Problem
Solution
For this case we know that the vertex is given by (3,6) and the genera equation for a parabola is given by:
y= a(x-h)^2 +k
Where h = 3, k=6 and replacing we have:
y= a(x-3)^2 +6
And we can find the value of a with the point given x= 4, y=4
4= a(4-3)^2 +6
4= a +6
a= 4-6=-2
And the correct equation would be:
d. y= -2(x-3)^2 +6
Answer:
1.Crosses
2.Touches
Step-by-step explanation:
...
Answer: 10.2 mph
Step-by-step explanation:
total runtime of the bike trip: 4hrs, 42 mi total
12 hrs has her 122 mi from home
our rate can be found by taking the miles and dividing it by the hours:
122/12 = 10.2
Answer:
Infinitely many
Step-by-step explanation:
I did it on edge 2020
I am somehow confused with the given matrix. Because usually, when the system of equations is given as:
ax + by = c
dx + ey = f
the matrix would be written in this manner:
![\left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%26c%5C%5Cd%26e%26f%5Cend%7Barray%7D%5Cright%5D%20)
Let me just assume that the arrangement of the given corresponds to this system of equations:
4x + 8y = 0
2x + 5y = 6
So you write it as
![\left[\begin{array}{ccc}4&8&0\\2&5&6\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%268%260%5C%5C2%265%266%5Cend%7Barray%7D%5Cright%5D%20)
In order to solve this, the matrix should look like this where x and y are the answers
![\left[\begin{array}{ccc}1&0&x\\0&1&y\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26x%5C%5C0%261%26y%5Cend%7Barray%7D%5Cright%5D%20)
So, the first thing to do is apply this pattern: Row 2 = Row 1 - 2*Row 2. The result will be
![\left[\begin{array}{ccc}4&8&0\\0&-2&-12\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%268%260%5C%5C0%26-2%26-12%5Cend%7Barray%7D%5Cright%5D%20)
Next, Row 1 = (Row 1/4) + R2:
![\left[\begin{array}{ccc}1&0&-12\\0&-2&-12\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-12%5C%5C0%26-2%26-12%5Cend%7Barray%7D%5Cright%5D%20)
Lastly, Row 2 = Row 2 / -2:
![\left[\begin{array}{ccc}1&0&-12\\0&1&6\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-12%5C%5C0%261%266%5Cend%7Barray%7D%5Cright%5D%20)
Thus, the answer is x=-12 and y=6.
