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3 years ago

Find the product of (x − 8)^2 and explain how it demonstrates the closure property of multiplication.

Mathematics

2 answers:

Goryan [66]3 years ago

6 0

Answer:x^2-16x+64

Step-by-step explanation:

in the attachment

Alona [7]3 years ago

6 0

Answer:

I know for sure that it’s x^2 - 16x + 64 is a polynomial

Step-by-step explanation:

I just took the test.

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Write a sequence of rhe transformations that maps quadrilateral ABCD onto quadrilateral A"B"C"D" in the picture below??

MariettaO [177]

Answer:

It is a reflection of the y axis, with 2 units down. :)

Step-by-step explanation:

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2 years ago

Read 2 more answers

Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (2a0 + 3a1 + 3a2) + (6a0 + 4a1 + 4a2)t

Svet_ta [14]

Answer:

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

Step-by-step explanation:

First we start by finding the dimension of the matrix [T]EE

The dimension is : Dim (W) x Dim (V) = 3 x 3

Because the dimension of P2 is the number of vectors in any basis of P2 and that number is 3

Then, we are looking for a 3 x 3 matrix.

To find [T]EE we must transform the vectors of the basis E and then that result express it in terms of basis E using coordinates and putting them into columns. The order in which we transform the vectors of basis E is very important.

The first vector of basis E is e1(t) = 1

We calculate T[e1(t)] = T(1)

In the equation : 1 = a0

$T(1)=(2.1+3.0+3.0)+(6.1+4.0+4.0)t+(-2.1+3.0+4.0)t^{2}=2+6t-2t^{2}$

$[T(e1)]E=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

And that is the first column of [T]EE

The second vector of basis E is e2(t) = t

We calculate T[e2(t)] = T(t)

in the equation : 1 = a1

$T(t)=(2.0+3.1+3.0)+(6.0+4.1+4.0)t+(-2.0+3.1+4.0)t^{2}=3+4t+3t^{2}$

$[T(e2)]E=\left[\begin{array}{c}3&4&3\\\end{array}\right]$

Finally, the third vector of basis E is $e3(t)=t^{2}$

$T[e3(t)]=T(t^{2})$

in the equation : a2 = 1

$T(t^{2})=(2.0+3.0+3.1)+(6.0+4.0+4.1)t+(-2.0+3.0+4.1)t^{2}=3+4t+4t^{2}$

Then

$[T(t^{2})]E=\left[\begin{array}{c}3&4&4\\\end{array}\right]$

And that is the third column of [T]EE

Let's write our matrix

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

T(X) = AX

Where T(X) is to apply the transformation T to a vector of P2,A is the matrix [T]EE and X is the vector of coordinates in basis E of a vector from P2

For example, if X is the vector of coordinates from e1(t) = 1

$X=\left[\begin{array}{c}1&0&0\\\end{array}\right]$

$AX=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]\left[\begin{array}{c}1&0&0\\\end{array}\right]=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

Applying the coordinates 2,6 and -2 to the basis E we obtain

$2+6t-2t^{2}$

That was the original result of T[e1(t)]

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3 years ago

A piece of cloth is folded into a square with a side length measuring x inches. When it is unfolded, it has an area of x2 + 27x

Dmitriy789 [7]

Our task here is to find possible factors of <span>x^2 + 27x + 162.
We need to check out possible factors of 162 first. Examples are:
2(81), 3(54), 6(27), 9(18), and so on. Notice that 9 and 18 add up to 27, so that the factors (x+9) and (x+18) produce x^2 + 27x + 162 when mult. together.</span>

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2 years ago

Given the definitions of f(x) and g(x) below, find the value of g(f(6)).

Fofino [41]

3 because it is a better Dona a toon

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anygoal [31]

Answer:

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Step-by-step explanation:

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