Quadratic functions 30pt

y= -x -3

Step-by-step explanation:

A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).

Let's find the slope of the line segment.

\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2

Slope of line segment

= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)

= \frac{4 + 8}{5 + 7}=5+74+8

= \frac{12}{12}=1212

= 1

The product of the slopes of 2 perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

m(1)= -1

m= -1

y= -x +c

To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.

Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.

\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)

Midpoint of line segment

= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)

= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)

= (-1, -2)

y= -x +c

When x= -1, y= -2,

-2= -(-1) +c

-2= 1 +c

c= -2 -1

c= -3

Thus, the equation of the perpendicular bisector is y= -x -3.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950