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Ahat [919]
3 years ago
10

If x is a number, which expression represents the statement below? 4 less than the product of 2 and a number

Mathematics
1 answer:
yulyashka [42]3 years ago
3 0

Answer:

2x-4

Step-by-step explanation:

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Which of the following is an equation for the plane through the point (1, 1, −1) and parallel
Bas_tet [7]

The given plane, x-y+z=3, has normal vector \vec n = \langle1,-1,1\rangle. Any plane parallel to this one has the same normal vector.

Let (x,y,z) be any point in the plane we want. The plane contains the point (1, 1, -1), so an arbitrary vector in this plane is

\langle x,y,z\rangle - \langle 1,1,-1\rangle = \langle x-1, y-1, z+1 \rangle

and this is perpendicular to \vec n.

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\langle x-1, y-1, z+1 \rangle \cdot \vec n = 0 \implies (x-1) - (y-1) + (z+1) = 0 \implies \boxed{x - y + z = -1}

or equivalently,

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1 year ago
16. Let W be the set of all vectors in R3 of the form a+2b b -3a Find a basis for Wand state the dimension of W.
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Answer:

W=\{\left[\begin{array}{ccc}a+2b\\b\\-3a\end{array}\right]: a,b\in\mathbb{R} \}

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\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{c}a+2b\\b\\-3a\end{array}\right]=a\left[\begin{array}{c}1\\0\\-3\end{array}\right]+b\left[\begin{array}{c}2\\1\\0\end{array}\right]

This means that each vector in W can be expressed as a linear combination of the vectors \left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]

Also we can see that those vectors are linear independent. Then the set

\{\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]\} is a basis for W and the dimension of W is 2.

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2 years ago
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Answer:

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Step-by-step explanation:

86 - 80 / 80 = 0.075

so 7.5%

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<h3>Answer: Radius</h3>

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