<em>c = 10</em>
Step-by-step explanation:
We can find out the missing side of a right triangle by using the Pythagorean theorem.
The Pythagorean theorem is...

We can even double check the first problem by plugging in everything into the theorem and solving, everything will come out correct. We can plug in the numbers from the second problem into the theorem and find c, also please note that the hypotenuse of a triangle will <em>always </em>be c. It doesn't matter which you put in for a or b, but since the problem gives us which one is a and which one is b, I'll just be plugging it in like that.



A lot of people will stop here and think that the answer is 100, but you need to find the square root of 100, since c is squared. The square root of 100 is 10, so...
<em><u>c = 10</u></em>
6
The upside down U means intersection
A intersect B intersect C is where all 3 circles overlap.
Sum up all the numbers to get 50
P (a intersect b intersect c) = 6/50 = 3/25
We are dealing with monomial function so we just focus on end behavior.
5x¹⁰ has both ends going up so it would have minimum value
-4x¹¹ has one end going down and other end going up so no minimum value
-x¹² has both ends going down so it opens downward thus no minimum value. Just maximum.
6x⁷ has one ends going up and other going down so no minimum value.
So final answer is y = 5x¹⁰
The initial height of the balloon is 10 feet which then increases by 70% to (10 ×1.7) = 17 feet, then to (17 × 1.7) =28.9 feet, and so fourth if the rate of increase is kept constant. Therefore, forming a geometric sequence such that to get any term in the sequence we use the formula ar∧(n-1), where a is the first term, r is the common ratio, and n is the term in the sequence. In this case a is 10 and r= 1.7 , to get the height in the fourth minute it means n =5 (for the first term there is 0 minutes, such that for 0 minutes n= 1)
Thus, 10 × 1.7 ∧ 4 = 83.521 feet.
Therefore, the answer is 83.521 feet