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Umnica [9.8K]
3 years ago
15

Write an equation of the line that is parallel to y = 1 2 x + 3 and passes through the point (10, -5). A) y = 2x - 15 B) y = -2x

+ 15 C) y = - 1 2 x Eliminate D) y = 1 2 x - 10
Mathematics
1 answer:
Annette [7]3 years ago
6 0

Answer:

<h2>B) y = -2x + 15</h2>

Step-by-step explanation:

\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\k\ \parallel\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\=============================\\\\\text{We have the equation}\ y=\dfrac{1}{2}x+3\to m_1=\dfrac{1}{2}.\ \text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{We have the equation}\ y=-2x+b\\\\\text{Put the coordinates of the point (10, -5) to the equation and solve}\\\text{for}\ b:\\\\-5=-2(10)+b\\-5=-20+b\qquad\text{add 20 to both sides}\\15=b\\\\\text{Finally we have:}\\\\y=-2x+15

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3 years ago
Suppose that there are 15 antennas in a store, of which 3 are defective. Assume all the defectives and all the functional antenn
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Answer:

Step-by-step explanation:

Total number of antenna is 15

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The functional antenna is 15-3=12.

Now, if no two defectives are to be consecutive, then the spaces between the functional antennas must each contain at most one defective antenna.

So,

We line up the 13 good ones, and see where the bad one will fits in

__G __ G __ G __ G __ G __G __ G __ G __ G __ G __ G __ G __G __

Each of the places where there's a line is an available spot for one (and no more than one!) bad antenna.

Then,

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The number of arrangement is

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14C3=14×13×12×11!/11!×3×2

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14C3=364ways

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3 years ago
Glenna says that the height of her house is 1 yard is her claim reasonable
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Step-by-step explanation:

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Step-by-step explanation:

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