Try this solution:
There are several ways to find the max or min of the given function:
1. to use derivative of the function. For more details see the attachment (3 basic steps); the coordinates of max-point are marked with green (-5; 14.5)
2. to use formulas. The given function is the standart function with common equation y=ax²+bx+c, it means the correspond formulas are (where a<0, the vertex of this function is its maximum):
Finally: point (-5;14.5) - maximum of the given function.
3. to draw a graph.
The answers are
a) the domain is all real numbers
d) the input to an exponential function is the exponent
e) the base represents the multiplicative rate of change
hope this helps :)
#1 second line: x-y=-3
x=y-3(isolating x to prepare for substitution)(what x is equivalent to)
get back to the first line
x+y=5
(y-3)+y=5(substituting the value of x of the first line with the value of x at the second line)(It is a process to find the intersection between the two lines(line#1 and line#2 are two linear functions)
2y-3=5(simplify)
2y=8(simplify)
y=4(simplify)
line#1 x+y=5
x+(4)=5(plug the value of y back into either line#1 or line#2 will work)(plugging in the y value of the point of intersection to solve for the x value of the point of intersection)
x=1(solve)
the two linear lines intersect at the point(1(x coordinate), 4(y coordinate))(1,4)
#2 (line#1) y=3x-1
(line#2) 2x+y=14
2x+(3x-1)=14
5x-1=14
5x=15
x=3
y=3(3)-1
y=9-1
y=8
(3,8)
#3 line#1 2x+3y=8
line#2 6x+9y=24
2x=8-3y
x=(8-3y)/2
6((8-3y)/2)+9y=24
24-9y+9y=24
24=24
(those two lines are on top of yeach other/the same line)
any point on the line
#4 line#1 3x-4y=12
line#2 y=3/4x-4
3x-4(3/4x-4)=12
3x-3x+16=12
16=12
parallel lines: lines with same slope and different y-intercept
No solution/they never intercept each other
I hope it is helpful, if you have any question, I will answer ASAP
The proportion that models the problem would be x/850 = 11/17. :)
