Triangle $abc$ has side lengths $ab = 9$, $ac = 10$, and $bc = 17$. let $x$ be the intersection of the angle bisector of $\angle a$ with side $\overline{bc}$, and let $y$ be the foot of the perpendicular from $x$ to side $\overline{ac}$. compute the length of $\overline{xy}$.

Step-by-step explanation:

Consider triangle ABC. Segment AX is angle A bisector. Its length can be calculated using formula

Hence,

By the angle bisector theorem,

So,

and

By the Pythagorean theorem for the right triangles AXY and CXY:

Thus,

Subtract from the second equation the first one:

Hence,

Step-by-step explanation:

The semiperimeter of triangle is , so by Heron's formula, the area of triangle is .

The area of triangle $PRX$ is

.By the angle bisector theorem, we have , so and , which means

.

Then is the height of triangle with respect to base , so , which gives us

.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.