Answer:
-2
Step-by-step explanation:
Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue. We have the work form of a positive upwards-opening parabola as

where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex. We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1). Now we will fill in the work form equation and solve for a:

which simplifies a bit to

and
-1 = a(1) - 3. Therefore, a = 2 and our parabola is

Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4. Do this by subbing in the values of x one at a time to find y. When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3). When x = -4, y = -1 so the coordinate of that point is (-4, -1). The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:

And there you have it! I'm very surprised that this question sat unanswered for so very long! I'm sorry I didn't see it earlier!
She earned $30 on commission and the total would be $110. Hope this helps
Answer:
106.81 mm
Step-by-step explanation:
C=2πr=2·π·17≈106.81415
Answer:
Step-by-step explanation:
We get possible sums from 1 + 1 = 2 to 6 + 6 = 12 when we toss two dices together. Total ways 6*6 = 36
a.
<u>Prime numbers:</u>
- 2, 3, 5, 7, 11 - total 5 outcomes with 15 ways (1+1, 1+2, 1+4, 1+6,2+1, 2+3, 2+5, 3+2, 3+4, 4+1, 4+3, 5+2, 5+6, 6+1, 6+5)
b.
<u>Perfect squares:</u>
- 4, 9 - total 2 outcomes with 3 ways for 4 (1 +3, 2+2, 3+1) and 4 ways for 9 (3+6, 4+5, 5+4,6+3)
- P(perfect square) = (3 + 4)/36 = 7/36
c.
<u>Perfect cube:</u>
- 8 - one outcome with 5 ways (2+6,3+5,4+4,5+3,6+2)
- P(perfect cube) = 5/36
Answer:
Approximately 12 pieces of yarn can be cut from the 96 inches roll of yarn
Step-by-step explanation:
Total length of the yarn = 96 inches
Length of each piece = 8 1/4 inches
Now, solving the mixed fraction
, we get
length of each piece =
=
inches
Now, the number of pieces = 
= 
⇒ number of pieces = 11.63
Hence approximately 12 pieces of yarn can be cut from the 96 inches roll of yarn.