You have to write the equation for a line that crosses the point (-4, -7) and is perpendicular to the line

When you have to determine a line that is perpendicular to a known line, you have to keep in mind that the slope of the perpendicular line will be the negative inverse of the first one.
If for exampla you have two lines, the first one being:

And the second one, that is perpedicular to the one above:

The slope of the second one is the negative inverse of the first one:

The slope of the given line y=-7/4+4 is m=-7/4
So the slope of the perpendicular line has to ve the inverse negative of -7/4

Considering it has to pass through the point (-4,-7) and that we already determined its slope, you can unse the point slope formula to determine the equation of the perpendicular line:

replace with the coordinates of the point and the slope and calculate:

Subtract 7 to both sides of the equation to write it in slope-intercept form:

Now you can graph both lines
Answer:
answers
Step-by-step explanation:
A. Vertex at (−6, 1)
Translating a graph upwards just means adding or subtracting a value from the initial function.
So to push a graph up, you just add (+) the number of units onto the original function.
Answer:
3/16
Step-by-step explanation:
Let the size of the whole apple be T
Given that 3/4 of the apple is left, it means the size left
= 3T/4
Since Victor plans to eat 1/4 of the pie that was left, this amounts to
1/4 * 3T/4
= 3T/16
This means that Victor will eat 3/16 of the whole pie tomorrow
Take the homogeneous part and find the roots to the characteristic equation:

This means the characteristic solution is

.
Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form

. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.
With

and

, you're looking for a particular solution of the form

. The functions

satisfy


where

is the Wronskian determinant of the two characteristic solutions.

So you have




So you end up with a solution

but since

is already accounted for in the characteristic solution, the particular solution is then

so that the general solution is