A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 \text{ cm}30 cm30, start text, space, c, m, end text, and the bicycle wheel makes 333 full rotations before stopping.
How long is the trace of water left on the floor?
Round your answer to the nearest \text{cm}cmstart text, c, m, end text

Check the picture below.

keeping in mind that perpendicular lines have negative reciprocal slopes, and that we also know that the line is a perpendicular bisector, namely it cuts that segment into two equal halves as you can see in the picture, so it really passes through the midpoint of that segment, so let's get the slope of that green segment

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{7}}} \implies \cfrac{4}{-8}\implies -\cfrac{1}{2}[/tex]

so for the perpendicular bisector that'd be

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1}\implies 2}}[/tex]

now let's check for the midpoint of the green segment

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 +7}{2}~~~ ,~~~ \cfrac{ 9 +5}{2} \right) \implies \left(\cfrac{ 6 }{2}~~~ ,~~~ \cfrac{ 14 }{2} \right)\implies (3~~,~~7)[/tex]

so we're really looking for the equation of a line whose slope is 2 and that it passes through (3 , 7)

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 2}(x-\stackrel{x_1}{3}) \\\\\\ y-7=2x-6\implies {\LARGE \begin{array}{llll} y=2x+1 \end{array}}[/tex]

The divisions problem are:

A decimal is a number that consists of a whole and a fractional part.

Given:

we have the condition as divisor in division are decimals

So, we know in division we have main two parts: Dividend and Divisor.

we have to take the divisor as decimals.

So let us take the example

4068 / 0.03

So, for solving it we can proceed as

4068 * 100 /3

= 1356 * 100

=135600

Similarly, there many like

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Answer:-2/1

Step-by-step explanation:

rise is -2 and 1 is run

Answer:

[tex]\csc ^2(\theta)[/tex]

Step-by-step explanation:

Using Pythagorean identity,

[tex]\mathrm{1+\cot ^2(x)=\csc ^2(x)}\\\mathrm{=\csc ^2(\theta)}[/tex]

Answer:

1 + cot² θ = sec² θ

Step-by-step explanation:

1 + cot²θ =

I know this identity to be true:

sin² θ + cos² θ = 1

Divide both sides by sin² θ.

sin² θ / sin² θ + cos² θ / sin² θ = 1 / sin² θ

1 + cot² θ = sec² θ

The correct answer is 11.834.

Decimal Fraction Math refers to the mathematical expression of a fraction or mixed number where the denominator is a power of 10, such as 10, 100, or 1000, etc. Mathematical operations can be performed on fractions more easily when they are expressed in decimal form.

From 0 to 9, single-digit numerals are read exactly as they are written. However, when two numerals are involved, the left digit implies 10 times what the right digit indicates. In the number 24, that is, 4 is 4 and 2 is 20. Together, they make 24.

The rightmost digit of a three-digit number has the same meaning as the middle one, which is ten times the digit, and the leftmost digit, which is 100 times the digit.

√97.5 + 1.96

=  9.874 + 1.96

=  9874/1000 + 1960/1000

=  11834/1000

=  11.834

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The coordinates of the midpoint are:

x = (A + C) / 2

y = (B + D) / 2

Where (A, B) and (C, D) are the coordinates of the points M and J.

The midpoint is the middle point of a line segment and it is equidistant from both endpoints.

We have,

M_______X_______J

MX : XJ = 1 : 1

The formula for finding the coordinates of the midpoint is:

x = (a + c ) / 2

y = ( b + d ) / 2

(x, y) = coordinates of the midpoint.

Where (a, b) and (c, d) are the coordinates of the two endpoints.

We can consider,

M = (A, B)

J = (C, D)

X = (x, y)

Thus the coordinates of the midpoint X are:

x = (A + C) / 2

y = (B + D) / 2

Where (A, B) and (C, D) are the coordinates of the points M and J.

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Answer:

1) [tex]m[/tex]∠JKL = 145°

2) [tex]m[/tex]∠IHG = 164°

3) [tex]m[/tex]∠NME = 50°

4) [tex]m[/tex]∠TUV = 178°

I hope this helps! (✿◠‿◠)

The distance between the points B and H on the coordinate plane is 4.48 units

See below for the complete question

The coordinates of the points B and H are given as:

(-2.63, 7) and (1.85,7)

Rewrite properly as

B = (-2.63, 7)

H = (1.85,7)

The distance between any two points on a coordinate plane is calculated using the following distance formula

d = √(x2 - x1)^2 + (y2 -y1)^2

Substitute the known values in the above distance equation

So, we have

d = √(-2.63 - 1.85)^2 + (7 - 7)^2

Evaluate the exponents

So, we have

d = √20.0704 + 0

Evaluate the sum

So, we have

d = √20.0704

Evaluate the exponent

So, we have

d = 4.48

Hence, the distance between the points B and H on the coordinate plane is 4.48 units

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Possible question

Find the distance between B (-2.63, 7) and H (1.85,7)

Answer:

78.75 or 78 3/4

Step-by-step explanation:

Answer:

1:12

Step-by-step explanation:

You have to convert both value to the same measurement, so you gonna find how many minutes is in 5 hours which is (300 minutes) then you put 25/300 then cancel out

25% in the decimal number system is 0.25.

So, we need to divide the number by 100 and we want to convert a number in percentage into decimals.

Then,

Therefore, 25% in decimals is 0.25.

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The total cost of business is 1,87,500

We are given the ratio of shares of two men. So, let the share of first person be 2x and share of second person be 3x.

It is also stated that smaller share is 75000. Out of the two shares, 2x is the smaller one. So, relating the two statements -

2x = 75000

x = 75000 ÷ 2

Performing division

x = 37500

So, finding the larger share now -

Larger share = 3x

Larger share = 3×37500

Performing multiplication

Larger share = 112500

Total cost of business = Smaller share + Larger share

Total cost of business = 75000 + 112500

Total cost of business = 1,87,500

Hence, the total cost of business is 1,87,500.

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The base of the $4,560 which is 65% of the base is $7,015.38.

This  represented by the symbol %, is the division of any number by 100. The expression 25%, for example, means that 25 parts of a whole were divided into 100 parts.

The portion of 65% means that the amount given as $4,560 is only a part of the   whole amount known as base, which is unknown as the base, in other words, the base amount can be determined the portion divided by the percentage of the portion:

65%=$4560

1%=$4560/65

1%=$70.1538461538462

100%=$70.1538461538462*100

100%=$ 7,015.38

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Using the change of base formula the evaluated value of [tex]log_{3} 33[/tex]  is 3.184

Change of base formula is used to change the base of logarithm. It is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm.

According to the change of base formula :

[tex]log_{a} b = \frac{log_{x} b}{log_{x} a}[/tex]      

where base x is base 10

According to the question, we have to find the value of [tex]log_{3} 33[/tex]

Thus applying change of base formula we get

  [tex]log_{3} 33 = \frac{log_{10} 33}{log_{10} 3}[/tex]

calculating the value of log from the calculator we get,

    [tex]log_{3} 33 = \frac{1.519}{0.477}\\log_{3} 33 = 3.184[/tex]  

Thus using the change of base formula the evaluated value of [tex]log_{3} 33[/tex] is 3.184

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Answer: rational

explain

Answer: The sum is always a rational number.

Step-by-step explanation:

Step-by-step explanation:

Given, sum of two rational numbers is always a rational number

We have to determine if the given statement is true or false

Consider two rational numbers 2/3 and 4/5

Sum of two numbers = 2/3 + 4/5

= [2(5) + 4(3)]/3(5)

= (10 + 12)/15

= 22/15

22/15 is a rational number.

Consider two rational numbers 2/3 and 1/3

Here, the denominators are same

Sum of two numbers = 2/3 + 1/3

= (2 + 1)/3

= 3/3

= 1/1

1/1 is also a rational number

Therefore, the given statement is true.

The constant average rates of change of 1/6y + 3/8x = 24 is -9/4

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The linear equation is given as

1/6y + 3/8x = 24

Multiply through the equation 1/6y+3/8x=24 by 24 to eliminate the fraction

So, we have

24 * 1/6y + 24 * 3/8x = 24 * 24

Evaluate the product

So, we have

4y + 9x = 576

Rewrite the equation as

So, we have

4y = - 9x + 576

Divide through the equation by 4

So, we have

y = - 9/4x + 144

A linear equation is represented as

y = mx + c

Where

m = rate of change

So, we have

m = -9/4

Hence, the constant average rates of change of 1/6y + 3/8x = 24 is -9/4

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The equation is [tex]\frac{1}{2}x + \frac{1}{2}x[/tex]

Let the amounts of water that Sue's water bottle holds = x

According to the question,

given that,

Sue's water bottle holds the water = [tex]\frac{1}{2}x + \frac{1}{2}x[/tex] = [tex]\frac{2}{2}x[/tex] = x

Thus, assumption is true

Hence, the equation is [tex]\frac{1}{2}x + \frac{1}{2}x[/tex]

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Different Types of Equations:

Some of the math equations used in algebra are:

Linear Equation

A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Quadratic Equation

This is a second-order equation. In quadratic equations, at least one of the variables should be raised to exponent 2.

Example:

[tex]a x^{2}[/tex] + b x + c = 0

Cubic Equation

This is a third-order equation. In cubic equations, at least one of the variables should be raised to exponent 3.

Example:

[tex]a x^{3}[/tex] + [tex]b x^{2}[/tex]+ cx + d = 0

[tex]a^{3}[/tex] – 27 = 0

Rational Equation

A rational equation is an equation that contains fractions with a variable in the numerator, denominator, or both.

Example:  

[tex]\frac{x}{2}[/tex] = [tex]\frac{x + c}{4}[/tex]

How to prove an equation

One way to prove that an equation is true is to start with one side (say, the left-hand side) and to convert it, by a sequence of equality-preserving transformations, into the other side. But remember that a proof must be easy to check, so each step deserves a justification. We keep the steps elementary, based on known facts of algebra. Also, a proof should always start with a statement of the claim that is being proved.

.

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The value of y when we make y the subject of the formula in 5x - 5y = 40 will be B. y = -3x - 8

It should be noted that an equation is simply used to show the relationship that exists between the variables that are given.

In this situation, the equation given s

is illustrated as:

-15x - 5y = 40

Divide through by -5

-3x - y = 8

Then make y the subject of the formula

y = -3x - 8

Therefore, value of y when we make y the subject of the formula in 5x - 5y = 40 will be y = -3x - 8.

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Answer:

5

Step-by-step explanation:

5+5=2(5)

10=10

The solution to the inequality is x ≥ -10 2/3. On the graph, the solution to the inequality is to the right of the line

From the question, we are to solve the given inequality

The given inequality is

3x + 27 ≥ -5

Solving the inequality

3x + 27 ≥ -5

Subtract 27 from both sides of the inequality

3x + 27 -27 ≥ -5 - 27

3x  ≥ -32

Divide both sides of the inequality by 3

3x/3 ≥ -32/3

x ≥ -10 2/3

The graph of the inequality is shown below

Hence, the solution to the inequality is x ≥ -10 2/3. On the graph, the solution to the inequality is to the right of the line

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Answer:

12,300

Step-by-step explanation:

To round to the nearest hundred look at the tens place and if the number is a 5 or above add 1 to the hundreds place, in this case though the number is below 5 so you drop all the numbers behind it and nothing happens to the hundreds place

12,(3)46.6789

this is the hundreds place

12,3[4]6.6789

go to the tenths place and since the number is a 4 you drop it and the other numbers behind it.

Giving you the answer 12,300

Answer:

NM=FG

Step-by-step explanation:

Answer:

Segment EG and segment OM

Step-by-step explanation:

Comparing the lengths of segment EG and segment OM satisfies the side-side correspondence required for AAS congruence.

Answer:

what is the question?

Step-by-step explanation:

There is no picture or question

Answer: Question

Step-by-step explanation:

The logarithm function ( log 64 ) is not a common logarithm function as it does not have a base 10 but ahs a base e.

In mathematics, the common logarithm is the logarithm with base 10.

It is also known as the decadic logarithm and as the decimal logarithm function.

Here, we have the logarithm function as:

( log 64 )

Now, we can see that:

It does not have a base.

So, we will take the base as e.

So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.

Therefore, we get that, the logarithm function ( log 64 ) is not a common logarithm function as it does not have a base 10.

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