Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 16 cm.

(1) How many equilateral triangles are there? _____

(2) What is the measure of each of the three angles in the equilateral triangle? _____

(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____

(4) What is the vocabulary word for the segment a? _____

(5) What is the length of the short side of one of the 30-60-90 triangles? _____

(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____

(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____

(8) What is the height of one of the the equilateral triangles? _____

(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____

(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____

Answer:

1. 900 grams

2. 3 eggs

Step-by-step explanation:

1. 150 x 6 = 900

2. 450 / 150 = 3

Answer:

900 grams of flour are needed if six eggs are used. 3 eggs are needed if 450 grams of flour are used.

Step-by-step explanation:

First, multiply the number of large eggs by grams per large egg: 150×6=900

Next, divide the number of grams of flour by grams per large egg: 450/150=3

The sum of all positive integers that satisfy the condition as described is; 100

The number set of n is therefore;

n = {1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

According to the question;

The data set therefore includes all odd numbers; This is so because the question says; if n is odd; then n is a multiple of 5.

The sum of all positive integers that satisfy the condition is therefore;

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1. 4

2. 6

3. 10

4. 30

5. 48

6. 55

7. 68

8. 148

9. 102

10. 38

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9514 1404 393

Answer:

  D. choosing first second-, and third-place winners in a cooking contest​

Step-by-step explanation:

Permutations are involved when order matters. The order of people surveyed, sundae flavors, and flowers are irrelevant. The order of first-second-third is entirely relevant.

Cooking contest winners involve permutations.

Answer:

they will need 2 gallons of punch

9514 1404 393

Answer:

  AED 5200

Step-by-step explanation:

The interest in the first year will be ...

  I = Prt . . . . principal P invested at rate r for t years

  I = 5000×0.04×1 = 200

The account will have AED 5200 in it after a year.

Answer:

i think its c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

because -100,-57/8,6

the absolute value of -6 is 6 and

-8 7/8 is 8×(-8)+7=-64+7/8=-57/8 because when negative plus positive we subtract and we take the sign of the larger number

Answer:

B) -g/-h

Step-by-step explanation:

-g/-h=g/h

Rewrite the fraction.

-(-g/h) = g/h

Hope this helps :)

Answer:

9-3=b

Step-by-step explanation:

9-3=b

Answer:

B=6

Step-by-step explanation:

Let "b" be the number of books Shemel has.

Let "a" be the number of books Wawra has.

Eqution:

A-3=B ("3" is given in question)

9-3=B (Substituting with variables given)

B=9-3

B=6

Hence, Shemel has "6" books.

Hope it helps !

Answer:

81 cm

Step-by-step explanation:

A square is equal an all sides so 9cm to the second power is 81 cm

Answer:

i think its the second graph

Step-by-step explanation:

Just because 2 things are related doesn't mean they will both be changed when one thing happens. For example steak and candy, just because they are both food doesn't mean they taste the same or interact with each other.

Answer:

=5880b2x4−6048bcx4+1512c2x4−3920b2x3+4032bcx3−1008c2x3+33320b2x2−34272bcx2+8568c2x2−82320b2x+84672bcx−21168c2x−31360b2+32256bc−8064c2+6x2+6x−24

Step-by-step explanation:

Answer:

In the graph locate the point (3,0) and draw a line parrallel to Y-axis passing through (3,0) .

Then your line will cut the graph of f(x) at some point, that point's y-coordinate will be your value of f(3).

Step-by-step explanation:

Hope it helps!

Answer:

c. 1.1

Step-by-step explanation:

-5.5(-1/5) = 5.5/5 = 1.1

Answer:

it should be 60°. the single marks on each side means they are all equal

Answer:

m∠L=60º

Step-by-step explanation:

The triangle is an equilateral triangle meaning that all angles and sides are equal.

m∠L=60º

Hope this helps :)

From the principles of geometry, we can see that the value of y is 3.

The lengths of the opposing sides in a rectangle are equal. A rectangle is a quadrilateral with four parallel opposed sides and four right angles (90-degree angles).

In specifically, a rectangle has two sets of equal-length opposite sides. In a rectangle, the lengths of the neighboring sides can vary, but the lengths of the opposing sides are always the same. This feature sets a rectangle apart from other quadrilaterals.

We know that;

10 = 2y + 4

10 - 4 = 2y

y = 6/2

y = 3

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Answer:

Step-by-step explanation:

First, we add 16 and 28 [tex]16+28=44[/tex]

Now we have to solve for x

We know we have to do parenthesis first so [tex](4+7)=11[/tex]

[tex]44=x(11)[/tex]

Then we divided both sides by 11

[tex]\frac{44}{11} =\frac{11x}{11}[/tex]

[tex]x=4[/tex]

To find the Prime Factorisation of 84 we have to divide 84 by the smallest prime number which is 2

So [tex]\frac{84}{2} = 42[/tex]

Since 42 is an even number we can still divide it by 2

So [tex]\frac{42}{2} = 21[/tex]

Now we can divide 21 by the 2nd smallest prime number which is 3

So [tex]\frac{21}{3} = 7[/tex]

So the prime factors of 84 would be [tex]2*2*3*7[/tex] or [tex]2^2*3*7[/tex]

El carro de mercancía experimenta una aceleración neta de 0.333 metros por segundo al cuadrado al soltarse.

En esta situación se requiere una fuerza de 30 N para alcanzar la fuerza estática máxima ([tex]f_{s}[/tex]), entonces la fuerza de fricción ([tex]f_{k}[/tex]) se reduce a 20 N mientras se encuentre en movimiento. Si consideramos que la fuerza externa de 30 N se mantiene durante el fenómeno físico, entonces tenemos que la aceleración neta ([tex]a[/tex]), en metros por segundo al cuadrado, experimentada por el carrito de mercancía es determinada a partir de las leyes de Newton:

[tex]a = \frac{F-f_{k}}{m}[/tex] (1)

Donde [tex]m[/tex] es la masa del carrito de mercancía, en kilogramos.

Si sabemos que [tex]F = 30\,N[/tex], [tex]f_{k} = 20\,N[/tex] and [tex]m = 30\,kg[/tex], entonces la aceleración neta del carro de mercancías es:

[tex]a = \frac{30\,N-20\,N}{30\,kg}[/tex]

[tex]a = 0.333\,\frac{m}{s^{2}}[/tex]

El carro de mercancía experimenta una aceleración neta de 0.333 metros por segundo al cuadrado al soltarse.

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Answer:

0 hours.

Step-by-step explanation:

He finished at the same time than Kenrick finished last week. So, he/she did not delay in mowing the lawn. Hoped this helped.

Answer:

The answer is D ane B

Step-by-step explanation:

The expression [tex](8z-4)(-7)[/tex] you would have to distribute -7 to get [tex]-56z+28[/tex]

The same goes for 40 in the expression [tex](-1.4z+0.7)*40[/tex]

Answer:

6

It's kind of blury, so I can't really see it.

Answer:

4

Step-by-step explanation:

Answer:the answer is 1/5

Step-by-step explanation:

[tex]y = x^{3} + 2[/tex]

[tex]y = g(x) + c[/tex]

Here,  [tex]g(x) = x^{3}[/tex] and [tex]c = 2[/tex], the parent function is [tex]g(x)[/tex]. Because [tex]c > 0[/tex], the graph undergoes a vertical shift 2 units up along the y-axis.

1) The cubic function is [tex]x^3+1[/tex] and the parent function is [tex]x^3[/tex].

2) The transformation from parent function to function is vertical stretch.

A cubic function is a polynomial function of degree 3. So the graph of a cube function may have a maximum of 3 roots. i.e., it may intersect the x-axis at a maximum of 3 points.

The general form of the cubic function is [tex]ax^3+bx^2+cx+d=0[/tex], where a, b, c and d are real numbers.

Let the cubic function be [tex]x^3+1[/tex] and the parent function be [tex]x^3[/tex].

To find the transformation, compare the function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis and if there is a vertical strech.

Horizontal shift: None

Vertical shift: Up 1 units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

Therefore,

1) The cubic function is [tex]x^3+1[/tex] and the parent function is [tex]x^3[/tex].

2) The transformation from parent function to function is vertical stretch.

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Answer:

2 1/4

Step-by-step explanation:

Answer:

20% of the invited people did not attend

Step-by-step explanation:

5 out of 25 people invited didn't attend Glen's party. That means the following:

[tex]\frac{5}{25}[/tex]  people didn't come which simplifies to  [tex]\frac{1}{5}[/tex]

Multiply [tex]\frac{1}{5}[/tex] by the giant one [tex]\frac{20}{20}[/tex] so the denominator is 100 which is the denominator used to find percentages.

You end up with [tex]\frac{20}{100}[/tex]

[tex]\frac{20}{100}[/tex] = 20%

20% is the percentage of the people whom Glen invited did not attend the party.

To find the percentage of people who did not attend the party, we will divide the number of people who did not attend (5) by the total number of people invited (25), and then multiply by 100.

Percentage = (Number of people not attended / Total number of people invited) × 100

Percentage = (5 / 25) × 100

Percentage = 20%

So, 20% of the people whom Glen invited did not attend the party.

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The fence around the edge of the garden is 17.86 m long.

The fence around the edge of the garden is the perimeter of the quarter circle. That is the length of the arc plus the two radii.

Since the radius is 5 units long, its length r = 5 m.

The length of the arc L = rθ where r = radius of quarter circle = 5 m and θ = angle subtended by the arc in radians = π/2 (90°)

So, the length of the fence L' = L + r + r

L' = L + 2r

L' = rθ + 2r

L' = r(θ + 2)

Substituting the values of the varaibles into the equation, we have

L' = r(θ + 2)

L' = 5 m(π/2 + 2)

L' = 5 m(1.571 + 2)

L' = 5 m × 3.571

L' = 17.855 m

L' ≅ 17.86 m

So, the fence around the edge of the garden is 17.86 m long.

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Answer:

Pink and Green are proportional

Step-by-step explanation:

A proportional graph is a straight line that always goes through the origin