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3 years ago

If triangle DEF is classified as equilateral, which statement must be true?

Mathematics

1 answer:

patriot [66]3 years ago

6 0

Answer:

all three sides are congruent.

Step-by-step explanation:

it is equiangular.

sides are equal.

angles are equal.

all three sides are congruent.

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Do y'all know vectors-? AHH

Sophie [7]

Answer:

yea kind of but not in detail

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2 years ago

Read 2 more answers

For f(x) = 3x + 1 and g(x) = x2 - 6, find (f + g)(x).

alexdok [17]

(3x + 1) + (x2 - 6)
x2 + 3x - 5

8 0

3 years ago

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are

alexgriva [62]

Answer:

$P=\left(\begin{array}{ccc}-\frac{2}{3}&-\frac{2}{3}&\frac{1}{3}\\\frac{1}{\sqrt{5}}&0&\frac{2}{\sqrt{5}}\\-\frac{4}{3\sqrt{5}}&\frac{\sqrt{5}}{3}&\frac{2}{3\sqrt{5}}\end{array}\right)$

Step-by-step explanation:

It is a result that a matrix $A$ is orthogonally diagonalizable if and only if $A$ is a symmetric matrix. According with the data you provided the matrix should be

$A=\left(\begin{array}{ccc}-9&-4&2\\ -4&-9&2\\2&2&-6\\\end{array}\right)$

We know that its eigenvalues are $\lambda_{1}=-14, \lambda_{2}=-5$ , where $\lambda_{2}=-5$ has multiplicity two.

So if we calculate the corresponding eigenspaces for each eigenvalue we have

$E_{\lambda_{1}=-14}=\langle(-2,-2,1)\rangle$ , $E_{\lambda_{2}=-5}=\langle(1,0,2),(-1,1,0)\rangle.$ .

With this in mind we can form the matrices $P, D$ that diagonalizes the matrix $A$ so.

$P=\left(\begin{array}{ccc}-2&-2&1\\1&0&2\\-1&1&0\\\end{array}\right)$

and

$D=\left(\begin{array}{ccc}-14&0&0\\0&-5&0\\0&0&-5\\\end{array}\right)$

Observe that the rows of $P$ are the eigenvectors corresponding to the eigen values.

Now you only need to normalize each row of $P$ dividing by its norm, as a row vector.

The matrix you have to obtain is the matrix shown below

3 0

3 years ago

Help! Need this done quickly! picture is upside down so please flip your screen! sorry!

iogann1982 [59]

Answer:

x=6

Step-by-step explanation:

Hi there!

<u>1) Determine the perimeter of the square</u>

We're given that the perimeters of the square and the rectangle are equal. Therefore, after finding the perimeter of the square, we will also know the perimeter of the rectangle.

Find the side length of the square using the area formula:

$A=l^2$ where l is the side length

Plug in the given area 121 in.²

$121=l^2$

Take the square root of both sides

$\sqrt{121} = \sqrt{l^2} \\11=l$

Therefore, the side length of the square is 11 inches. Plug this into the perimeter formula:

$P=4l$ where l is the side length

$P=4(11)\\P=44$

Therefore, the perimeter of the square is 44 inches. The perimeter of the rectangle is also 44 inches.

<u>2) Determine the value of x</u>

Use the formula for the perimeter of a rectangle:

$P=2(l+w)$ where l is the length and w is the width

Plug in 3x and x-2 as the length and width

$P=2(3x+(x-2))\\P=2(3x+x-2)\\P=2(4x-2)$

Plug in the perimeter 44 in.

$44=2(4x-2)$

Expand the parentheses

$44=8x-4$

Add 4 to both sides to isolate 8x

$44+4=8x-4+4\\48=8x$

Divide both sides by 8 to isolate x

$\frac{48}{8}=\frac{8x}{8} \\6=x$

Therefore, the value of x is 6.

I hope this helps!

4 0

3 years ago

Im dying bro help The vertices of a quadrilateral are (2, 3), (3, 8), (7, 5), and (6, 2). Draw the quadrilateral in the coordina

Solnce55 [7]

Okay to the first number in the ordered pair is the x and the second is the y. So (x,y) when you put a dot on the coordinate plane such as (2,3), you have to go the the horizontal line which is x and go over right 2 spaces(depending on how many numbers is one space) then go up 3. Do that same thing for each of the order pairs. Eventually you will have 4 dots. Connect those dots then you will have the quadrilateral. I hope this helps you!

7 0

3 years ago