A regular hexagon is rotated 360° about its center. How many times does the image of the hexagon coincide with the pre image during the rotation?
A. 1 time
B. 3 times
C. 12 times
D. 6 times

(x + a)^2 + b form can be achieved by a method known as completing the square.

Step 1: Divide the b term by 2 and square it

8 / 2 = 4

4^2 = 16

Step 2: Add and subtract 16 from the expression

---Adding 16 creates a perfect square trinomial between x^2 + 8x + 16. But, if we add 16, we also need to subtract it. So, we will subtract 16 from our c term, 14.

x^2 + 8x + 16 + 14 - 16

x^2 + 8x + 16 - 2

Step 3: Factor the perfect square trinomial

(x^2 + 8x + 16) - 2

(x + 4)(x + 4) - 2

(x + 4)^2 - 2

Answer: (x + 4)^2 - 2

Hope this helps! :)

Answer: c

Step-by-step explanation:

The length of the ladder needed to reach the top of the house is 31.2 feet.

Trigonometric ratio is used to show the relationship between the sides and the angles of a right angled triangle.

Let d represent the length of the ladder. Using trigonometric ratio:

[tex]sin(60)=\frac{27}{d} \\\\d=\frac{27}{sin(60)} =31.2\ feet[/tex]

The length of the ladder needed to reach the top of the house is 31.2 feet.

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Answer:

D is the correct answer

Step-by-step explanation:

Answer:

12.0

Step-by-step explanation:

Answer:

452.4

Step-by-step explanation:

Answer:

3.2t -2.4

Step-by-step explanation:

Combine like terms then solve (-1.9t +5.1t)+(-3.6+1.2)

Answer:

2,3,4

Step-by-step explanation:

Answer:

2x+5

Step-by-step explanation:

Equation  y = 3x + 5  correctly represents the situation.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Darrian creates caricatures for an initial fee of $5 then charges $2 each minute.

Let x be the number of each extra minutes.

And y be the total fees.

So, the equation;

The total fee = Charges of x minutes + initial fee.

y = 3x + 5

Therefore, the equation is  y = 3x + 5.

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Answer:

∠DAB=140

∠BAC=60

∠EBF=40

∠ACB=80

∠BCG=100

Step-by-step explanation:

The school band could have a profit of $ 60 for selling 30 T-Shirts.

For the sale of each T-shirt the school band have a net profit of $ 6, of which $ 4 are discounted by concept of flyers and, thus, this band has a final profit of $ 2 for the sale of a T-shirt. The total profit for T-shirt sales equals the product of number of T-shirts sold and the final profit for each T-shirt sold.

Hence, the profit for selling 30 T-shirts is shown below:

[tex]C = (\$\,2)\cdot (30)[/tex]

[tex]C = \$\,60[/tex]

The school band could have a profit of $ 60 for selling 30 T-Shirts.

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Answer:

A. Slope is -12 feet per second

B. Yes, it is constant.

Skills needed: Linear Equations, Substitution and Division

Step-by-step explanation:

1) Solving Part A (we need to find the slope):

2) Using the y-values of 1150 and 1090, and their corresponding x-values (5 and 10 respectively), we can get the slope:

- [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] ==> [tex]\frac{1090-1150}{10-5}[/tex] ==> [tex]1090-1150=-60, 10-5=5[/tex] ==> [tex]\frac{-60}{5}[/tex]

[tex]\frac{-60}{5} =-12[/tex], so the slope is -12.

==================================================================

1) Part B (analysis)

We can see that no matter what 2 y-values and their corresponding x values we use, the slope always is the same. This means that the rate of change is constant.

Answer:

b

Step-by-step explanation:

Answer: 11/24

Step-by-step explanation:I turned 2 and 3/4 into an improper fraction which got me 11/4.

There are 5 friends and him so that's 6 people.

So we can't do 11/4 divided by 6 so we must put 6 over 1.

So 11/4 divided by 6/1

Then we do "Keep Change Flip"

We keep 11/4

We change the division sign to multiplication

Then we flip 6/1 to 1/6

Then the problem is re wrote as:

11/4 times 1/6

And that equals 11/24 as your answer

So each person gets 11/24 of the pies.

Answer:

[tex]\huge\purple{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]

»ANSWER«

(1) Write properties of function:

x intercept/zero:

[tex] x_{1} = \frac{3}{4} [/tex]

y intercept:

[tex]y = - 12[/tex]

domain:

[tex]( - \infty \: \infty )[/tex]

type of function: cubic fraction

standard form:

[tex]f(x) = 4 {x}^{3} - 3 {x}^{2} + 16x - 12[/tex]

factorize form:

[tex]f(x) = (4x - 3)( {x}^{2} + 4)[/tex]

even/odd/neither: neither

bounce/cross x axis:

[tex]x = \frac{3}{4} \: across[/tex]

increasing interval:

[tex]( - \infty \: \infty )[/tex]

decreasing interval: no

number of positive real zeros: 1

number of possible turning point: 2

order/degree: 3

leading term:

[tex]4x ^{3} [/tex]

leading coefficent: 4

constant term: -12

end behavior:

[tex]as \: x \: → \infty f(x) → \infty \: as \: x → - \infty f(x) → - \infty [/tex]

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Answer:

V≈471.4cm³

Step-by-step explanation:

V =

[tex] \frac{1}{3} \times \sqrt{2} \times {a}^{3} [/tex]

V= 471.4

Answer:

Here we have given that the all edges if octahedron are 10 cm. We need to find the volume of regular octahedron.

[tex] \rule{300}{1.5}[/tex]

As we know that the formula of volume of octahedron is :

[tex]\longrightarrow{\pmb{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} {a}^{3}}}}[/tex]

Substituting all the given values in the formula to find the volume of regular octahedron :

[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} {a}^{3}}}}[/tex]

[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(10)}^{3}}}}[/tex]

[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(10 \times 10 \times 10)}}}}[/tex]

[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times {(1000)}}}}[/tex]

[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{1}{3} \times \sqrt{2} \times 1000}}}[/tex]

[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = \dfrac{ \sqrt{2} }{3} \times 1000}}}[/tex]

[tex]{\longrightarrow{\sf{Volume_{(Octahedron)} = 0.471404 \times 1000}}}[/tex]

[tex]{\longrightarrow{\sf{\underline{\underline{\red{Volume_{(Octahedron)} \approx 471.404 \: {cm}^{3}}}}}}}[/tex]

Hence, the volume of regular octahedron is 471.404 cm³.

[tex] \rule{300}{1.5}[/tex]

Answer:

last one

Step-by-step explanation:

Answer:

12x - 6

Step-by-step explanation:

4 + 15x - 10 -3x

(15x - 3x) + (4-10)

12x - 6

Answer:

5y - 6x = 8 or y = 6x/5 + 8/5

Step-by-step explanation:

let M1= gradient of line AB and M2= gradient of the second line

When two lines are perpendicular, the product of their gradients is -1

i.e, M1M2= -1

M2= -1/M1

A(2,9) and B(8,4)

gradient= (y2-y1)/(x2-x1)

M1= (4-9)/(8-2)

= -5/6

M2= -1÷ -5/6

-1 × -6/5= 6/5

Equation of the line passing through C(-3,-2)

[y-(-2)]/[x-(-3)= 6/5

(y+2)/(x+3)= 6/5

5(y+2)= 6(x+3)

5y+10=6x+18

5y= 6x + 8

y= 6x/5 + 8/5

As per the slope-intercept form of a straight line, the equation of the required line is 5y = 6x + 8.

The slope-intercept form of a straight line is: y = mx + c

Here, m = slope of the line , c = y-intercept

If the slope of a line is 'a', then the slope of the line that is perpendicular to the given line is (- 1/a).

The given coordinates of the points A, B, C are (2, 9); (8, 4); and C(- 3, - 2) respectively.

Therefore, the slope of the line AB is (m)

= (y₂ - y₁)/(x₂ - x₁)

= (4 - 9)/(8 - 2)

= (- 5)/6

Slope of the required line is perpendicular to AB.

Therefore, the slope of the required line is

= - 1/(- 5/6)

= 6/5

This line passes through point C(- 3, - 2).

- 2 = - 3(6/5) + c

⇒ c = -2 + 18/5

⇒ c = 8/5

The equation of the required line is

y = (6/5) x + (8/5)

⇒ 5y = 6x + 8

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Answer:

Your answer would be y= -x + 5

Step-by-step explanation:

Hope I helped!

Answer:

-x+5

Step-by-step explanation:

khan told me ;p

Answer:

- 2 < x < 6

Step-by-step explanation:

- 6 < x - 4 < 2 ( add 4 to each interval )

- 2 < x < 6

Answer:

yooo i got the new rank im now expert :0

Step-by-step explanation:

XD

Answer:

5/72

Step-by-step explanation:

this is the answer hope it helps

Answer:

correct answer is 10

Step-by-step explanation:

5/6÷1/12

5/6×12/1

5×2

=10

Answer:

The second one:

x 2-2 3-3

y 5 5 7 7

Step-by-step explanation:

Each domain value or x can only have one range, y, so, with that said, the second one is the answer.

Answer:

3i square root 2

Step-by-step explanation:

Answer:

the 4th choice

Step-by-step explanation:

hope this helps

MAy I get braineist pls????????

Answer:

[tex]-2\frac{2}{5}[/tex]

Step-by-step explanation:

[tex]\frac{-4}{5} *\frac{3}{1}[/tex] multiply across

[tex]\frac{-12}{5}[/tex] turn into mixed number

[tex]-2\frac{2}{5}[/tex]

Answer:

r=0.5d

Step-by-step explanation:

Answer:

2nd choice

Step-by-step explanation: