Which explanation can be used to derive the formula for the circumference of a circle? Will give brainliest!
A) Find the length of the diameter and double this length. Multiply this length by ​π​ and set equal the to the circumference. Substitute the diameter for 2 times radius.
B) Find the difference between the length of the circumference and diameter. Set up an equation showing the relationship of the circumference to diameter to the difference. Rearrange the equation to solve for the circumference. Substitute the diameter with 2 times the radius.
C) Find the ratio of the diameter to the area of the circle. Use this ratio to set up an equation to show this ratio equaling ​π​. Substitute the area with 3 times the circumference. Then rearrange the equation to equal to the circumference.
D) First find the relationship of the circumference to its diameter by finding that the length of the diameter wraps around the length of the circumference approximately ​π​ times. Use this relationship to write an equation showing the ratio of circumference to diameter equaling ​π​ . Then rearrange the equation to solve for the circumference. Substitute the diameter for 2 times the radius.

THIS IS THE COMPLETE QUESTION BELOW;

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?

Answers:

(–3, –0.90)

(–2.5, –0.75)

(4.5, 1.35)

(8, 2.40)

Answer

(8, 2.40)

Step by step Explanation

✓We can denote the number of days library book is late = X,

✓We can denote the the total fee = Y.

We were told $0.30 fee is charged at midnight.

Then for lateness for just 1day,the charged fees= 1day ×

$0.30

For X number of days the charged fees= Xday ×$0.30

Therefore, total charge for lateness for X number of days late = Y.

Then can be expressed as

Y= 0.30 * X...............eqn(1)

We can now test the option one after the other

FIRST OPTION (-3, -0.9)

Here we should know the number of days cannot be negative so there is no need of testing in the equation (1)

SECOND OPTION (-2.5, -0.75)

Here we should know the number of days cannot be negative so there is no need of testing in the equation (1)

THIRD OPTION(4.5, 1.35)

here the number of days will definitely be a whole number not 4.5, it's either

charge for 4 days or 5 days.

FORTH OPTION (8, 2.40)

this should be correct because the number of days is whole number and not negative, then if we test it from our equation it satisfy the equation too

Y= 0.30 * X...............eqn(1)

Y= 0.30 * X

2.40= 0.30 * 8

2.40 = 2.40.

Therefore, (8, 2.40) is the answer

Answer:

8

Step-by-step explanation:

Given hotel bill = ₹4800

Let initially, number of people = [tex]x[/tex]

Initial Bill of each person = Hotel bill divided by number of people = [tex]\frac{4800}{x}[/tex]

4 people are added to the hotel stay.

i.e. new number of people = [tex]x+4[/tex]

New bill becomes ₹200 less for each person.

New bill for each person = [tex]\frac{4800}{x}[/tex] - 200

Hotel bill remains the same i.e. ₹4800 = New bill for each person multiplied by new number of people.

[tex]4800 = (\dfrac{4800}{x}-200) (x+4)\\\Rightarrow 4800 = \dfrac{4800}{x}\times x -200\times x + \dfrac{4800}{x}\times 4 - 200\times 4\\\Rightarrow 4800 = 4800 -200 x + \dfrac{4800}{x}\times 4 - 800 \\\Rightarrow 800 = -200x+\dfrac{19200}{x}\\\Rightarrow 4 = -x+\dfrac{96}{x}\\\Rightarrow x^2+4x-96=0 \\\Rightarrow x^2+12x-8x-96=0\\\Rightarrow x(x+12)-8(x+12)=0\\\Rightarrow \bold{x = 8}, x= -12\ not\ possible[/tex]

Answer:

x = -8

Step-by-step explanation:

16+6-6x-4=-7x+3+7

Combine like terms

18 -6x = -7x+10

Add 7x to each side

18-6x+7x = -7x+7x+10

18+x = 10

Subtract 18 from each side

18+x-18 = 10-18

x = -8

Answer:

x = -8

Step-by-step explanation:

16+6-6x-4 = -7x+3+7

18 - 6x = -7x + 10

-6x + 7x = 10 - 18

x = -8

Check:

18 - 6*-8 = -7*-8 + 10

18 + 48 = 56 + 10 = 66

Answer:

17/21

Step-by-step explanation:

102/126

Divide the top and bottom by 6

17/21

Answer:

17/21

Step-by-step explanation:

102/2=51  126/2=63

51/3=17  63/3=21

17/21

Start with the parent function [tex]y = |x|[/tex] which is a V shape graph that has its vertex at (0,0) and it is the lowest point. Every point has a positive y coordinate other than the vertex of course.

Reflect over the y axis to get [tex]y = -|x|[/tex], so now everything is negative or below the x axis, other than the vertex point.

Lastly, shift everything up 1 unit by adding 1 onto the right side getting [tex]y = -|x|+1[/tex]

Answer:

y=absolute value brackets -x end absolute value brackets +1

Step-by-step explanation:

this is the equation that matches

Answer:

4

Step-by-step explanation:

Given that :

Clients are interviewed in groups of 2 on the first day; meaning two persons at a time

Second day, clients are interviewed in groups of 4; meaning 4 persons at a time.

Therefore, if the same number of clients are to be interviewed on each day, the smallest number of clients that could be interviewed each day could be obtained by getting the Least Common Multiple of both numbers: 2 and 4

- - - - 2 - - - 4

2 - - - 1 - - - 2

2 - - - 1 - - - 1

Therefore, the Least common multiple is (2 * 2) = 4

Therefore, the smallest number of clients that could be interviewed each day is 4.

Answer:

Scalene Right Triangle

Step-by-step explanation:

A possible type of triangle that has no equal sides and one right angle is a right triangle.

Right triangles have just one angle that is equal to 90°, and they can be either isosceles or scalene triangles.

Hope this helped!

Answer:

600 is the missing space

Step-by-step explanation:

rate me brainliest plz

Answer:

The shaded area is 18 ft^2

Step-by-step explanation:

First find the area of the total trapezoid

A = bh

A = 1/2 ( b1+b2) *h

   = 1/2 ( 6+12) *6

   = 1/2 ( 18)*6

   =54

Now find the area of the triangle

A = 1/2 bh

   = 1/2 ( 12) * 6

   = 36

Subtract the triangle from the trapezoid

54-36

18

The shaded area is 18 ft^2

Answer:

D. 18 sq.ft

Step-by-step explanation:

Lets make it simple and short.

Area of a triangle is 1/2 b h

b = 6

h = 6

Area = 1/2 * 6 * 6

Area = 18 sq.ft

Answer:

1. ( I didnt understand the question but I divided them using the calculator.)

A.) 76543

÷ 2= 38,271.5

÷ 3= 25,514.333...

÷ 9= 8,504.777...

÷ 11= 6,958.454545...

B.) 98765436

÷ 2= 49,382,718

÷ 3= 32,921,812

÷ 9= 10,973,937.333...

÷ 11= 8,978,676

2. B

A.) 67894

÷ 4= 16,973.5

÷ 8= 8,486.75

B.) 9685048

÷ 4= 2,421,262

÷ 8= 1,210,631

Explanation:

I used the calculator to divide.

I hope this helps! I'm sorry if it's wrong.

The triangle ABC, triangle FDE, and triangle GIH are congruent with each other.

Three sides and three internal angles define a triangle, a basic shape. The symbol is used to represent one of the geometric shapes in which the three corners are connected to one another. Triangles are categorized according to their sides into numerous different forms.

As per the given data in the question,

Sides AB = DF, AB = GI, BC = HI, and DE = HI are equal to each other.

Also, the angles, m∠B = m∠D = m∠I are equal.

Then by the property of the side angle side all the triangles are congruent with each other.

To know more about Triangle:

https://brainly.com/question/2773823

#SPJ3

Answer:

A.  ΔABC, ΔFDE, and ΔGIH

[tex]t=\sqrt{\dfrac{ab-s}{r+ak}}\\\\t^2=\dfrac{ab-s}{r+ak}\\\\rt^2+akt^2=ab-s\\\\akt^2-ab=-rt^2-s\\\\a(kt^2-b)=-(rt^2+s)\\\\a=-\dfrac{rt^2+s}{kt^2-b}\\\\a=-\dfrac{rt^2+s}{-(b-kt^2)}\\\\a=\dfrac{rt^2+s}{b-kt^2}[/tex]

Answer:

about 2.72 cm.

Step-by-step explanation:

Since, all the bowls are identical, I just added the heights of bothe stacks together and I divided that sum by the number of bowls in each stack all added together.

16.82+21.2=38.02 cm in total height of both stacks.

8+6=14 bowls in all from both stacks

38.02 cm/14 bowls=2.71571428, or rounded, about 2.72 cm

Answer:

8-1

Step-by-step explanation:

theres 8 boxes they crossed off one of them, now theres 7

Step-by-step explanation:

the answer to the question is C. 64.

Answer:

22.5º

Step-by-step explanation:

The angle of one shaded part and one unshaded part is 90º

We have shaded part ([tex]s[/tex]) and unshaded part ([tex]u[/tex])

[tex]90\º = u+s[/tex]

[tex]$u=\frac{s}{3} $[/tex]

[tex]$90\º = \frac{s}{3} +s$[/tex]

[tex]$90\º = \frac{s}{3} +\frac{3s}{3} $[/tex]

[tex]$90\º = \frac{4s}{3} $[/tex]

[tex]$270\º = 4s $[/tex]

[tex]s=67.5\º \implies u=22.5\º[/tex]

Answer: 22.5º

Step-by-step explanation:

Answer:

1 1/7.

Step-by-step explanation:

-9 2/7 - (-10 3/7)

= -9 2/7  + 10 3/7

= - 9 + 10 - 2/7 + 3/7

= 1 + 1/7

= 1 1/7.

Answer:

Option B is the correct option

Step-by-step explanation:

[tex] \mathsf{ - 9 \frac{2}{7} - ( - 10 \frac{3}{7}) }[/tex]

First thing we have to do is that convert the mixed number into improper fraction .

[tex] \blue{ \mathsf{how \: to \: convert \: \: the \: improper \: fraction \: to \: mixed \: number}}[/tex]

Follow the steps:

Now, let's do it!

[tex] \mathsf{ - \frac{ 9 \times7 + 2 }{7} - ( - 10 \frac{3}{7} )}[/tex]

⇒[tex] \mathsf{ - \frac{65}{7} - ( - 10 \frac{3}{7} )}[/tex]

When there is a ( - ) in front of an expression in the

parentheses , change the sign of each term in the expression

⇒[tex] \mathsf{ - \frac{65}{7} + 10 \frac{3}{7} }[/tex]

Convert mixed number into improper fraction

⇒[tex] \mathsf{ - \frac{65}{7} + \frac{73}{7} }[/tex]

While performing the addition and subtraction of like fractions , you just have to add or subtract the numbers for respectively in which the denominator is retained same

⇒[tex] \mathsf{ \frac{ - 65 + 73}{7} }[/tex]

Calculate

⇒[tex] \mathsf{ \frac{8}{7} }[/tex]

Convert the improper fraction into mixed fraction.

( Since 8 is being divided by 7 , I am gonna use long division )

( See attached picture )

⇒[tex] \mathsf{1 \frac{1}{7} }[/tex]

Hope I helped!

Best regards!!

Answer:

Hey there!

That would result in 0.00735.

Let me know if this helps :)

Hence, the significant figures are [tex]0.00735.[/tex]

What is the approximation?

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations.

Here given that,

Approximate [tex]0.007349[/tex] to  significant figures​

So, the significant figures are [tex]0.00735.[/tex]

Hence, the significant figures are [tex]0.00735.[/tex]

To know more about the approximation

https://brainly.com/question/29580932

#SPJ2

Answer:

Step-by-step explanation:

The maximum possible distance between  two posts for the fence will be given by HCF ( highest common factor ) of 24 and 64

24 = 8 x 3

64 = 8 x 8

highest common factor is 8 .

So distance between two poles ( maximum separation ) will be 8 m .

Ans : 8 m .

Answer:

Step-by-step explanation:

When you go shopping for anything, you know that the more of that something you buy, the more money you are going to spend. In other words, the amount of money you spend depends directly upon the amount of stuff you buy. So the number of boxes of cookies you buy is the independent variable and the amount of money you spend on the cookies is the dependent variable.

Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

So your remainder would be 3

Hope this helps

Answer:

quotient

Step-by-step explanation:

Answer:

quotient

Step-by-step explanation:

Cancelling identical factors in the numerator and the denominator will give the quotient. For example,x2+5x+6x+3=(x+2)(x+3)x+3 = x + 3

Answer:

Step-by-step explanation:

18n - 7p-15n = 5p

To solve for n first make n the subject

Group like terms

That's

18n - 15n = 5p + 7p

Simplify

3n = 12p

Divide both sides by 3 to make n stand alone

That's

3n/3 = 12p/3

We have the final answer as

Hope this helps you

Answer:

D) n = 4p

Step-by-step explanation:

18n - 7p - 15n = 5p

18n - 15n = 5p + 7p

Add like terms

3n = 12p

Divide both sides by 3

3n/3 = 12p/3

n = 4p

ABC is a equilateral triangle .

Proof :-

Let's assume both circles as C1 and C2 [ as shown in the figure ]

AC is the radius of circle C1.

BC is the radius of circle C2 .

AB and AC both are radius of circle C1 so both are equal ie AB = AC .

AB and BC both are radius of circle C 2 so both are equal ie AB = BC .

Hence we conclude that .

AB = BC = AC.

So the triangle is equilateral triangle.

Answer:

102

Step-by-step explanation:

Answer:

-49152

Step-by-step explanation:

The pattern is:

multiply for 4

then:

-3, -12, -48, -192, -768, -3072, -12288, -49152

Answer:

  55°

Step-by-step explanation:

Perhaps you want the measure of angle B. (There is no "b" in the figure.)

That measure is half the measure of the intercepted arc:

  m∠B = 110°/2 = 55°

Angle B is 55°.

Answer:

78

Step-by-step explanation:

A 45-45-90 triangle has sides like..

So the height of the parallelogram is 6.5

6.5 x 12 = 78

Answer:

78 in^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = ( 12) * h

We can find the height  from using trig functions

tan 45 = h /6.5

6.5 tan 45 = h

A = ( 12) * 6.5 tan 45

   =12 ( 6.5) * 1

   =78

Answer:

N1356

Step-by-step explanation: I hope it helps :)

[tex]Profit \% = 15\%\\Selling -Price = N1560.00\\C.P = ?\\\\CP = ( SP \times 100 ) / ( 100 + percentage \: profit).\\C.P =\frac{Selling \:price \times 100}{100+ Profit \%} \\\\C.P = \frac{1560\times 100}{100+15} \\\\C .P = \frac{156000}{115} \\\\C.P =N1356.5[/tex]

Answer:

h = 112.5 feets

Step-by-step explanation:

The equation for horizontal distance "h" in feet of a projectile with initial velocity v₀ and initial angle theta is given by :

[tex]h=\dfrac{v_o^2}{16}\sin\theta\cos\theta[/tex]

We know that, [tex]2\sin\theta\cos\theta=\sin2\theta[/tex]

So,

[tex]h=\dfrac{v_o^2}{32}\sin2\theta[/tex]

Now we need to find the maximum horizontal distance possible and at what angle does this occur.

For maximum distance angle should be 45 degrees. Som,

[tex]h=\dfrac{60^2}{32}\sin2(45)\\\\h=112.5\ \text{feet}[/tex]

So, 112.5 feets is the maximum possible distance.