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1 year ago

Please help me solve this with multiplication. Thankl you!

Mathematics

1 answer:

sergij07 [2.7K]1 year ago

8 0

Answer:

1/6x² -1/6x -1/8

Step-by-step explanation:

The distributive property applies. Fractions are multiplied and added in the usual way.

<h3>Product of binomials</h3>

The distributive property is used to eliminate parentheses. It can be convenient to write the fractions with a common denominator, then simplify the final product.

$\left(\dfrac{1}{2}x+\dfrac{1}{4}\right)\left(\dfrac{1}{3}x-\dfrac{1}{2}\right)=\dfrac{2x+1}{4}\cdot\dfrac{2x-3}{6}=\dfrac{1}{24}((2x)(2x-3)+1(2x-3))\\\\=\dfrac{1}{24}(4x^2-6x+2x-3)=\boxed{\dfrac{1}{6}x^2-\dfrac{1}{6}x-\dfrac{1}{8}}$

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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

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4 years ago

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.

Dahasolnce [82]

Answer:

Option B , C and E are correct

$y^2-5y =750$

$750 -y(y-5)=0$

(y+25)(y-30)=0

Step-by-step explanation:

Given : Area of rectangular room is 750 square feet.

Width of the room is 5 feet less than the length of the room.

Let y be the length of the room

then,

As per the given condition

width of the room is: y-5

Area of rectangle is multiply the length by its width.

Area of rectangle = $length \times width$

Substitute the given values in above formula we get;

$750 = y(y-5)$ ......[1]

or we can write this as;

750 -y(y-5)=0

[1] ⇒ $y(y-5) =750$ or

$y^2-5y =750$ or

$y^2-5y-750=0$

$y^2-25y+30y-750=0$

(y+25)(y-30)=0

Therefore, the equation which can be used to solve for y are;

$y^2-5y =750$ , $750 -y(y-5)=0$ and (y+25)(y-30)=0

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3 years ago

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What is the Y intercept of the line described by the equation below Y equals X -3

irina [24]

Answer:

Y-int = (0,3)

Step-by-step explanation:

Set the equation = to 0 and whatever x will equal is your y intercept

X-3=0

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3 years ago

Ms. Thornton is buying treats for her top 10 algebra students in each of her two classes (20 treats total). She’s only willing t

Paladinen [302]

Answer:

Mrs Thornton can buy almost 17 candy packs if she has $30 to spend and one pack cost $1.75.

No, it will not be enough because total students are 20 and total candy packs that can be bought are 17.

Step-by-step explanation:

Total treats to buy = 20

Total cost to spend = $30

Price of one candy pack = 1.75

We need to find:

a) What is the maximum number of packs that she will be able to buy?

Price of 1 candy pack = $1.75

If she spends $30, divide 30 by 1.75 to get the number of candy packs she can buy

Number of candy packs = $\frac{30}{1.75} = 17.14 \approx 17$

So, Mrs Thornton can buy almost 17 candy packs if she has $30 to spend and one pack cost $1.75

b) Will that be enough for all of her students?

No, it will not be enough because total students are 20 and total candy packs that can be bought are 17.

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