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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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yawa3891 [41]

Answer:

The value of a₁₀ is -1352

Step-by-step explanation:

a₂ = -8

a₅ = -512

Now,

a₂ = -8 can be written as

a + d = -8 ...(1) and

a₅ = -512 can be written as

a + 4d = -512 ...(2)

Now, from equation (2) we get,

a + 4d = - 512

a + d + 3d = - 512

(-8) + 3d = - 512 (.°. <u>a + d = </u><u>-8</u><u>)</u>

3d = - 512 + 8

3d = - 504

d = - 504 ÷ 3

d = - 168

Now, for the value of a put the value of d = -168 in equation (1)

a + d = -8

a + (-168) = -8

a - 168 = -8

a = 168 - 8

a = 160

Now, For a₁₀

a₁₀ = a + 9d

a₁₀ = 160 + 9(-168)

a₁₀ = 160 - 1512

a₁₀ = -1352

Thus, The value of a₁₀ is -1352

<u>-TheUnknownScientist</u>

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Step-by-step explanation:

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Aljan and Bella are both driving from Cleveland to Chicago. Aljan leaves at
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Answer:

Bella will pass Ajjan after 4h and they will have travelled 260 miles.

Step-by-step explanation:

In order to calculate the number of hours, "x", that it'll take for Bella to pass Aljan, we need to find the value of "x" that makes both equations equal. Therefore,

60*x + 20 = 65*x\\65*x - 60*x = 20\\5*x = 20\\x = \frac{20}{5} = 4

In order to calculate the distance they traveled, we must use this value for "x" in any of the equations, as done below:

y = 65*4\\y = 260

Bella will pass Ajjan after 4h and they will have travelled 260 miles.

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