On my 30th birthday, I plan to light 30 candles on my cake and blow 30% of them. How many candles will stay lit after I'm done?

Answer: Circle C has a radius of 7 cm.

Explanation:

Referring to the illustration below:

Let's denote the radius of circle C as x.

Circle A's radius can be represented as 2x.

Circle B's radius can be expressed as 4x.

The length of side AC in triangle ΔABC becomes x + 2x = 3x.

For side BC of triangle ΔABC, we get 4x + x = 5x.

Similarly, for side AB of triangle ΔABC, it is 4x + 2x = 6x.

Given that the perimeter of triangle ΔABC totals 98 cm.

Remember, the perimeter refers to the total length around the triangle.

Hence, Perimeter = 6x + 5x + 3x = 98 cm.

Thus, 14x = 98.

From this, we find x = .

Therefore, x = 7.

This concludes that the radius of circle C is 7 cm.

Answer:

Step-by-step explanation:

First, we apply the Pythagorean theorem to determine the distance from Manuel’s home to the resort.

S1 = √50²+20²

S1 = √2500+400

S1 = √2900

S1 = 53.85m

Next, we find the distance from Manuel's home to his friend’s residence.

S2 = √15²+10²

S2 = √225+100

S2 = √325

S2 = 18.03m

The distance between the two boys and the resort will be represented as ∆S = S2 - S1.

∆S = 53.84 - 18.03

∆S = 35.81m