3 years ago

Lines m and p are perpendicular. if the slope of line m is -3 what is the slope of line p

1 answer:

ivann1987 [24]3 years ago

4 0

For two lines to be perpendicular, their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1, in this case our reference line has a slope of -3 so:

-3m=-1 divide both sides by -3

m=-1/-3

m=1/3

So the perpendicular line will have a slope of 1/3

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A parallelogram has a 70 degree angle and sides 6 cm and 10 cm long. How long are its diagonals?

Verdich [7]

Let the shorter diagonal be x, then
x^2 = 6^2 + 10^2 - 2 x 6 x 10 x cos 70 = 36 + 100 - 120 cos 70 = 136 - 41.04 = 94.96
x = sqrt(94.96) = 9.7 cm

The other angle of the parallelogram is 1/2(360 - 2(70)) = 1/2(360 - 140) = 1/2(220) = 110
Let the longer diagonal be y, then
y^2 = 6^2 + 10^2 - 2 x 6 x 10 x cos 110 = 36 + 100 - 120 cos 110 = 136 + 41.04 = 177.04
y = sqrt(177.04) = 13.3 cm.

Therefore, the length of the diagonals are 9.7 cm and 13.3 cm.

6 0

3 years ago

Evaluate 1 3 m − 1 − 1 2 n 3 1 m−1− 2 1 nstart fraction, 1, divided by, 3, end fraction, m, minus, 1, minus, start fraction,

luda_lava [24]

Answer:

Step-by-step explanation:

Apparently, you want the value of ...

$\dfrac{1}{3}m-1-\dfrac{1}{2}n = \dfrac{m}{3}-\dfrac{n}{2}-1\\\\=\dfrac{21}{3}-\dfrac{12}{2}-1=7-6-1\\\\=\boxed{0}$