Step-by-step explanation:
(116-718) /(2.805+118) [as, there cannot be two decimals in one numbers
=-602/120.805
=0.498
(y^2-y-12)/(y^2-2y-15) factor both the numerator and denominator...
(y^2-4y+3y-12)/(y^2-5y+3y-15)
(y(y-4)+3(y-4))/(y(y-5)+3(y-5))
((y-4)(y+3))/((y-5)(y+3)) so the (y+3) terms cancel leaving
(y-4)/(y-5)
8.75 9.00 that’s the answer
If the sequence is quadratic, then the <em>n</em>-th term (<em>n</em> ≥ 1) is
![p_n = an^2 + bn + c](https://tex.z-dn.net/?f=p_n%20%3D%20an%5E2%20%2B%20bn%20%2B%20c)
We're given the first four terms,
![\begin{cases}p_1=-4\\p_2=1\\p_3=12\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dp_1%3D-4%5C%5Cp_2%3D1%5C%5Cp_3%3D12%5Cend%7Bcases%7D)
Using the formula for the <em>n</em>-th term, this turns into a system of equations,
![\begin{cases}a+b+c=-4\\4a+2b+c=1\\9a+3b+c=12\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Da%2Bb%2Bc%3D-4%5C%5C4a%2B2b%2Bc%3D1%5C%5C9a%2B3b%2Bc%3D12%5Cend%7Bcases%7D)
Solve the system:
• Eliminate <em>c</em> :
(4<em>a</em> + 2<em>b</em> + <em>c</em>) - (<em>a</em> + <em>b</em> + <em>c</em>) = 1 - (-4) ===> 3<em>a</em> + <em>b</em> = 5
(9<em>a</em> + 3<em>b</em> + <em>c</em>) - (<em>a</em> + <em>b</em> + <em>c</em>) = 12 - (-4) ===> 8<em>a</em> + 2<em>b</em> = 16
• Multiply the second equation by 1/2 to get 4<em>a</em> + <em>b</em> = 8, then eliminate <em>b</em> and solve for <em>a</em> :
(4<em>a</em> + <em>b</em>) - (3<em>a</em> + <em>b</em>) = 8 - 5 ===> <em>a</em> = 3
• Solve for <em>b</em> and <em>c</em> :
3<em>a</em> + <em>b</em> = 9 + <em>b</em> = 5 ===> <em>b</em> = -4
<em>a</em> + <em>b</em> + <em>c</em> = 3 - 4 + <em>c</em> = -4 ===> <em>c</em> = -3
Then the rule for the <em>n</em>-th term is
![p_n = \boxed{3n^2 - 4n - 3}](https://tex.z-dn.net/?f=p_n%20%3D%20%5Cboxed%7B3n%5E2%20-%204n%20-%203%7D)
Answer:
Decimal form = 0.68199836