Answer:
Smallest of the three = 40
Step-by-step explanation:
Consecutive means: x+x+1+x+2 = 123 set X as the smallest number.
x+x+x+1+2=123
3x+3=123
3x= 120
x=40
Answer:

Step-by-step explanation:
The distance between the focus and the directrix is the vertical distance from the point to the line:
1 -(-3) = 4
The vertex is half that distance between the point and the line, so is at x=2 and ...
y = (-3 +1)/2 = -1
The vertical scale factor of the quadratic is 1/(4p) where p is the distance from vertex to focus. Here, that distance is 2, so the equation in vertex form is ...
y = (1/(4·2))(x -2)² -1
y = (1/8)(x -2)² -1
_____
<em>Check</em>
Any point on the parabola is equidistant from the focus and directrix. This is easily checked at the vertex, which is halfway between focus and directrix, and at the points having the same y-value as the focus. Those two points are (-2, 1) and (6, 1), both of which are 4 units from the focus and 4 units from the directrix.
Answer:
6i
Step-by-step explanation:
Answer:
(D) 
Step-by-step explanation:
One could run this on a computer and verify the best fit through brute force. The more elegant way is, as usual, to think: What are special values of x for an exponential function? Zero, for starters - anything to the power of zero is 1. The function value for x=0 in the table is 10. Which choices A through D are close to 10 for x=0? Well, (C) and (D), the rest is too far. Next, what is the function value for the next easy one, x=1? The table says 30. Which of (C) and (D) is close to 30 for x = 1. It turns out we can safely exclude (C) because 10.84*1.77 is about 19 and that's way too far from 30. Let's check (D): 8.46*3.51=29.7 - that's quite close. Since there is no other candidate left, I bet my money on (D). Feel free to verify closeness for the other values of x if you are unconvinced yet.
Hello,
2x+y=1
3x-y=-6
==>5x=-5
==>x=-1 and y=1-2*(-1)=3
Sol={(-1,3)}
Answer A