5 × ⅔???????????????

If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.

Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.

The top angle of each triangle is obtained by dividing the full angle by 8.

So, each top angle = [tex]\frac{360}{8}[/tex]

= 45°

Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.

This altitude OC bisects the top angle 45°.

Therefore, ∠ AOC = 22.5°.

Now, in Δ AOC,

[tex]sin 22.5=\frac{AC}{OA}[/tex]

[tex]=\frac{AC}{x}[/tex]

So, AC = x sin 22.5°

Note that, AB = 2 AC.

Therefore, AB = 2x sin 22.5°.

Also, [tex]cos 22.5=\frac{OC}{OA}[/tex]

[tex]=\frac{OC}{x}[/tex]

So, OC = x cos 22.5°.

Area of Δ AOB = [tex]\frac{1}{2}(AB)(OC)[/tex]

= [tex]\frac{1}{2}[/tex] × (2x sin 22.5°) × (x cos 22.5°)

= [tex]\frac{1}{2} x^{2}[/tex] (2 sin 22.5° cos 22.5°)

= [tex]\frac{1}{2} x^{2}[/tex] sin 45°

= [tex]x^{2}[/tex] / [tex]2\sqrt{2}[/tex]

Area of the octagonal gazebo = 8 × one triangular area

= 8 × ([tex]x^{2}[/tex] / [tex]2\sqrt{2}[/tex])

[tex]=2\sqrt{2} x^{2}[/tex]

[tex]=2.828x^{2}[/tex]

Area required for mulch = circular area - area of the gazebo

[tex]=3.14x^{2} -2.828x^{2}[/tex]

[tex]=0.312x^{2}[/tex]

Now, cost per unit area = $1.50.

Hence, total cost g(m) = area × cost per unit area

Total cost g(m) = [tex]0.312x^{2}[/tex] × 1.5

[tex]=0.468x^{2}[/tex]

Hence, total cost g(m) = [tex]0.468x^{2}[/tex].

Answer:

1.50(piexsqared-2root2xsqared) or on edge A

Step-by-step explanation:

i just did it

The slope of a line from the given graph is -2/3. Therefore, option B is the correct answer.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

From the given graph,

Slope (m) = Rise/Run

= -1/1.5

Multiply both numerator and denominator by 2, we get

= -2/3

Therefore, option B is the correct answer.

To learn more about the slope of a line visit:

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Area of the horizontal rectangle.

A = L *W

L = 8cm

W = 3 cm

Area = 8 * 3 = 24 cm^2

Area of the Vertical Rectangle

The vertical rectangle has the same dimensions

L = 8 cm

W = 3 cm

Area = L * W

Area = 8 * 3

Area = 24 cm^2

Combined Area

Area = 24 + 24

Area = 48 cm^2  <<< Answer

Hey there!!

In order to solve for the area, let's divide this figure into two rectangles.

Area of a rectangle = Length × Breadth

First rectangle at the top - Length = 8 and width = 3

Hence, the area would be = 24cm²

The second triangle measures : Length = 3 and the width = 5

Area = 3 × 5

... 15cm²

Total area = 24cm² + 15cm²

... 24 + 15 cm²

... 39cm²

Hope my answer helps!!

3.- 5x-6=y

First you leave the variable alone along with 5 and you pass to the other side number 6 with the opposite sign

5x=y+6

then as 5 is multiplying you pass it dividing

         y+6                                                                                                                                                                    x=        5

4.-2x-3y=8

First you leave the variable with 3 alone and you pass the 2x to the other side subtracting

-3y=8-2x

Then as -3 is multiplying you pass it dividing

y= 8-2x/-3

12.-7x-y=14

First you leave the variable with the 7 alone and you pass the -y to the other side adding

7x=14+y

then as 7 is multiplying you pass it dividing

x=14+y/7

18.-12x-4y=20

First you leave the variable y with the -4 alone and you pass the 12x to the other side subtracting

-4y=20-12x

Then as -4 is multiplying you pass it dividing

y= 20-12x/-4

20.- R-C/N=P

First you leave the R and the C alone and as N is dividing you pass it multiplying

R-C=PxN

Then as C is subtracting you pass it adding

R= (PxN)+C

I haven't done these types of problems in forever, so I did a few of the easier ones before I went onto a few of the harder ones. Sorry if 20 is incorrect, I wasn't too sure.

SOLUTION: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures. Question 345899: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures.

Originally Dan has X amount of base ball cards.

So the equation would be

(x+6)/2=29

multiply both sides by 2

x+6=58

subtract 6

x=52

Check your work: 52+6=58/2=29

4/10 Probability

-Hiadamcom

Answer:

2/5

Step-by-step explanation:

4 ÷ 10= 2/5

(4 ÷10 is for 4/10 which is red marbles to the total marbles)

The probability of the compliment is 3/5(for edge students)

Answer:

a=43

Step-by-step explanation:

90+47=137    180-137=43

Answer:

2

Step-by-step explanation:2+2

The side lengths of a square in which the perimeter of a square is greater than its area is 1 unit, 2 units, and 3 units.

A square is a 2D figure of which all sides are equal.

We know that the perimeter of a square is the sum of the lengths of all the sides and the area of a square is (side)².

Assuming a square has a side length of 4 units.

Therefore the perimeter of the square is 4×side = 4×4 = 16 units.

Now the area of the square will be (4)² = 16 sq units.

Now assuming the side length of the square is 2 units.

The area of the square is (2)² = 4 units and the perimeter is (2×4) = 8 units.

∴ The side length which provides a counter-example is 2 units.

Basically, we have to determine the numbers that when multiplied by 4 are greater than it's square such numbers are 1, 2, 3.

learn more about squares here :

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See the attached picture:

Given equation: 3 + x/2 = 10

1st step subtract 3 from each side:

x/2 = 7

2nd step multiply both sides by 2:

x = 14

Step 1)        

3 + x/2 = 10 ..............This is given

Step 2)

x/2 = 7 ....................... Multiplication property of equality.

This step is wrong. This step is called "Subtraction property of equality". This means you have to subtract 3 from both sides

3 + x/2 - 3 = 10 - 3

Simplifying

x/ 2 = 7

Step 3)

x = 14 ....This is called "Multiplication property of equality" because you multiply both sides by 2.

Hope that helps.

We know that the perimeter is 72 meters, so we have

[tex] y+2x+(2x+6)=72 \iff y+4x+6=72 \iff y=-4x+66 [/tex]

Now we can use the pythagorean theorem: the sum of the squares of the legs is the square of the hypotenuse:

[tex] (2x)^2+(2x+6)^2 = y^2 \iff (2x)^2+(2x+6)^2 = (-4x+66)^2 [/tex]

Expand the squares to get

[tex] 8 x^2 + 24 x + 36 = 16 x^2 - 528 x + 4356 [/tex]

Bring everything to the right hand side to get

[tex] 8 x^2 - 552 x + 4320 = 0 [/tex]

Divide both sides by 8:

[tex] x^2 - 69x + 540 = 0 [/tex]

This equation has solutions [tex] x=9,\ x=60 [/tex]

This solutions would yield the following side lengths:

[tex] x=9\implies\begin{cases} 2x = 18\\2x+6=24\\-4x+66=30\end{cases}[/tex]

[tex] x=60\implies\begin{cases} 2x = 120\\2x+6=126\\-4x+66=-174\end{cases}[/tex]

Since we can't have negative side lengths, we can only accept the solution x=9.

In fact, you can check that 18,24,30 is a pythagorean triplet, i.e.

[tex] 18^2+24^2=30^2 [/tex]

Answer should be 132

Answer:

Step-by-step explanation:

The lines can be related in following three ways

Now three real life examples of above three scenarios are described below:

Answer:

1. KI

2. HI and DF

3. 8

4. 4 and 7

Step-by-step explanation:

The different forms you can convert 6 2/3 to would be 20/3 and 6.6 but I'd have to say 20/3 would be the simplest form to convert it to. Hope this helps <3

20/3 thats the exact form

38a) $10.50 To get this answer, you need to multiply $1.50 by 7

38b) $25.50 To get this answer, you need to subtract $10.50 from $36

40) The answer would be $13.7694 and it could be rounded to $13.77. To get this answer .you need to multiply $12.99 by 1.06 since it has a 6% sales tax.

Answer:

A. consume food

Step-by-step explanation:

The food they eat has energy. One eaten the energy the food had is passed along to the animal.

There are no graphs shown, but the vertical line test is something you can use to find out if a function works. If you make a vertical line anywhere on one of the graphs, it should only pass through one point. For example, a regular straight line almost always passes the vertical line test. If it's a sideways parabola, it will not.

Answer:

(1+2i)(1-2i)

Step-by-step explanation:

Answer:

(1+2i)(1-2i)

Step-by-step explanation:

Following are the pairs of the complex number:

(1+2i)(8i),

(1 + 2i)(2 – 5i)

(1+2i)(1-2i) and (1+2i)(4i)

We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".

A. [tex](1+2i)(8i)= 8i+16i^{2}[/tex]

                        =[tex]8i-16[/tex]

B. [tex](1+2i)(2-5i)=2-i-10i^{2}[/tex]

                           =[tex]12-i[/tex]

C. [tex](1+2i)(1-2i)=1^{2}-4i^{2}[/tex]

                          =[tex]5[/tex]

D. [tex](1+2i)(4i)=4i+8i^{2}[/tex]

                        =[tex]4i-8[/tex]

Since, A,B,D contains the term "i" which means they are not real valued, therefore option C that is (1+2i)(1-2i) has a real number product.

you can do that on here

fraction-1/3

decimal- 0.3333333333333333333333333333333333333333333333333333333333333333333333

(they are equal)

-hope this helps

-i hope u get the 0.3 part it will never end its just that i since it never ends i can't but th e whole thing

Thus, the proportion of female wolves that do not hunt in medium sized packs is 4/10 or 0.4. When expressed as percent, this is 40%.

Jasmine is 23 years old. Three years less, 20, half is 10. If I am correct, George is 10.

Answer:

C) x also increases 5 times its original value

35/5=7

70/10=7

Step-by-step explanation:

There is 1 solution, which is 3/4.

To show this, you actually have to solve the equation. First, you distribute -1 into(9 - 3h) and distribute -3 into (h + 2). In doing so, you should be left with "6h - 9 + 3h = 6 - 3h - 6". Next you combine like terms on each side, so you add 3h to 6h and you subtract 6 from 6. Now you should have "9h - 9 = -3h". Then, you start to solve by subtracting 9h from both sides. You should have -9 = -12h, which you divide -12 on both sides to get h by itself. Finally, you have h = 9/12 (since the negatives on the top and bottom cancel out) which simplified (divided by 3/3) is 3/4. Thus meaning there is only 1 answer.

I hope this helps!

First of all remeber that "a number" means we don't know the number or it could be many but not all numbers, so it is represented by x.

5. 1/2x + 6 > 20

6. 12 + 3x < -11  (They asked for the opposite of 11, the opposite of a positive number is always the negative of that number, and the opposite of a negative number is the positive of that number).

7. 2x - 8 < 5

Answers:

5) 1/2n + 6 > 20

6) 12 + 3n < -11

7) 2x - 8 < 5

Hope this helps :-)

0.0365 is the standard form for this

Total: 2p + 50 < 150

                 -50   -50

         2p          < 100

          [tex]\frac{2p}{2} < \frac{100}{2}[/tex]

            p < 50

Answer: 2p + 50 < 150    , p < 50

The perimeter is adding all the outside edges together:

4 + 1 +4 +1 + 3 + 1 = 14 cm.

x² + 3x + 2 = (x + 2)(x + 1)

consider the factors of the constant term ( + 2 ) which sum to give the coefficient of the x- term ( + 3)

These are + 2 and + 1

x² + 3x + 2 = (x + 2 )(x + 1)