f(0) means the function output when the input is x = 0. This is the same as saying the y value when x = 0.
f(x) = 3-2x
f(0) = 3-2(0)
f(0) = 3
The point (0,3) is on the graph. This is the y intercept which is where the graph crosses the y axis. The y intercept always occurs when x = 0.
So in other words, the special name for f(0) is the y intercept.
A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.
Let's look at the four equations, with each solved as needed, into y = mx + b form.
A: 2x + y = 5
y = 5 - 2x
y = -2x + 5
Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.
B: y = 2x + 5
Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.
C: 2x - 4y = 10
-4y = 10 - 2x
-4y = -2x + 10
y = 2/4x -10/4
Here the slopes are different, so, like A this is not a good choice.
D: 2y - 4x = -10
2y = =10 + 4x
2y = 4x - 10
y = 2x - 5
Compared to y = 2x + 5 we have the same slopes and different y intercepts. The lines will be parallel and the system is inconsistent.
Thus, D is the best choice.
Answer:
$966
Step-by-step explanation:
6/7 = 828/x
Write a proportion.
6x = 7(828) Use cross products.
6x = 5796 Multiply.
x = 966 Divide both sides by 6.
Paul's investment was $966.
Answer:
d. (9, 0)
Step-by-step explanation:
(x, y) so...
Where the line crosses the x-plane, x = 9
Since this is the x-intercept y will always equal zero
Therfore x-int = (9, 0)
Suplementary is angles add up to 180 degrees
C=180-D
C=180-84
C=96 degrees
Hope this helped :)
