A paved walkway around a garden has an outer diameter of 80 ft and an inner diameter of 40 ft. A diagram is shown below.
What is the approximate area of the paved walkway?

Answer:

20 gray squares

Step-by-step explanation:

Given

See attachment for squares

Required

Number of gray squares when white = 16

First, we calculate the equation that represents both squares.

The white squares

[tex]a = 2[/tex] --- initial

[tex]d = 4 - 2 = 6 - 4[/tex]

[tex]d = 2[/tex] -- difference between successive gray squares

So, the nth term is:

[tex]W_n = a + (n - 1)d[/tex]

[tex]W_n = 2 + (n - 1)*2[/tex]

[tex]W_n = 2 + 2n - 2[/tex]

[tex]W_n = 2n[/tex]

The gray squares

[tex]a = 6[/tex] --- initial

[tex]d = 8-6=10-8[/tex]

[tex]d = 2[/tex] -- difference between successive gray squares

So, the nth term is:

[tex]G_n = a + (n - 1)d[/tex]

[tex]G_n = 6 + (n - 1) *2[/tex]

[tex]G_n = 6 + 2n - 2[/tex]

[tex]G_n = 4 + 2n[/tex]

When the white squares is 16

[tex]W_n = 16[/tex] --- Calculate n

[tex]W_n = 2n[/tex]

[tex]16 = 2n[/tex]

[tex]8 = n[/tex]

[tex]n = 8[/tex]

To get the number of gray squares;

Substitute [tex]n = 8[/tex] in [tex]G_n = 4 + 2n[/tex]

[tex]G_n = 4 + 2 * 8[/tex]

[tex]G_n = 20[/tex]

Answer:

3

Step-by-step explanation:

[tex]\frac{3y+6}{2x} \\\\\frac{3(4)+6}{2(3)} \\\\\frac{12+6}{6} =\frac{18}{6} \\\\3[/tex]

Answer:

[tex]y=[/tex] [tex]-\frac{5}{6}x - 1[/tex] is the answer

Step-by-step explanation:

Equation of the line: y = 6/5x + 1

                        = 5y = 6x + 5

                        = 6x - 5y + 5

Equation of the perpendicular line: bx - ay + k = 0

                                                       = -5x -6y + k = 0

Equation passes through (6,-6),

-5(6) -6(-6) + k = 0

-30 + 36 + k = 0

6 + k = 0

k = -6

Substituting,

-5x -6y + k = 0

-5x -6y -6 = 0

-6y = 5x + 6

[tex]y=[/tex] [tex]-\frac{5}{6}x - 1[/tex] (Slope-Intercept form)

Answer:

20 ÷ 4 = 5

(Brainliest please! :D)

Answer:

5

Step-by-step explanation:

5

5

5

5

See how I put five 4 times? Multiply 5 by 4 and you get 20. 20 divided by 4 equals 5. Just like how 20 divided by 5 equals 4. You just flip it.

Answer:

You need to sell 39 Student tickets minimum to be able to cover the cost over all.

Step-by-step explanation:

If they sell 65 adult tickets, then you have to do 65 x 10.50 = $682.5

with that in mind you will take 308 + 682.5 because that equals 990.5 that would be the minimum amount but you would need to to take 39 x 8 to get 312 because 38 x 8 is 304 so that isn't enough.

Answer:

3617 cubic feet

Step-by-step explanation:

V = 2/3 * π * r³

V= 2/3 * 3.14* 12(cubed)

V=2/3 * 5426

V= 2 * 5426 ÷ 3

V= 3617 Cubic feet

Answer:

oh, well, sorry

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Slope is rise over run.

Answer:

A=25m

Step-by-step explanation:

Answer:

900 people

Step-by-step explanation:

540 / 60 = 9

10% = 9

9 x 100 = 900 people

Hope that helps!

Answer: the answer is 5/24

Step-by-step explanation:

If you do 7/8 - 2/3 you get 5/24 and to check your work, do 7/8 - 5/24 and you get 2/3

Hope this helps ^^

Answer: I think if you run away you should get closes and a lot of food go somewhere were she won't find you

Step-by-step explanation:

Answer:

Option: A

Step-by-step explanation:

Hope it helps you!

Answer:

angle 6 and angle 3

Step-by-step explanation:

angle 1 and angle 6 add up to 90 degrees

angle 6 is vertical to angle 3, so 1 is complementary to 3 as well

Answer:

V=1582.56 cubic cm

Step-by-step explanation:

Answer: 46 puzzles  

Step-by-step explanation:

There are 70 puzzles in total in the book.

Jackie has completed / of those puzzles. In whole numbers that is:

= 2 /5 * 70

= 28 puzzles

She then completes 18 more puzzles.

Total that she has completed is:

= 28 + 18

= 46 puzzles  

Answer:

y = x - 1

Step-by-step explanation:

Put it in point-slope form:

y - 0 = 1(x - 1)

y = x - 1

Answer:

72.5°

Step-by-step explanation:

180° - 35° = 2y°

145° = 2y

145/2 = 50+22+0.5 = 72.5

Answer:

Don Abel debe construir un cuadrado con lados de 25 metros de longitud.

Step-by-step explanation:

Geométricamente hablando, el área y el perímetro del rectángulo rodeado por el cerco son representadas por las siguientes fórmulas:

[tex]A = w\cdot l[/tex] (1)

[tex]p = 2\cdot (w+l)[/tex] (2)

Donde:

[tex]A[/tex] - Área, en metros cuadrados.

[tex]p[/tex] - Perímetro, en metros.

[tex]w[/tex] - Ancho, en metros.

[tex]l[/tex] - Longitud, en metros.

Puesto que el área a cercar debe ser la máxima posible y la longitud disponible de malla es de 100 metros, cabe despejar el ancho en (2):

[tex]w = \frac{p}{2}-l[/tex]

Ahora, aplicamos esta expresión en (1) y expandimos la expresión resultante:

[tex]A = \left(\frac{p}{2}-l\right) \cdot l[/tex]

[tex]A = \frac{p\cdot l}{2} -l^{2}[/tex] (3)

A continuación, obtenemos la primera y segunda derivada de (3):

[tex]A' = \frac{p}{2}-2\cdot l[/tex] (4)

[tex]A'' = -2[/tex] (5)

Igualando (4) a cero, tenemos que el valor crítico de la longitud del rectángulo es:

[tex]\frac{p}{2}-2\cdot l = 0[/tex]

[tex]2\cdot l = \frac{p}{2}[/tex]

[tex]l = \frac{p}{4}[/tex]

Por (5), sabemos que ese valor crítico está asociado al área máxima.

Si sabemos que [tex]p = 100\,m[/tex], entonces la longitud del rectángulo es:

[tex]l = 25\,m[/tex]

Ahora, tenemos el ancho de la figura por (2):

[tex]w = \frac{p}{2}-l[/tex]

[tex]w = 25\,m[/tex]

En consecuencia, don Abel debe construir un cuadrado con lados de 25 metros de longitud.

Answer:

Eh cafe donete mal reo jama kolotake? 24 eh moi -09....? kelare mei osaje.

Step-by-step explanation:

The inequality that describes the solution is 3x < 12.

The cost of each pineapple is less than $4.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Number of pineapples = 3

Cost of each pineapple = x

Now,

The cost of all the 3 pineapples = less than $12.

The cost of 3 pineapples.

3x < 12

x < 12/3

x < 4

Thus,

The inequality is 3x < 12.

The cost of each pineapple is less than $4.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ2

Answer:

1DK

Step-by-step explanation:

Answer:

dogs = 2

cats = 80

Step-by-step explanation:

Here I will assume that cats and dogs are proportional

c = y d, if you substitue, you get

10 = y 4, which rearranged, becomes

y = 10/4 = 2.5

now that we know y, we can work out x and y, the missing dogs and cats

4 = 2.5 d

here, dogs = 2

c = 2.5 * 32

2.5 * 32 = 80

here, cats = 80

Answer:

It adds by +5

Step-by-step explanation:

Answer:

2650

Step-by-step explanation:

Ok so,

3000-(3.5(100))

3.5 multiplied by 100 is 350, (move the decimal place 2 times to the right)

so it would be:

3000-350

Simply subtract.

3000-350= 2650

Answer: 2650

Cheers! I hope you can understand it well.

I have attached an image showing the graph of the function.

Answer:

Zeros are x = $15 and x = $70 and they are the prices at which the woodworker will neither loss nor gain money.

Step-by-step explanation:

First of all, the zeros of a function f(x) are defined as the values of x where f(x) = 0. That is the points where the graph curve touches the x-axis.

Now, from the attached graph, when we locate the point that the curve touches the x-axis, it's at x = 15 and at x = 70.

This means that f(x) = 0 at x = 15 and at x = 70.

Now, from the graph; f(x) is the profit function. So when f(x) = 0, it means there is zero profit which implies no gain and no loss.

Thus, we can conclude that the prices at which the woodworker will neither loss nor gain money is when the price is; x = $15 and x = $70

Answer:

Step-by-step explanation: