Line t passes through (4, 5) and is perpendicular to the line shown on the coordinate grid.

a coordinate plane with a line passing through two points at 0 comma 3 and 5 comma 2

what is the equation of line t in standard form?

5x − y = 15
−5x − y = 15
x − 5y = −75
x + 5y = 75

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

To find the slope of the plotted line, we need two points, according to the image we have:

The slope is:

Therefore, the equation is of the form:

We substitute one of the points and find "b":

Finally, the equation of the graph is:

By definition, if two lines are perpendicular then the product of their slopes is -1. Thus, the slope of a perpendicular line will be:

Thus, the equation of the line t is of the form:

y = 5x + b

We substitute the point and find "b":

Finally, the equation is of the form:

Option A

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204