Answer:
3rd choice
Step-by-step explanation:
Answer:![\frac{5}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7D)
Step-by-step explanation:
breaststroke=50
backstroke=60
ratio=breaststroke:backstroke
=50:60=5:6
The system of equations of two unknowns is formulated and solved.
![\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ x\times y = 4 \\ x^2+y^2 = 17 \end{matrix}\right. \ \Longrightarrow \ y=\dfrac{4}{x}} \end{gathered}$}](https://tex.z-dn.net/?f=%5Clarge%5Cdisplaystyle%5Ctext%7B%24%5Cbegin%7Bgathered%7D%5Csf%20%5Cbf%7B%20%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D%20%5C%20x%5Ctimes%20y%20%3D%204%20%5C%5C%20x%5E2%2By%5E2%20%3D%2017%20%5Cend%7Bmatrix%7D%5Cright.%20%5C%20%5CLongrightarrow%20%5C%20y%3D%5Cdfrac%7B4%7D%7Bx%7D%7D%20%20%5Cend%7Bgathered%7D%24%7D)
![\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+\left (\dfrac{4}{x} \right )^2=17\ \Longrightarrow\ x^4+16=17x^2 } \end{gathered}$}](https://tex.z-dn.net/?f=%5Clarge%5Cdisplaystyle%5Ctext%7B%24%5Cbegin%7Bgathered%7D%5Csf%20%5Cbf%7B%20x%5E2%2B%5Cleft%20%28%5Cdfrac%7B4%7D%7Bx%7D%20%5Cright%20%29%5E2%3D17%5C%20%5CLongrightarrow%5C%20x%5E4%2B16%3D17x%5E2%20%20%7D%20%5Cend%7Bgathered%7D%24%7D)
![\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} 0&=(x^2)^2-17(x^2)+16\\ =(x^2-16)(x^2-1) \\ \ \ \ \ \ \ \ \ \ \ =(x+4)(x-4)(x+1)(x-1) \end{gathered}$}](https://tex.z-dn.net/?f=%5Clarge%5Cdisplaystyle%5Ctext%7B%24%5Cbegin%7Bgathered%7D%5Csf%20%5Cbegin%7Balign%2A%7D%200%26%3D%28x%5E2%29%5E2-17%28x%5E2%29%2B16%5C%5C%20%3D%28x%5E2-16%29%28x%5E2-1%29%20%5C%5C%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%3D%28x%2B4%29%28x-4%29%28x%2B1%29%28x-1%29%20%5Cend%7Bgathered%7D%24%7D)
Possible number pairs are 4, 1 and -4, -1 .
A₁ = -8 This is the first term in an arithmetic sequence.
d = 3, the common difference
a(n) = a₁ + d(n-1)
a₇ = -8 + 3(7-1)
a₇ = -8 + 3(6)
a₇ = -8 + 18
a₇ = 10
To check:
a₁ = -8
a₂ = -8 + 3 = -5
a₃ = -5 + 3 = -2
a₄ = -2 + 3 = 1
a₅ = 1 + 3 = 4
a₆ = 4 + 3 = 7
a₇ = 7 + 3 = 10