Help picture below problem 17

Mathematics

1 answer:

mixas84 [53]3 years ago

3 0

Answer:

Step-by-step explanation:

Angle KPJ is going to have the same measure as Angle DPE. This problem is a bit tricky, but I'll try my best to explain it. A straight angle is basically just a straight line, and it equals 180 degrees. Angle FPG is a straight angle.

To find the measure of Angle KPJ, we first have to find the measure of angle DPE, and the way we're gonna do that is add together the other angles in the straight angle (which would be Angle FPD and Angle EPG) and then subtract that from 180 (measure of a straight angle).

That might have sounded a bit confusing, but that's the best way I could explain it. Now, let's add Angle FPD and Angle EPG.

105 + 35 = 140

Now, let's subtract that from 180.

180 - 140 = 40

We now know that the measure of Angle DPE is 40, and since it's equivalent to Angle KPJ, our answer is 40!

I know that was confusing, but I hope it helped a little bit! Have a lovely day!! :)

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Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (3,3), (-13, −5), and (-5,3)

Aliun [14]

This problem will be solved both analytically and graphically.
The epicenter lies on a circle with radius=5 from X(3,3). Therefore
(x-3)² + (y-3)² = 25 (1)
Y(-13,-5) has the epicenter on a circle with radius=13, therefore
(x+13)² + (y+5)² = 169 (2)
Z (-5,3) has the epicenter on a circle with radius = 5, therefore
(x+5)² + (y-3)² = 25 (3)

Subtract (1) from (3).
(x+5)² - (x-3)² = 0
x² + 10x + 25 - x² + 6x - 9 = 0
16x = -16
x = -1
From (1), obtain
16 + (y-3)² = 25
(y-3)² = 9
y = 0 or y = 6

Check answers with (2).
When x=-1, y=0. obtain
(x+13)² + (y+5)² = 169 (Correct, Accept)
When x=-1, y=6, obtain
(x+13)² + (y+5)² = 265 (Incorrect, Reject)

The epicenter is at (-1,0).

Graphical solution (see the figure below).
From X (3,3), draw a circle with radius =5.
From Z (-5, 3), draw a circle with radius = 5.
The only point where all three circles intersect is (-1, 0) approximately.

Answer: The epicenter is at (-1,0)