally, add them both together since it is the area and set it equal to 24.

Answer:

-15

Step-by-step explanation:

3(2 - 7)​

PEMDAS says parentheses first

Subtract

3 (-5)

Multiply

-15

Answer:

(0,-41)

Step-by-step explanation:

You can see that for each 9 units that x goes up, y goes up by 19. If we continue this pattern, it will take 2 more jumps of 9 units for the x value to be 0 or to reach the y intercept. Adding 19 twice to -79 gives -41. Hope this helps!

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:

less than

[tex]1 \frac{1}{2} [/tex]

I believe

Answer:

Step-by-step explanation:

Hard to figure out huh

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: 8

Step-by-step explanation:

Ella tiene que bajar los 6 pisos, mas 2.

6+2=8

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.