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2 years ago

Determine whether the lines are parallel, perpendicular or neither: Line 1:4y−12=3x Line 2:2y−1.5x=−14

Mathematics

1 answer:

Kamila [148]2 years ago

6 0

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We manipulate the expressions to model them in the pending-intersection form

Line 1:

$4y-12=3x\\4y=3x+12\\y=\frac{3}{4}x+\frac{12}{4}\\y=\frac{3}{4}x+3\\y=0.75x+3$

Line 2:

$2y - 1.5x = -14\\2y = 1.5x-14\\y = \frac {1.5} {2} x- \frac {14} {2}\\y = \frac {1.5} {2} x-7\\y = 0.75x-7$

By definition, we have that if two lines are parallel then their slopes are equal. It is observed that the slopes of both lines are equal, so the lines are parallel.

ANswer:

The lines are parallel

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2 years ago

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posledela

Answer:

P=0.0000037

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Step-by-step explanation:

Probability

A standard deck of 52 playing cards has 4 aces.

The probability of getting one of those aces is

$\displaystyle \frac{4}{52}=\frac{1}{13}$

Now we got an ace, there are 3 more aces out of 51 cards.

The probability of getting one of those aces is

$\displaystyle \frac{3}{51}=\frac{1}{17}$

Now we have 2 aces out of 50 cards.

The probability of getting one of those aces is

$\displaystyle \frac{2}{50}=\frac{1}{25}$

Finally, the probability of getting the remaining ace out of the 49 cards is:

$\displaystyle \frac{1}{49}$

The probability of getting the four consecutive aces is the product of the above-calculated probabilities:

$\displaystyle P= \frac{1}{13}\cdot\frac{1}{17}\cdot\frac{1}{27}\cdot\frac{1}{49}$

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P=0.00037%

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2 years ago

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2 years ago

What is the argument of -5\sqrt{3}+ 5i?

Shtirlitz [24]

Answer:

150 degrees

Step-by-step explanation:

Graphing the complex number we see the angle terminates in the second quadrant. This means the argument, the angle, will be between 90 degrees and 180 degrees.

So if we create a right triangle with that point after graphing it. We see the height of that triangle is 5 because that is the imaginary part. The base of that triangle has length $5\sqrt{3}$ . The problem is this doesn't give us any part of the angle we want, but it does give us the complementary of the part of the angle that is in second quadrant.