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Fudgin [204]
2 years ago
5

Which graph represents the system of inequalities? y+2<5x y+3x>4 y≥2x

Mathematics
1 answer:
Lostsunrise [7]2 years ago
4 0

Answer:

2nd graph above the one you chose

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What is the average rate of change from x = −3 to x = −4?
Vika [28.1K]

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

y=a(x-h)^2+k

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:

-1=a(-2-(-3))^2-3

which simplifies a bit to

-1=a(1)^2-3

and

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

y=2(x+3)^2-3

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:

m=\frac{-1-(-3)}{-4-(-3)} =\frac{2}{-1}=-2

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!

5 0
2 years ago
Renee is a sales associate at a store. She earns $80 a week plus a 15% commission on her sales. Last week, she sold $200 worth o
Y_Kistochka [10]
She earned $30 on commission and the total would be $110. Hope this helps
6 0
2 years ago
Read 2 more answers
At the bakery where Finn works, one of the cups in a cupcake tray has a diameter of 34 millimeters. What is the cup's circumfere
wlad13 [49]

Answer:

106.81 mm

Step-by-step explanation:

C=2πr=2·π·17≈106.81415

5 0
2 years ago
See image for question.
klio [65]

Answer:

  • See below

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)
  • P(prime number) = 15/36

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
8 0
3 years ago
How many 8 1/4 inch pieces of yarn can be cut from a roll that has 96 inches of yarn
Arada [10]

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 8\frac{1}{4} , we get

length of each piece =   8\frac{1}{4}  = \frac{(8)(4) + 1}{4}= \frac{33}{4} inches

Now, the number of pieces = \frac{\textrm{Total length of the Yarn}}{\textrm{Length of ecah piece}}

= \frac{96}{\frac{33}{4} }  = 96 \times \frac{4}{33}  = 11.63

⇒ number of pieces = 11.63

Hence approximately 12 pieces of yarn can be cut from the 96 inches roll of yarn.

3 0
2 years ago
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