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2 years ago

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Mathematics

2 answers:

astraxan [27]2 years ago

8 0

Answer:

The width is 5 feet.

Step-by-step explanation:

If the length of the banner is 15 feet, and the length of the banner is 3 times the width of the banner, then set up an equation to find the width of the banner.

banner length/3 = banner width

15/3 = w

w = 5

The width of the banner is 5 feet.

avanturin [10]2 years ago

5 0

The width of the banner is 5 feet. Hope that helps.

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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)]

8 0

3 years ago

Simplify the expression (-3x^-4)^2

Bond [772]

$(-3x^{-4})^2\\9x^{-8}$

7 0

3 years ago

Use the given frequency table to find mean, median,mode,and range.

galina1969 [7]

Answer:

Mode:6

median: 5.5

mean: 5.25

range : 2

Step-by-step explanation:

7 0

2 years ago

What is the slope of the line through (2,-2)(2,−2)left parenthesis, 2, comma, minus, 2, right parenthesis and (9,3)(9,3)left par

Alecsey [184]

Answer:

Slope=5/7

Step-by-step explanation:

Slope=Δy/Δx=(3-(-2)) /(9-2)=5/7

3 0

3 years ago

How many solutions does an equation have when you isolate the variable and it equals a constant?

OLEGan [10]

1 solution is available when variable equals a constant.

Answer: Option B.

<u>Explanation:</u>

You will be able to determine if an equation has one solution (which is when one variable equals one number), or if it has no solution (the two sides of the equation are not equal to each other) or infinite solutions (the two sides of the equation are identical).

The ordered pair that is the solution of both equations is the solution of the system. A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a consistent system has exactly one solution, it is independent.

3 0

3 years ago