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Dahasolnce [82]
2 years ago
14

hey, can someone please double check these questions for me / or help me solve them if they are incorrect? thank you U-U ​

Mathematics
1 answer:
zzz [600]2 years ago
8 0

Question 11

The directrix is a horizontal line, which means the parabola opens either upward or downward. In this case, it opens downward. This is because all answer choices have a negative leading coefficient. Also, it's because the focus is below the directrix.

For vertically opening parabolas, we use this form

4p(y-k) = (x-h)^2

where (h,k) is the vertex and p is the focal distance, aka the distance from the vertex the focus. To find (h,k), we start at the focus (0,-4) and move directly up until we reach the directrix y = 4. We'll arrive at (0,4). The midpoint of (0,-4) and (0,4) is (0,0) which is the vertex's location. So (h,k) = (0,0).

Note that in moving from (0,-4) to (0,4) is a span of 4 units. So this is the value of p.

Plug h = 0, k = 0, p = 4 into the equation mentioned and solve for y

4p(y-k) = (x-h)^2

4*4(y-0) = (x-0)^2

16y = x^2

y = (1/16)x^2

The only adjustment we need to make is to change the 1/16 to -1/16 so that the parabola opens downward.

<h3>Answer:  Choice D.  y = -(1/16)x^2</h3>

===============================================

Question 3

The given equation is in the form y = ax^2+bx+c

In this case,

  • a = 2
  • b = 4
  • c = 3

Let's compute the x coordinate of the vertex h

h = -b/(2a)

h = -4/(2*2)

h = -1

This h value is plugged into the original function to find k

f(x) = 2x^2+4x+3

f(-1) = 2(-1)^2+4(-1)+3

f(-1) = 1

We find that h = -1 and k = 1 pair up together. In short, (h,k) = (-1,1) is the vertex.

<h3>Answer: Choice B.  (-1,1)</h3>
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Answer: Downhill:10mph   Uphill:5mph

Step-by-step explanation:  

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Let  

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We divide the distance by the rate in each row and place the expression in the time column.

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20

r−5

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20

r

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40r−100

0

0

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=

=

=

=

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6

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6

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5

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The solution  

5

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3

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5 mph⋅

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Uphill:

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10−5 mph

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The total time traveled was  

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Dennis’ downhill speed was  

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So the train is pulling about 50 cars in total, and there's about 30 boxes of freight in each car.


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The best estimate would be near 1500 boxes of freight through the whole train.

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y=2.62x+b

Step 2: Find the b value (y intercept) - this is where the line goes through the y axis. In this case, it's 15.7

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kkurt [141]

Eleven times a number X, minus a second number Y

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