Determine the mean, median, mode, and range of 2,5,9,13,4,9,8,11,4

Mathematics

1 answer:

Debora [2.8K]3 years ago

4 0

Answer:

Step-by-step explanation:

Mean you add them all and divide by how many numbers.

Median you out then in order and find the middle number

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Find x and y. please help

anygoal [31]

Answer:

$x = 4 \sqrt{2}$

$y = 4 \sqrt{6}$

Step-by-step explanation:

$\sin 45 \degree = \frac{x}{8} \\ \\ x = 8 \sin 45 \degree \\ \\ x = 8 \times \frac{1}{ \sqrt{2} } \\ \\ x = \frac{8 \sqrt{2} }{2} \\ \\ x = 4 \sqrt{2} \\ \\ \\ \tan 30 \degree = \frac{x}{y} \\ \\ \frac{1}{ \sqrt{3} } = \frac{4 \sqrt{2} }{y} \\ \\ y = 4 \sqrt{6}$

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Find the distance from point (-1, 3) to the line 5 x - 4 y = 10.

Wewaii [24]

We could use the formula, derive the formula, or just work it out for this case. Let's do the latter.

The distance of a point to a line is the length of the perpendicular from the line to the point.

So we need the perpendicular to 5x-4y=10 through (-1,3). To get the perpendicular family we swap x and y coefficients, negating one. We get the constant straightforwardly from the point we're going through:

4x + 5y = 4(-1)+5(3) = 11

Those lines meet at the foot of the perpendicular, which is what we're after.

4x + 5y = 11

5 x - 4y = 10

We eliminate y by multiplying the first by four, the second by five and adding.

16x + 20y = 44

25x - 20y = 50

41x = 94

x = 94/41

y = (11 - 4x)/5 = 15/41

We want the distance from (-1,3) to (94/41,15/41)

$d = \sqrt{ (-1 - 94/41)^2 + (3 - 15/41)^2 } = \dfrac{27}{\sqrt{41}}$

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