Answer:
2 3/5
Step-by-step explanation:
6 = 30/5
3 2/5 = 17/5
30/5 - 17/5 = 13/5
13/5 = 2 3/5
I got D because the correct equation is supposed to be y=mx+b n 50 is the slope (m) so it should be D
Answer:
Presumably this is a multiple choice question, and without seeing the potential answers, we can't tell you which ones are correct.
A few things can however be said about this function:
1) It describes a parabola that extends upward infinitely. We can see this because it's in the classic format ax² + bx + c, and all terms are positive.
2) We can find the x-intercepts by solving for zero. In this case we can do that by factoring it:
x² + 9x + 18 = 0
x² + 3x + 6x + 18 = 0
x(x + 3) + 6(x + 3) = 0
(x + 6)(x + 3) = 0
So the x intercepts occur at (-6, 0) and (-3, 0)
3) we can find its vertex by taking its derivative and solving for zero:
f'(x) = 2x + 9
0 = 2x + 9
x = -4.5
We can then plug that coordinate into the original function to find the y coordinate:
f(x) = x² + 9x + 18
f(-4.5) = 20.25 - 40.5 + 18
= -2.25
So the vertex is at (-4.5, -2.25)
4) As mentioned, the derivative of f(x) is f'(x) = 2x + 9. The integral is:
x³ / 3 + 9x² / 2 + 18x + C
Answer:
A function can be reflected about an axis by multiplying by negative one. To reflect about the y-axis, multiply every x by -1 to get -x. To reflect about the x-axis, multiply f(x) by -1 to get -f(x).
Step-by-step explanation:
First of all let's rearrange the equation for the given line:
4x + 7y + 3 = 0
7y = -4x - 3
y = (-4/7)x - 3/7
Now we know that the gradient of the line is -4/7
The gradients of two perpendicular lines multiply by each other to give -1, ie.
(-4/7)*m = -1
m = -1/(-4/7)
= 7/4, therefor the gradient of the perpendicular line is 7/4
Now we can substitute this and the point (-2, 1) into the equation y - y1 = m(x - x1)
y - 1 = 7/4(x - (-2))
y = 7/4x + 7/2 + 1
y = 7/4x + 9/2
If we look at the given answers then C is correct, since 9/2 = 18/4 and so the equation may also be written as y = 7/4x + 18/4
