Rashad is considering two designs for a garden. In Design 1 he would use fencing to surround a square plot of land that has an area of 1,296 square feet. In Design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections.

Two designs for a garden are shown. Design 1 is a square with an area of 1,296 square feet. Design 2 is 2 rectangles with lengths of 15 feet and 36 feet that are connected at one side.

Which plan would cost less in fencing? Explain.

Design 1, because it requires 12 fewer feet of fencing than Design 2
Design 1, because it requires 24 fewer feet of fencing than Design 2
Design 2, because it requires 12 fewer feet of fencing than Design 1
Design 2, because it requires 24 fewer feet of fencing than Design 1

a) The growth function has the form:

where:

Considering the values we get the function:

b) Number of years between 2012 and 2018 is:

Find the population, using the above equation:

c) Find the value of x when P(x) = 10 million

d) Find the doubling time:

Answer:

[tex]\textsf{a)} \quad f(x)=6.93(1.0218)^x[/tex]

b)  7.89 million (2 d.p.)

c)  2019

d)  32.14 years (2 d.p.) after 2012

Step-by-step explanation:

Exponential Function

   [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part (a)

If the exponential growth rate was 2.18% per year, then each year there would be 102.18% of the previous year's population.

⇒ b = 1.0218

Given:

Substitute the given values into the formula to create an exponential growth function:

  [tex]f(x)=6.93(1.0218)^x[/tex]

Part (b)

To estimate the population of the city in 2018, determine the value of x:[tex]x = 2018 - 2012 = 6[/tex]

Substitute the found value of x into the found exponential function:

[tex]\implies f(6)=6.93(1.0218)^6=7.89 \: \sf million\:(2\:d.p.)[/tex]

Part (c)

To determine when the population of the city will be 10 million, set the function to 10 and solve for x:

[tex]\implies 6.93(1.0218)^x=10[/tex]

[tex]\implies (1.0218)^x=\dfrac{10}{6.93}[/tex]

[tex]\implies \ln (1.0218)^x= \ln \left(\dfrac{10}{6.93}\right)[/tex]

[tex]\implies x\ln (1.0218)= \ln \left(\dfrac{10}{6.93}\right)[/tex]

[tex]\implies x= \dfrac{\ln \left(\frac{10}{6.93}\right)}{\ln (1.0218)}[/tex]

[tex]\implies x=17.00496413...[/tex]

To find the year, add the found value of x to 2012:

[tex]\implies \sf 2012 + 17.00496413... = 2019[/tex]

Part (d)

To find the doubling time, set the function to double the initial population and solve for x:

[tex]\implies 6.93(1.0218)^x=6.93 \cdot 2[/tex]

[tex]\implies (1.0218)^x=2[/tex]

[tex]\implies \ln (1.0218)^x= \ln (2)[/tex]

[tex]\implies x \ln (1.0218)= \ln (2)[/tex]

[tex]\implies x = \dfrac{\ln (2)}{\ln (1.0218)}[/tex]

[tex]\implies x=32.14107014...[/tex]

Therefore, the doubling time is 32.14 years (2 d.p.) after 2012.

Answer:

Yes

Step-by-step explanation:

Answer:

98/22 or 4.4545

Step-by-step explanation:

Perimeter of a rectangle: 2*width+2*length

4x*2+7x*2 = 98

8x+14x = 98

22x = 98

x = 98/22 or 4.4545

The fourth proportionals are bc/a and st/r

Segments a, b and c

Let the fourth segment be x.

So, we have the following equivalent ratio

a : b = c : x

Express as fraction

a/b = c/x

Make x the subject

x = bc/a

Segments r, s and t

Let the fourth segment be x.

So, we have the following equivalent ratio

r : s = t : x

Express as fraction

r/s = t/x

Make x the subject

x = st/r

Hence, the fourth proportionals are bc/a and st/r

Read more about proportions at:

https://brainly.com/question/1781657

#SPJ1

The volume of the sphere shown below with a radius of 9 is 3052.08 cubic units

The formula for calculating the volume of a sphere is expressed as;

V = 4/3πr³

where

r is the radius of the sphere

Substitute

V = 4/3π(9)³

V = 4/3(3.14)*729

V = 3052.08 cubic units

Hence the volume of the sphere shown below with a radius of 9 is 3052.08 cubic units

Learn more on volume of sphere here: https://brainly.com/question/22807400

#SPJ1

Answer:

[tex]\frac{247}{200}[/tex]

Step-by-step explanation:

1.235

= 1 + 0.235 ( the place value of the 5 is thousandths ) , then

= [tex]\frac{1000}{1000}[/tex] + [tex]\frac{235}{1000}[/tex]

= [tex]\frac{1235}{1000}[/tex] ( divide numerator/denominator by 5 )

= [tex]\frac{247}{200}[/tex] ← in simplest form

Answer:

its easy

Step-by-step explanation:

you should change all into degrees

The ride takes  1.5 hours for a speed of 10 miles per hour.

The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.

A body's speed can be defined as how quickly it is going. The equation for a given body's speed can be written as,

Speed=Distance/Time

According to the question,

Speed=10 miles per hour

Distance=15 miles

Time=[tex]\frac{15}{10}[/tex]=1.5 hours

Learn more about speed here:

https://brainly.com/question/4931057

#SPJ4

Answer:

EF = 22 , AB = 1

Step-by-step explanation:

the midsegment of a trapezoid is equal to half the sum of the parallel bases

EF = [tex]\frac{1}{2}[/tex] (AB + DC ) ← substitute values

x + 6 = [tex]\frac{1}{2}[/tex] (2x - 9 + x + 5) ← multiply both sides by 2 to clear the fraction

2x + 12 = 3x - 4 ( subtract 3x from both sides )

- x + 12 = - 4 ( subtract 12 from both sides )

- x = - 16 ( multiply both sides by - 1 )

x = 16

Then

EF = x + 6 = 16 + 6 = 22

Similarly

EF = [tex]\frac{1}{2}[/tex] (AB + DC ) , that is

x + 3 = [tex]\frac{1}{2}[/tex] (4x - 3 + 2x + 5 ) ← multiply both sides by 2 to clear the fraction

2x + 6 = 6x + 2 ( subtract 6x from both sides )

- 4x + 6 = 2 ( subtract 6 from both sides )

- 4x = - 4 ( divide both sides by - 4 )

x = 1

Then

AB = 4x - 3 = 4(1) - 3 = 4 - 3 = 1

Answer:

0.71

Step-by-step explanation:

- Please see the attached picture for full solution!:)

------------ HappY LearninG <3 -----------

Answer:

150

Step-by-step explanation:

The area of the trapezoid is (½)(14+10)(2) = 24.

The area of the rectangle is (14)(9) = 126.

Adding these together, we get 126 + 24 = 150.

Answer:

D

Step-by-step explanation:

By observation we just know that one of the angles of two triangles is the same.

There are two sides that are not equal in ability to determine similarity.

In the given triangle, the length of BC is 10.25 cm

From the question, we are to determine the length BC

The triangle is a right triangle, then we can write that

/AB/² = /AC/² + /BC/² (Pythagorean theorem)

From the given information,

/AB/ = 13 cm

/AC/ = 8 cm

Putting the parameters into the equation, we get

13² = 8² + /BC/²

169 = 64 + /BC/²

/BC/² = 169 - 64

/BC/² = 105

/BC/ = √105

/BC/ = 10.25 cm

Hence, the length of BC is 10.25 cm

Learn more on Calculating a right triangle here: https://brainly.com/question/8196729

#SPJ1

Answer:

Yes, it is a function

Step-by-step explanation:

A function has only one output for each input. So a function can have the same output for different input, but one input can only have one output. In this case none of the inputs output more than one output, so it is a function.

The speed of the plane after it encounters the wind is C.285mph

Since the plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph it's velocity is v = (320cos270°)i + (320sin270°)j

= (320 × 0)i + (320 × -1)j

= 0i - 320j

= - 320j mph

Also, the plane encounters a 35 mph wind blowing directly north. The velocity of the wind is v' = 35j mph

So, the velocity of the plane after it encounters the wind is the resultant velocity, V = v + v'

= -320j mph + 35j mph

= -285j mph

So, the speed of the plane after it encounters the wind is the magnitude of V = |-285j| mph

= 285 mph

So, the speed of the plane after it encounters the wind is C.285mph

Learn more about speed of plane here:

https://brainly.com/question/3387746

#SPJ1

2) [tex]ABCD[/tex] is a rhombus (a parallelogram with perpendicular diagonals is a rhombus)

3) [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex] (diagonals of a rhombus bisect the angles from which they are drawn)

Answer:

60 degrees.

Step-by-step explanation:

A reflection does not alter the size of the angles of the triangle so B = 60 degrees.

Answer:

No solutions

Step-by-step explanation:

First  ADD  4 /(X+4)   to both sides of the equation to get

( x+4)/ (x+ 4)  = 3

1 = 3 ????    There are no solutions

[tex]\dfrac{x}{x+4}=3-\dfrac{4}{x+4}\qquad(x\not=-4)\\\\x=3(x+4)-4\\x=3x+12-4\\2x=-8\\x=-4[/tex]

Which contradicts initial assumption, therefore [tex]x\in\emptyset[/tex].

Answer:

There are two equations and two variables, so this is a system of linear equations.

c + h = 360

4c = h

Step-by-step explanation:

Answer:

The linear equations would be c = 4h and 1.5c + 2h = 360.

Step-by-step explanation:

First we have to create a table for our data.

c = total number of cold beverages sold.

h = total number of hot beverages sold.

The total cost of both beverages sold -

1.5c + 2h = 360

The amount of cold beverages -

c = 4h

Now we just need to substitute the second equation to the first one.

1.5 * (4h) + 2h = 360

= 6h + 2h = 360

= 8h = 360

= h = 45

Now we need to find the value of c.

c = 4* 45 = 180

Therefore 180 cold beverages were sold and 45 hot beverages were sold.

But the linear equations would be c = 4h and 1.5c + 2h = 360.

Hope this helped! :D

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads:}[/tex]

[tex]\large\textbf{Which is equivalent to }\rm{\bf \dfrac{3}{125}}\large\textbf{ ?}[/tex]

[tex]\huge\textbf{Solving for your fraction:}[/tex]

[tex]\mathbf{\dfrac{3}{125}}[/tex]

[tex]\mathbf{= \dfrac{3\times2}{125\times2}}[/tex]

[tex]\mathbf{\approx \dfrac{3 + 3}{125 + 12{5}}}[/tex]

[tex]\mathbf{= \dfrac{6}{250}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\dfrac{6}{250}}}\huge\checkmark[/tex]

[tex]\large\text{By the way, they are a lot more fractions that are equivalent to}\\\large\text{the given equation (}\rm{\dfrac{3}{125}}\large\text{) but we only labeled one that is the very}\\\large\text{first fraction that is equal to it. }[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

8m and 12a

Like terms are terms that can be combined to condense a mathematical expression or equation.

Unlike Terms

Unlike terms are defined as terms that have different variables or powers.

If terms meet either of these requirements, they are unlike. On the other hand, for terms to be like they must have both the same variable and power. The coefficients for the terms are not important.

Final Answer

All of the answer choices are to the first power, so the exponents are not important for this question. However, the last 3 answer choices all share the same variable. This means that they are all like terms.

The first answer choice, 8m and 12a, have different variables. This means that they cannot be combined and are unlike terms.

Answer:

A 3.5

Step-by-step explanation:

To Break it down there 1 3/4 so to put in halve it would be 1/2 1/2 1/2 1/4 so u have 3 feet because 1/2 in is 3 feet then u have a 1/4 inch so that is half of a feet 1 + 1 + 1 + 1/2 is 3 1/2 converted to decimal is 3.5.

Answer:

um tbh me dont know

Step-by-step explanation:

The length of AB would be 38 units

The attached image represents the missing piece in the question

Considering the triangle BCD;

Calculate the length BC using the following Pythagoras theorem

BC^2 = CD^2 + BD^2

This gives

BC^2 = 10^2 + 8^2

Evaluate

BC^2 = 164

Considering the triangle CBA;

Calculate the length AB using the following Pythagoras theorem

AB^2 = AC^2 - BC^2

This gives

AB^2 = 40^2 - 164

Evaluate

AB^2 = 1436

Take the square root

AB = 38 (approximated)

Hence, the length of AB would be 38 units

Read more about right triangles at:

https://brainly.com/question/2437195

#SPJ1

Answer:

x + y ≤ 12

Step-by-step explanation:

Inequality:

   Not more than 12 means less than or equal to 12

x + y ≤ 12

By seeing where the curves intercept, we conclude that the solutions are:

(0.22, -1.22) and (-2.12, 1.12)

Here we just need to graph the equations:

y = log(-5.6*x + 1.3)

y = -1 - x

And see in which points the curves intercept.

The graph can be seen below:

There we can see that the intersections (and solutions) are the points:

(0.22, -1.22) and (-2.12, 1.12)

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)

In this question we have a trigonometric equation and we are supposed to find an expression not equivalent to the former. Herein we have that the cosine of a double angle is equivalent to the following expressions:

cos 2θ = cos² θ - sin² θ     (1)

cos 2θ = 2 · cos² θ - 1     (2)

cos 2θ = 1 - 2 · sin² θ     (3)

The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)

To learn more on trigonometric functions: https://brainly.com/question/14434745

#SPJ1

Answer:

65fghxtt

Step-by-step explanation: