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3 years ago

Find the area if a rectangle with a length of x+1 and a width of x+3

Mathematics

1 answer:

fenix001 [56]3 years ago

5 0

You multiply x times x
=x
1 x 3
=3
It is x+3

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Let T be the linear transformation whose standard matrix is Aequals[Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column negative

Scilla [17]

Answer:

Yes the linear transformation is one to one and it maps a set of real numbers R cubed onto set of real numbers R cubed

Step-by-step explanation:

To show that the linear transformation is one to one, we must show that the columns are linearly independent columns (i.e it must have the trivial solution)

$A = \left[\begin{array}{cccc}1&-2&3&0\\-1&3&-4&0\\-5&-2&9&0\end{array}\right]$

For the Augumented matrix A and applying Row Reduction Formula we have that

= $\left[\begin{array}{cccc}1&-2&3&0\\0&1&-1&0\\0&0&-18&0\end{array}\right]$

we can deductively see that $x_{3} = 0, x_{2} = 0, x_{1} = 0$

Since the columns are linearly independent, Hence it is a one-to-one transformation and it maps a set of real numbers R cubed onto set of real numbers R cubed

4 0

3 years ago

Read 2 more answers

Solve the following quadratic equation by completing the square

horsena [70]

Step-by-step explanation:

x=-14 plus/minus squared root of 1394 over 7

3 0

3 years ago

There are three kids. The sum of individual squares of their body weights (2 + 2 + 2) is 100. The sum of the product of their we

Mashcka [7]

Answer:

Step-by-step explanation:

Givens

Let child one = x

Let child two = y

Let child three = z

Equations

x^2 + y^2 + z^2 = 100

xy + xz + yz = 150

Solution

There's a trick here. The square of their weights added together is equal (with some modification) to the given conditions. Start by squaring (x+y+z).

(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz

Take out 2 as a common factor from the last three terms.

(x + y + z)^2 = (x^2 + y^2 + z^2+ 2(xy + xz + yz) )

Substitute the given conditions into the equation. (x^2 + y^2 + z^2) = 100 and 2*(xy + xz + yz) = 2 * 150

(x + y + z)^2 = 100 + 2*150

(x + y + z)^2 = 100 + 300

(x + y + z)^2 = 400

Take the square root of both sides.

sqrt(x+y+z)^2 = sqrt(400)

x + y + z = 20

Note

This answer tells you nothing about the values of x y and z. On the other hand it does not ask for the values of x y and z.