In Cedarburg, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 12 kilometers and
the distance between the courthouse and the city pool is 13 kilometers, how far is the library
from the community pool?
kilometers

Step-by-step explanation:

so, it is

3³ × (3⁴)^(0.5) ?

remember, when multiplying exponents of the same base, we add the exponents : e.g.

a⁵ × a³ = a⁸

when we have exponents in exponents we multiply the exponents : e.g.

(a³)⁴ = a¹²

now, also remember the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

now, let's look at our expression again :

3³ × (3⁴)^(0.5)

since we only want to simplify and not to calculate, we leave (3⁴) alone, because the only thing we could do would be to actually calculate 3⁴.

so,

(3⁴)^(0.5) = 3^(4×0.5) = 3²

and then,

3³ × 3² = 3^(3+2) = 3⁵

so, the simplified expression is 3⁵.

which is 243 ...

The (0, 2) and (3•π, 6) minimum and maximum points on the graph of the sinusoidal function indicates that the function is as follows

[tex]y = 2\cdot sin\left(\dfrac{1}{3} \times \left(x - \dfrac{3\times \pi}{2} \right)\right) + 4[/tex]

A sinusoidal function is a function based on the trigonometric function of sine.

The points on the graph of the sinusoidal function are;

Minimum point of the function; (3•π, 6)

Maximum point of the function; (0, 2)

The general form of the equation of a sinusoidal function is presented as follows;

The sinusoidal function equation is; y = a×sin(b×(x - h)) + k

The amplitude, a, is half the distance between the maximum and minimum points, therefore;

a = (6 - 2)÷2 = 2

a = 2

From the information in the question, when x = 0, y = 2

Plugging in the values of x = 0, y = 2in the equation, y = a×sin(b×(x - h)) + k, produces;

2 = 2×sin(b×(0 - h)) + k

The point (0, 2) is a minimum point, therefore; sin(b×(0 - h)) = -1

2 = 2×sin(b×(0 - h)) + k = 2×(-1) + k = -2 + k

k = 2 + 2 = 4

At the minimum point the value of sine is -1, which indicates that the value of the argument, (b•(0 - h)) = -π/2

Therefore; -b•h = -π/2

h = π/(2·b)

At the maximum point, (b×(x - h)) = π/2

Therefore; (b×(3×π - π/(2×b))) = π/2

b = 1/3

Therefore;

h = π/(2×b) = 3×π/2

y = 2×sin((1/3)×(x - 3×π/2)) + 4

The function is; y = 2×sin((1/3)×(x - 3×π/2)) + 4

The formula of the function for the graph is therefore; y = 2×sin((1/3)×(x - 3×π/2)) + 4

Learn more about the sinusoidal function in mathematics here:

https://brainly.com/question/26288131

#SPJ1

Answer: I believe y=1x+0 (or y=x)

Step-by-step explanation: if you copy the slope and make the line go through (2,2), you get this line.

Answer:

1, 2, 4, 7,  14 and 28

Step-by-step explanation:

1 x 28 = 28

2 x 14 = 28

4 x 7 = 28

Answer:

 1, 2, 4, 7, 14 and 28

Step-by-step explanation:

The area of the rectangle is, 24 square centimeter.

What is area?

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let, the perimeter of the rectangle is 20 centimeter.

The length is 6 centimeter.

Suppose the width of the rectangle is y.

So,

Perimeter = 2(6) + 2(y)

           20 = 12 + 2y

             8 = 2y

             y = 4

Hence, the width of the rectangle is 4 centimeter.

Since,

Area of rectangle = length x width

                          A =  6 x 4

                          A = 24

Therefore, the area of the rectangle is, 24 square centimeter.

To know more about the area, click on the link

https://brainly.com/question/25292087

#SPJ4

In exponential relations, we can represents given values like this:

[tex]f(x)=a*c^x[/tex]

We're given:

⇒ Plug this information into [tex]f(x)=a*c^x[/tex]:

[tex]f(x)=27,100*(0.93)^x[/tex]

Why input 0.93 and not 0.07? Let's think of it this way: To calculate the new price of the car after one year, we find 93% of 27,100.

The dependent variable is the price (y) and the independent variable is the time in years (x).

Therefore, to find the value of the car after 6 years, we plug in 6 as x:

[tex]f(x)=27,100*(0.93)^6[/tex]

[tex]V=27,100*(0.93)^6[/tex]

1/2 x + 8 = 15  Grace will pay for a student ticket

the question requests the cost of a "student ticket." Because we don't know, let's assume the student ticket price is "x" dollars.

Because we know from the question that "the price of an adult ticket is half the price of a student ticket plus $8.00," we can represent the adult ticket price as follows:

1/2 x + 8

If we also get "An adult ticket costs $15.00" from the question, we can write the equation as:

1/2 x + 8 = 15

Grace will pay for a student ticket

To learn more about Cost:

https://brainly.com/question/15135554

#SPJ4

Answer:

There are 10 marbles, 2 are yellow

The probability would be 2:10 but in simplest form 1:5

The probability of picking both the same = 1:5 x 1:5 = 1:25

Step-by-step explanation:

Answer:

the answer i think it is 432

The next term of the given geometric series is the fifth term which is; a₅ = 4

We are given the geometric series as;

1024, -256, 64, -16,.....

The formula to find the nth term of a geometric series is;

aₙ = ar^(n - 1)

where;

a is first term

r is common ratio

n is position of term

Thus, from the given series, we have that;

a = 1024

r = -256/1024

r = -1/4

Thus, the formula for the nth term of the series is;

aₙ = 1024(-¹/₄)^(n - 1)

Next term is the fifth term and so we have;

a₅ = 1024(-¹/₄)^(5 - 1)

a₅ = 1024(-¹/₄)^(4)

a₅ = 4

Read more about nth term of geometric series at; https://brainly.com/question/24643676

#SPJ1

[tex]2\div \cfrac{3}{7}\implies \cfrac{2}{1}\div \cfrac{3}{7}\implies \cfrac{2}{1}\cdot \cfrac{7}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]

The quotient for the expression is 4.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

2 ÷ [tex]\frac{3}{7}[/tex]

= 2 / (3/7)

= (2 x 7) / 3

= 14/3

Now,

3 ) 14 ( 4

    12

      2

Remainder = 2

Quotient = 4

Thus,

The quotient is 4.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:26

Step-by-step explanation:

The values of x, y and z in the angles are as follows

When parallel lines are cut by a transversal line, angle relationship are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.

The parallel lines forms angles relationships.

Therefore,

x = 2y (alternate angles)

z = 2x + 90 (alternate angles)

Using substitution,

z = 2(2y) + 90

z = 4y + 90

x + 2x + 90 = 180 (sum of angles on a straight line)

3x  = 180 - 90

3x = 90

x = 90 / 3

x = 30°

Hence,

30 = 2(y)

y = 30 / 2

y = 15

z = 4(15)+ 90

z = 60 + 90

z = 150°

learn more on angles here; https://brainly.com/question/11553350

#SPJ1

Answer: 1.72

Step-by-step explanation:

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{10})\hspace{10em} \stackrel{slope}{m} ~=~ 8 \\\\\\ \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}{10}=\stackrel{m}{ 8}(x-\stackrel{x_1}{2}) \\\\\\ y-10=8x-16\implies {\Large \begin{array}{llll} y=8x-6 \end{array}}[/tex]

Answer:

[tex]x=1+5\sqrt{2}, 1-5\sqrt{2}[/tex]

Step-by-step explanation:

[tex](x-1)^2=50 \\ \\ x-1=\pm 5\sqrt{2} \\ \\ x=1 \pm 5\sqrt{2}[/tex]

The vertex form of the quadratic equation is f(x) = -3(x - 2)² + 5. The coordinates of the vertex are (2, 5).

We are given a quadratic function. The equation of the quadratic function is f(x) = -3x² + 12x - 7. We need to convert the equation to vertex form. We can convert a quadratic equation to its standard vertex form by "completing the square" method. The calculations are done below.

f(x) = -3x² + 12x - 7

f(x) = -3(x² - 4x) - 7

f(x) = -3(x² - 4x + 2² - 2²) - 7

f(x) = -3(x² - 4x + 2²) - 7 + 3*2²

f(x) = -3(x - 2)² - 7 + 12

f(x) = -3(x - 2)² + 5

The coordinates of the vertex are (2, 5).

To learn more about vertex, visit :

https://brainly.com/question/29030495

#SPJ1

Answer:

8 hours

Step-by-step explanation:

if it takes 2hrs to do 4 pages it takes an hour to do 2 pages

2*8=16

1*8=8

8 hours

hope it helps

Answer:

1. 190 degrees

2.

For the red triangle

-2,4, -4,2 -2,1

For the blue triangle

-2,-5 -5,-5 -7,-4

I don't know if this is correct but I hope this helps :)

Answer:

9/14 (9 over 14)

Step-by-step explanation:

Answer:

what are the instructions

Step-by-step explanation:

please repost with instructions

Answer:

10,101

Step-by-step explanation:

Percent (%) means 'out of one hundred'

29.5%= 29.5/100 'out of one hundred'

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

How to increase the number 7,800

by 29.5% of it's value?

1.) Calculate the new value of the number increased by the percentage of it's initial value

The new value=

7,800+ The value of the percentage increase=

7,800 + (29.5% x 7,800) =

7,800 + 29.5% x 7,800=

(1 + 29.5%) x 7,800=

(100% + 29.5%) x 7,800=

129.5% x 7,800

129.5 ÷ 100 x 7,800=

129.5 x 7,800 ÷ 100=

1,010,100 ÷ 100=

10,101

-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-••-

I hope this was helpful!

Answer:

D

Step-by-step explanation:

500 user in a day that mean in 2 days you get 1000 user cause the double of 500 is 1000

Answer:

Step-by-step explanation: If the square is 30 ft on one side the other side must be too. So 30x30 = 900. Now, we know the rectangle must also be 900 in area. So, the width must be 10feet and the length must be 90ft because 10x90 is also 900. How I got the length? I did 10x2+70.

The expression that is equivalent to x is ∛4/s

In this question, the mathematical statement of the equation is given as

5x to the power of 7 times s = 20x to the power of 4

When the mathematical statement is represented as an equation, we have the following representation

5x⁷ * s = 20x⁴

Divide both sides by x⁴

So, we have the following representation

5x⁷/x⁴ * s = 20x⁴/x⁴

Evaluate the quotients

This gives

5x³ * s = 20

Divide both sides by 5

x³ * s = 4

So, we have

x³ = 4/s

Take the cube root of both sides

x = ∛4/s

Hence, the solution is x = ∛4/s

Read more about equivalent expressions at

https://brainly.com/question/15775046

#SPJ1

The given logarithmic equation solved for x is x = 10

From the question, we are to solve the given logarithmic equation.

The given logarithmic equation is

log((4x)/(8)) = log(x - 5)

To solve the given logarithmic equation, we will determine the value of the unknown variable.

The unknown variable in the equation is x.

From one of the rules of logarithm, we have that

If logₓY = logₓZ

Then,

Y = Z

Thus,

From log((4x)/(8)) = log(x - 5)

We can write that

(4x)/(8) = (x - 5)

Now, solve for x

(4x)/(8) = (x - 5)

Multiply both sides by 8

8 × (4x)/(8) = (x - 5) × 8

4x = 8x - 40

Subtract 8x from both sides of the equation

4x - 8x = 8x - 8x - 40

-4x = -40

Multiply both sides by -1

-1 × -4x = -1 × -40

4x =40

Divide both sides by 4

4x/4 = 40/4

x = 10

Hence, the solution of the equation is x = 10

Learn more on Solving logarithmic equation here: https://brainly.com/question/237323

#SPJ1

The future value of ordinary annuity $1000 a year for 10 years at 10% year compounded annually is $15937.

The value of a sum of money that will be paid on a specified date in the future is known as its future value. Since each payment is made at the end of a period, the formula for the future value of an ordinary annuity refers to the value on a specified future date of a series of periodic payments.

Given,

R=$1000, n=10, i=10%=10/100=0.1

The formula to calculate the future value is

FV=R[(1+i)^n-1]/i

[tex]FV=R(\frac{(1+i)^{n} -1}{i})[/tex]

[tex]FV=1000(\frac{(1+0.1)^{10} -1}{0.1})[/tex]

[tex]FV=1000(\frac{(1.1)^{10} -1}{0.1})[/tex]

[tex]FV=1000(\frac{1.593742}{0.1})[/tex]

[tex]FV=1000\times15.9374[/tex]

[tex]FV=15937.4[/tex]

Future Value approximately equal to $15937.

Therefore, the future value of the ordinary annuity $100 a year for 10 years at 10% compounded annually is $15937, Option c is the correct answer.

To learn more on future value here:

https://brainly.com/question/8286272#

#SPJ4

An equation for the trend line shown on the scatter plot is y = 5x + 15.

In order to determine a linear equation for the trend line (line of best fit) that models the data points described in the scatter plot above, we would have to calculate the slope of this line.

By critically observing the scatter plot, we can reasonably and logically deduce the following points through which the trend line passes through:

Points (x, y) = (2, 25)

Points (x, y) = (6, 45)

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (45 - 25)/(6 - 2)

Slope, m = 20/4

Slope, m = 5.

At point (2, 25), a linear equation for the trend line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given parameters into the formula, we have;

y - y₁ = m(x - x₁)

y - 25 = 5(x - 2)

y - 25 = 5x - 10

y = 5x - 10 + 25

y = 5x + 15.

Read more on slope here: brainly.com/question/25239789

#SPJ1