The general formula for the sides of right triangle is
a² + b² = c²
Subtitute the equation of a and b to the formula a² + b², evaluate if the answer will be the same as the equation of c²
a² + b²
= (m² - n²)² + (2mn)²
= (m² - n²)(m² - n²) + (2mn)(2mn)
= (m⁴ - 2m²n² + n⁴) + 4m²n²
= m⁴ + 2m²n² + n⁴
Factorize the result
m⁴ + 2m²n² + n⁴
= (m² + n²)(m² + n²)
= (m² + n²)²
= c²
It's proven by the formula that c² = (m² + n²)²
so the c will be m² + n²
The answer would be 177.4
Answer:
Larissa takes 59.141 seconds to complete both laps.
Step-by-step explanation:
The complete time is the sum of time taken on each lap. We translate the two statements into mathematical expressions to determine the required output:
(i) <em>She completes her first lap in 31.135 seconds</em>:

(ii) <em>She completes her second lap 3.129 seconds faster than the first lap</em>:



Then, the time taken by Larissa to complete both laps is:


Larissa takes 59.141 seconds to complete both laps.
Answer:
(-6,4)
Step-by-step explanation:
The equations are:

Solving for x^2 of the 2nd equation and putting that in place of x^2 in the 2nd equation we have:

Now we can solve for y:

So plugging in y = 4 into an equation and solving for x, we have:

So y = 4 corresponds to x = 6 & x = -6
The pairs would be
(6,4) & (-6,4)
<u><em>we see that (-6,4) falls in the 2nd quadrant, thus this is the solution we are looking for.</em></u>