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3 years ago

Find the missing side length assuming lines that appear to be tangent are tangent. Show work on piece of paper.

Mathematics

1 answer:

KIM [24]3 years ago

3 0

Answer:

Step-by-step explanation:

Since the line of length 16 is a tangent to the circle, then the angle between it and the radius is right.

? is the hypotenuse of the right triangle formed.

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

?² = 12² + 16² = 144 + 256 = 400 ( take the square root of both sides )

? = $\sqrt{400}$ = 20

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Which equation shows an example of the associative property of addition? (–7 + i) + 7i = –7 + (i + 7i) (–7 + i) + 7i = 7i + (–7i

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3 years ago

Find the area of the convex polygon with vertices (0,5), (-1,2), (4,4), (-3,-4) and (2,0).

Afina-wow [57]

The area of the convex polygon is 43/2 square units

<h3>How to determine the area of the convex polygon?</h3>

The vertices are given as:

(0,5), (-1,2), (4,4), (-3,-4) and (2,0)

The area is then calculated as:

$A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )$

So, we have:

$A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)$

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$A = \frac12 * (|-43|)$

Remove the absolute bracket

$A = \frac12 * 43$

This gives

$A = \frac{43}2$

Hence, the area of the convex polygon is 43/2 square units