a hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. the chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$.

The measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.

An angle that has a measure that is less than 90 degrees is classified as an acute angle.

Given the diagram below, the angle that is formed by rays AO and CO is angle AOC. The instrument shows that angle AOC is exactly 30 degrees.

30 degrees is less than 90 degrees and can therefore be termed an acute angle.

Therefore, the measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.

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As per the drawing scale, the actual length is 16m.

What is a drawing scale?

Given scale is,

19:8

Therefore,

To determine the, actual length,

[tex]\frac{19}{8} =\frac{38}{actual\ length}[/tex]

⇒ actual length = [tex]\frac{38}{19}*8[/tex] = 16m.

Hence, as per the drawing scale the actual length is 16m

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The length of the segment BC is equal to 5√3 π / 3.

Herein we find the a geometric system formed by a circle and an inscribed  right triangle formed by two right triangles. By a quick inspection we find the following measures:

AD = 10π, m ∠ BCD = 60°, m ∠ BDC = 30°, m ∠ BDA = 60°, m ∠ BAD = 30°

Then, by 30-60-90 right triangle theorem we find that:

DB = (1 / 2) · AD

DB = (1 / 2) · 10π

DB = 5π

DB = √3 · BC

BC = (√3 / 3) · DB

BC = 5√3 π / 3

The length of the segment BC is equal to 5√3 π / 3.

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Based on the fact that the employer is changing the pay period to semimonthly, John's semimonthly salary to the nearest cent is $956.50

John's annual salary can be found to be $24,869

If a person is paid semimonthly, it means that they are paid twice a month or every two weeks.

This means that John's semimonthly salary is:
= 478.25 x 2

= $956.50

In a year, John's annual salary will be:

= 478.25 x 52 weeks

= $24,869

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Answer:

298781

Step-by-step explanation:

[tex]2xy \sqrt[3]{3y {}^{ \: 2} } [/tex]

The value of the expression given as −26.6/−1 is 26.6

The expression is given as

−26.6

-----------

−1

Rewrite the above expression properly as follows

So, we have

−26.6/−1 or −26.6 ÷ −1

This is so because the expression is a quotient expression

So, we have

−26.6/−1

Express −26.6 as -13.3 - 13.3

So, we have the following equation

−26.6/−1 = (−13.3  −13.3)/−1

Expand the expression

So, we have

−26.6/−1 = (−13.3)/−1 + (−13.3)/−1

Evaluate the quotients in the above equation

So, we have

−26.6/−1 = 13.3 + 13.3

Evaluate the quotients in the above equation

So, we have

−26.6/−1 = 26.6

Hence, the value of the expression given as −26.6/−1 is 26.6

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Answer:

k = x^3+y^3+z^3

Step-by-step explanation:

Solve for k by simplifying both sides of the equation, then isolating the variable.

Hope this helps.

Step-by-step explanation:

[tex] \frac{46}{62} \times 100 = 74.19 percent \\ 100 - 74.19 = 25.81 \: percent \\ her \: loss \: was \: 25.81 \: percent[/tex]

Answer:

z divided by 4 is 12

48 divided by 4 is 12

It is "false" that a cylinder is a polyhedron where two faces are parallel and congruent and the remaining faces are parallelograms. Its is a prism.

A polyhedron of two polygonal faces in parallel planes & parallelograms on the other faces is called prism.

Some features regarding the prism are-

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Answer:

∠ 2 = 60°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 remote interior angles.

123° is an exterior angle of the triangle , then

∠ 2 + 63° = 123° ( subtract 63° from both sides )

∠ 2 = 60°

Answer:

60

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180° so we can write the following equation to find the value of missing angle:

∠2 + 63 + 57 = 180 add like terms

∠2 + 120 = 180 subtract 120 from both sides

∠2 = 60

Answer:Q

Step-by-step explanation:1+2-3+4=1

Answer:

A. the number of bacteria colonies doubling every 80 minutes.

Step-by-step explanation:

A. 2 cells = 80 mins

B. 4 cells = 80 mins

how to check;

multiply both sides by 2 in equation A

2 × 2 = 80 × 2

4 cells = 160 mins

change the mins into hours

4 cells = 160 ÷ 60

4 cells.= 2 hrs 40 mins

coagulate results

equation A. is 4 cells = 2hrs 40 mins

equation B. is 4 cells = 4 hrs

therefore equation A. is faster

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x= 29 which is Friday of that Month.

As 1st February 2008 is Friday

By adding 7 to the date we will get the next Friday Date of that month

i.e., 1 + 7= 8

i.e., 8 is Friday

Again if we will add 7 in 8 then we will get another Friday

so by adding again i.e., 8 + 7= 15 which is again Friday

Then 15 + 7 = 22 which is Friday.

adding again we will reach final to final answer 22+ 7 = 29 which is Friday

after adding 29 with 7 we will get 36 and as we know there are only 30/31 days in a month.

So, by adding 7 to the date we will reach the next week.

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Answer: 57.75 m or about 57.8m

Step-by-step explanation:

Jupiter is 5,751.51 times more massive than Mercury.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The mass of the planet Jupiter is given below.

1,898,000,000,000,000,000,000,000,000 kg.

The scientific notation is:- 2 x 10²⁷ kg.

The mass of the planet Mercury is given below.

330,000,000,000,000,000,000,000 kg.

The scientific notation is:- 3.30 x 10²³ kg.

Divide the mass of the planet Jupiter by the mass of the planet Mercury. Then we have

Jupiter / Mercury =  2 x 10²⁷  / 3.30 x 10²³

Jupiter / Mercury = 5,751.51

Your question was incomplete, but the complete question was given below.

The most massive planet in the solar system, Jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg.

The least massive planet is Mercury, which has a mass of about 330,000,000,000,000,000,000,000 kg.

Use your estimates to find out how many times more massive Jupiter is than Mercury. Express your answer in standard form (without using a power of 10).

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Answer:

D is the answer

Step-by-step explanation:

please make my answer as brainelist

Answer: Can you give choices that in the problem

Step-by-step explanation:

After solving the expressions we get the value for each of it as:

a. 1/108

b. 7/18

Given:

a. 12x⁰(x⁻⁴)

Apply the multiplication property of exponents.

when variables multiply, the powers are added.

12x⁰⁻⁴

12x⁻⁴

substitute the value of x = 6 in the above term.

12(6)⁻⁴

12 × 1/6⁴

12 × 1/1296

1/108

b. 14(x⁻²)

The algebraic technique for resolving simultaneous linear equations is called the substitution method. The value of a variable from one equation is substituted in the second equation in this procedure, as the name implies.

directly substitute the value of the x in the expression.

14(6)⁻²

14 × 1/6²

14 × 1/36

7/18

hence after evaluating expressions we get the values as 1/108 and 7/18.

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Answer:

184

Step-by-step explanation:

The standard form the Complex number having real part "a" and imaginary part"b" is a+ib.

Complex number:

Basically, a Complex number is made up of two numbers: a real number and an imaginary number. A+iB, where an is a real number and ib is an imaginary number, is a Complex number. A and B are real numbers.

As a result, a Complex number is just a straightforward way to describe the addition of two integers, a real number and an imaginary number. It is divided into two parts: a pure actual component and a pure fictitious part.

Therefore,The standard form the complex number having real part "a" and imaginary part"b" is a+ib.

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Answer:It’s a+bi

Step-by-step explanation:

Answer:

y = 7/2x - 5/2 ; gradient is 7/2

y = 5/3x - 4/3 ; gradient is 5/3

y = -2/3x - 10/3; gradient is -2/3

Step-by-step explanation:

2y = 7x-5

5x - 3y=4

10 - 2x+3y = 0

NOTE: The gradient is the slope

Answer:

14. 41

15. 4

Step-by-step explanation:

I used Substitution.

2(14)+13 = 41

3(2) - 2 = 4

Answer: EF = 29 units and KM = 22 units

Step-by-step explanation: For the first one, we just add EF and FG, x+14 and 14, and make it equal to EG, 2x+13. We then get x+28 = 2x+13, x = 15. EF = x + 14 and then sub in 15 for x to get 29.

For KM, same deal as the first one. KL and LM, 6 and 2x, equals to KM, 3x-2. 2x+6 = 3x - 2. x = 8. KM = 3x - 2. sub in 8 for x and then we get 22.

When the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.

The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]

The general equation of the circle is [tex]x^{2} +y^{2}+2gx+2fy+c=0[/tex]

Where (-g,-f) is the coordinates of the circle

The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]

Divide the equation by 2

[tex]x^{2} +y^{2}-6x+4y-12=0[/tex]

Compare the equation with general form

2g= -6

g= -3

2f= 4

f= 2

The center of the circle (-g,-f) = (3,-2)

The radius of the circle = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]

Substitute the values in the equation

r= [tex]\sqrt{(-3)^{2}+2^{2}- (-24) }[/tex]

[tex]=\sqrt{9+4+24} \\=\sqrt{37}[/tex]

=6.08 units

Hence, when the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.

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Answer: See below

Step-by-step explanation:

1) For the first question, we have to multiply the width by the length to find the area of the whole rectangle:

(4x-4)(x+1)= 4x^2 -4

2) For the second question, we have to multiply the width by the length to find the area of the shaded area in the rectangle:

(2x+2)(x-1)= 2x^2-2

3) The total area of the unshaded part of the whole triangle equals the area of the whole rectangle minus the shaded area:

4x^2-4 - 2x^2 -2 = 2x^2 - 6

The given statement is true because it is the definition of nonlinear optimization.

it is the branch of mathematics with deals with the basic mathematical operators called arithmetic operators are addition, division, multiplication and subtraction.

Here,

The nonlinear optimization problem is an optimization problem in which at least one term in the objective function or a constraint is nonlinear, is true, Since its the basic definition of nonlinear optimization.

Thus, the given statement is true.

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Using linear function concepts, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.

A linear function is modeled by:

y = mx + b

In which:

From the table, we have that:

Thus, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.

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At Maryland, the mean number of points per player per game is greater than the median number of points per player per game. The mean number of points per player per game is the same at all 3 schools.

Given that in Baylor's University that there are 6 players who each score 12 points per game, and 6 players who each score 0 points per game.

The scores are 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12.

Mean = Sum/Count = 72/12 = 6.

Median is the average between the nth  and (n+1)th  term.

(0+ 12)/2 = 6

In Maryland university 1 player scores 58 points per game, 1 player scores 14 points per game, and the rest of the 10 score 0 points per game,

58, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Mean = Sum/Count = 72/12 = 6.

Median is 0

In Dartmouth, university, 4 players score 5 points per game, 4 players score 6 points per game, 4 players score 7 points per game.

The scores are

5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7

Mean = Sum/Count = 72/12 = 6

Median =(6+6)/2= 6

​

At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.

The mean number of points per player per game is the same at all 3 schools.

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Answer:

x=3

Step-by-step explanation:

4x-2x+6=-7+5x+4

2x+6=-7+5x+4

2x+6-6=5x-3-6

2x=5x-9

-3x=-9

x=3