1) For each of these, keep in mind vertex form: f(x)=a(x-h)^2+k. With vertex form, a is the direction and width, h is the horizontal placement of the vertex, and k is the vertical placement. For the first one, notice that "a" is positive 1, so it faces up. This means that D, the one facing down, cannot be the answer. "h" is 1, so we will move the vertex to the right one unit (keep in mind (x-h), so if it were to be (h+3) you would move it to the left, not the right). "k" is -3, so we would move the vertex down 3 units. That said, the vertex should be at (1,-3) so the answer is C, or the one right below the first one.
2) The graph of f(x)=|2x| translated 5 units to the left means that h is equal to -5. When we plug -5 into vertex form, it should look like: g(x)=|2(x+5)|. The answer to this is A.
3) The equation for reflection on the x axis is f(x)=-a(x-h)+k. So, if the parent function f(x)=4|x| were to be reflected on the x axis, the function would look like this: g(x)=-4|x|. The answer to this should be B.
4) Since h=1 and k=0 in the function f(x)=-3|x-1|, the vertex will be (1,0).
5) This can also be written as g(x)=|x|-3. This means that k=-3, and will be a vertical translation of 3 units down.
Answer:
--
x = 2.3
Step-by-step explanation:
3 x + 5 = 17
- 5 = -5
------------------------
3x 7
----- = -----
3 3
-------------------------
---
x = 2. 3
Answer:
Im taking this right now so Im not 100% sure
Step-by-step explanation:
y-intercept: 2 because the slope is passing through 2.
slope: take points (-1,2) and (-1,3)
m=Y2-Y1/X2-X1
m=3-2/-1-1
m=-1/2 or 1/-2(there is no difference)
so the slope is -1/2
b=2
in slope intercept, its going to be:y=-1/2x+2
btw, i noticed that the point isn't -1 it's 0.75 i think. Substitute the -1 for -0.75(-3/4) and finish the math. Sorry.
Answer:
(a) dy/dt = 68 - 3.72t
(b) 64.28m/s
Step-by-step explanation:
Given y = 68t - 1.86t²
Average Speed is rate of chance of distance with respect to time. Written as dy/dt
To obtain dy/dt, we differentiate y with respect to t, doing that, we have
dy/dt = 68 - 2(1.86)t
= 68 - 3.72t
(a) dy/dt = 68 - 3.72t
(b) To estimate the speed when t = 1, we substitute t = 1 in dy/dt .
dy/dt at t = 1 is
68 - 3.72(1)
= 68 - 3.72
= 64.28
The speed at t = 1 is 64.28m/s
Answer:
Below in bold.
Step-by-step explanation:
The identity is of the form
(a + b)^2 = a^2 + 2ab + b^2.
a) Sqrt 49 = 7 and we need + 28 as the middle coefficient . We get this with
2*7 + 2*7 so the first coefficient is 2*2 = 4.
So * = 4a^2.
(2a + 7)^2 = (2a + 7)(2a + 7) = 4x^2 + 14a + 14a + 49.
b) -6 * -6 = 36 -24 = 2*-6 + 2 *-6 so the last term is 4x^2
c) The middle term must be an 'ab' term.
sqrt 6.25 = 2.5 and sqrt 1/4 = 1/2
So the coefficient of the middle term is 2.5 * 1/2 + 2.5 * 1/2
= 2.5
So the middle term is 2.5ab.
d) The first term will be in b^2.
100 = 10* 10 and we need 2 as a middle term so coefficient of the first term
will be 1/100 or 0.01. as the 2 comes from 0.1 * 10 + 0.01 * 10 and (0.1)^2 = 0.01
So it is 0.01b^2.
