<h3>
Answer:</h3>
f(x) = -(x -2)² +3
<h3>
Step-by-step explanation:</h3>
We can fill in the vertex (h, k) values immediately in the vertex form ...
... f(x) = a(x -h)² +k
To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:
... -1 = a(0 -2)² +3
... -4 = 4a . . . . . . . . . subtract 3, simplify
... -1 = a . . . . . . . . . . . divide by 4
Now, we know the function is ...
... f(x) = -(x -2)² +3
Answer:
8 days
Step-by-step explanation:
On day 8, Isabella will save 256 nickels, bringing her total to 510.
_____
The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.
_____
The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.
__
The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...
an = a1·r^(n-1) = 2·2^(n-1) = 2^n
The sum of n terms of the sequence is ...
S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)
S = 2^(n+1) -2
__
We want S > 500, so ...
500 < 2^(n+1) -2
502 < 2^(n+1)
251 < 2^n
log(251) < n·log(2)
n > log(251)/log(2)
n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels
The answer would be <span>6.5.12
A triangle couldn't be made if the total sum of the two shortest side is less than the longest side. In this case, the two shortest side would be 5 and 6. The longest side would be 12.
If you try to add the two lowest side, the result would be 5+6=11. That means even if you make the triangle with 179.99 degrees that the 5 and 6 look like a straight line, the longest side it can achieve is 11.</span>
If you are multiplying by 100, the decimal will move 2 places to the right.
It moves to the right when multiplying because the number is getting greater, and there are 2 zeroes in 100 so it moves twice.
<span> The coordinates of point P on a coordinate grid are (−5, −6). Point P is reflected across the y-axis to obtain point Q and across the x-axis to obtain point R. What are the coordinates of points Q and R? Q(5, 6) and R(−5, −6) Q(−5, −6) and R(5, 6) Q(−5, 6) and R(5, −6) Q(5, −6) and R(−5, 6). </span><span>
</span>
