What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ?

1 answer:

3 0

Plot the points on a graph. Connect the dots into a triangle. See that the height of the triangle is from y=5 down to y=1. So the height is 4 units.
Area of a triangle: A = (1/2)BH

You need to find the length of the base. Which is from point (-4,1) to (0,1). You can use the distance formula r just see from the graph that the base is 4 units.

A = (1/2)(4)(4)
A = 8

** Distance formula fyi
d² = (X-x)² + (Y-y)²
with points (X,Y) and (x,y)

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If sec theta = - √30 / 3, find cos theta. if sin(-theta) = -0.97, find cos (π/2 - theta).

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Step-by-step explanation:

$\cos \theta = \frac{1}{ \sec\theta } = - \frac{3}{ \sqrt{30} } = - \frac{3 \sqrt{30} }{30} = - \frac{ \sqrt{30} }{10}$

$\cos( \frac{\pi}{2} - \theta )= \cos \frac{\pi}{2} \cos \theta + \sin \frac{\pi}{2} \sin \theta$

Note that

$\sin( - \theta) = - \sin \theta$

$\cos \frac{\pi}{2} = 0 \: \: \: \: \: \sin \frac{\pi}{2} = 1$

Therefore,

$\cos( \frac{\pi}{2} - \theta ) = 0.97$

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3 years ago

Relate Fractions, Decimals, and Money. Write the money amount as a fraction in terms of dollars. The problems are $0.66 and $1.0

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You convert a decimal to a fraction by putting the digits to the right of the decimal point over "1" followed by the same number of zeros. (Most folks learn this in 3rd or 4th grade.)

0.66 = 66/100 . . . . . 2 decimals, so the denominator is 100

Then you reduce the fraction by canceling common factors. It helps to know your times tables and divisibility rules. (Or you can have your calculator do it.)

0.66 = 66/100 = 33/50
1.00 = 100/100 = 1