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KengaRu [80]
3 years ago
12

3. Use the diagram of a REGULAR HEXAGON and follow these steps to solve for the area of a hexagon with sides equal to 4 cm. Leav

e radicals in your answers.
How many equilateral triangles are there? __________
If we cut an equilateral down the middle (green line) what special triangle do you create? __________
Sketch and label all side lengths of the 30-60-90 triangle by itself below.
What is the length of the short side of one 30-60-90 triangle? __________
What is the length of the hypotenuse of one 30-60-90 triangle? __________
Apply properties of 30-60-90 triangles to calculate the long leg: ¬¬¬¬___________
What is the vocabulary word for the long side of the 30-60-90 called in the polygon (green line)? ____________
What is the height of the equilateral triangle? _________
Apply triangle area formula to calculate the area of one equilateral triangle: ____________
Calculate the area of the complete hexagon by multiplying area of one equilateral triangle by # of triangles: _____

Mathematics
1 answer:
Delicious77 [7]3 years ago
3 0

Answer:

There are 6 equilateral triangles

you get an isosceles triangle

the height of the equilateral triangle is 4

this is all I have so far :)

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Peter received a trophy at the state math competition. His trophy is in the shape of a square pyramid and is covered in wrapping
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Answer:315 cm

Step-by-step explanation:

7x7

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6 0
3 years ago
All vectors are in Rn. Check the true statements below:
Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that ||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then ||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||.

C) Consider S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2. This set is orthogonal because (0,2)\cdot(2,0)=0(2)+2(0)=0, but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in \mathbb{R}^n. Then the columns of A form an orthonormal set. We have that A^{-1}=A^t. To see this, note than the component b_{ij} of the product A^t A is the dot product of the i-th row of A^t and the jth row of A. But the i-th row of A^t is equal to the i-th column of A. If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then A^t A=I    

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set \{u_1,u_2\cdots u_p\} and suppose that there are coefficients a_i such that a_1u_1+a_2u_2\cdots a_nu_n=0. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then a_i||u_i||=0 then a_i=0.  

5 0
3 years ago
Of
ollegr [7]
The answer is 25 I think sorry if it’s wrong :)
3 0
2 years ago
Read 2 more answers
How many solutions does the following equation have?
RoseWind [281]

Answer:

There will be No solution for the equation 9x - 4 = - 3x + 5 + 12x. Option B is correct.

Step-by-step explanation:

We need to determine how many solutions the equation 9x - 4 = - 3x + 5 + 12x have.

Solving the equation and finding the solutions

9x - 4 = - 3x + 5 + 12x

Combining like terms, Moving 3x and 12x to left side of equality and changing their signs and moving 4 on right side of equation and changing sign.

9x +3x-12x =  5 + 4

Simplifying

12x-12x =  9\\0=9

Solving the equation we get 0=9 which is false. So, there will be No solution for the equation 9x - 4 = - 3x + 5 + 12x. Option B is correct.

5 0
2 years ago
State the angle from 1:00 to 2:30
charle [14.2K]

Answer:

Im pretty sure its 45°

Step-by-step explanation:

7 0
3 years ago
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