Answer:
see the attachment
Step-by-step explanation:
1. Two angles that sum to 90° are <em>complementary</em>, whether they are adjacent or not. Angles LMN and NMP are also <em>adjacent</em>.
2. Vertical angles created by two distinct lines are <em>never adjacent</em>. The sides of the angles are created by the same lines, and the angles share a vertex, but there is no ray that is a side common to both angles.
3. Angle GMK is supplementary to angle JMG.
4. Vertical angles are congruent. See question 2.
5. See question 1.
Answer:
The correct choice is (0,-3)
Step-by-step explanation:
To convert from polar coordinates to rectangular coordinates, we use the parametric equations:
and 
The point given to us in polar coordinates is 
.
where 
and 
and 
and 
The correct choice is (0,-3)
The initial fee of $50 is essentially the y intercept because this is the value when x = 0 (x is the number of labor-hours). So b = 50.
The slope is m = 30 because each increase of 1 hour leads to the cost bumping up by 30 dollars. In other words, slope = rise/run = (change in cost)/(change in hours) = 30/1
So we plug m = 30 and b = 50 into the y = mx+b formula to get y = 30x+50
Replace y with f(x) to get f(x) = 30x+50
The linear function for the cost is f(x) = 30x+50
Note: Some books may use other letters (instead of x and f(x)), but the idea is still the same
Once you know the cost function, you replace x with 4.5 to find the amount it will cost to have a painter work for 4.5 hours.
f(x) = 30x+50
f(4.5) = 30*4.5+50
f(4.5) = 135+50
f(4.5) = 185
It will cost 185 dollars to have the painter work for 4.5 hours
Answer:
see below
Step-by-step explanation:
1.
a)
the relation is
b)
we can use it because for every value of x there is just one value, as the definition of function states
c)
and
2.
the points are
(-2,2) with
(1,-3) with
so the change in y is 
and the change in x is 
so the slope is
and the general formula is
so with a=-5/3
we plug in point 1
so the formula is
expressed as a function is
3.
this is bassically all the work of number 2, so we have
(-2,-5)
(4,31)
so the slope will be
the change in y
the change in x
so the slope will be
(the triangle means change)
so the formula we have
we plug some point, let's say 1
so the formula is
as a function is
so there you have it
Just as a note, for the next one, put more points :)
