Find the measures of the acute angles of the right triangle shown
1 answer:
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<h2>Steps</h2>
- Standard Form Equation: f(x) = ax² + bx + c
So firstly, since (0,5) is one of our values we can plug it into the standard form equation to solve for the c variable (since 0 will cancel out the a and b variable):
Now we know that the value of c is 5. Next, plug in (-1,12) into the standard form equation and simplify (remember to also plug in 5 for the c variable):
Next, plug (2,15) into the standard form equation and simplify:
Now, with our last two simplified equations we will create a system of equations:
Now, I will be using the elimination method with this system. With the system, add up the equations together and you will get:
From here, we can solve for the a variable. With it, just divide both sides by 3:
Now that we know the value of a, plug it into either equation to solve for the b variable:
Putting all of our obtained values together, your final answer is:
Answer:
= 2n - 3
Step-by-step explanation:
Note the difference in consecutive terms is constant, that is
1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2
This indicates that the terms are an arithmetic sequence with
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 1 and d = 2, thus
= - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3