Answer:
- 
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x - 2 ← is in slope- intercept form
with slope m = 5
Given a line with slope m then the slope of a line perpendicular to it is
= - 
= -
Answer: QE = 10
Step-by-step explanation: To solve this problem, it's important to understand that the diagonals of a parallelogram bisect each other.
This means that E is the midpoint of diagonal SQ.
So we can setup the equation x² + 9x = 4x + 6.
To solve this polynomial equation, set it equal to zero first.
So we have x² + 5x - 6 = 0 and we get (x + 6)(x - 1) = 0
when we factor the left side of the equation.
So this means that x = -6 or x = 1.
However, -6 will give us a negative length when we plug it in
to find QE so this will not work.
However, plugging 1 in will give us 10 as a length so QE = 10.
Let point C has coordinates 
Consider vectors
Since the ratio AB to BC is 1:4, you have that
Find 
and 
Answer: C(4,-6)
The equation is already is slope intercept form where you can easily point out the gradient, or the slope, and the y intercept.
y=mx+b where m is the gradient, and b is the y intercept.
Since there is no m, the gradient is 1.
The y intercept had x=0 and y=b
b in this case is 6
the y intercept= (0,6)
The number who drink coffee is 3/4 of 8000, so ...
... (3/4)×8000 = 6000.
Of those, 1/5 add cream, so the number of coffee drinkers who add cream to their coffee is ...
... (1/5)×6000 = 1200.
_____
Alternate solutions
We have computed ...
... (1/5)×((3/4)×8000) = 1200
Since multiplication is associative, you can multiply the fractions first, if you wish:
... ((1/5)×(3/4))×8000 = (3/20)×8000
... = 24000/20 = 1200
or
... = 3×(8000/20) = 3×400 = 1200
