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pochemuha
3 years ago
14

Please help guys!!

Mathematics
1 answer:
NikAS [45]3 years ago
6 0

Answer:

and the question is? I'm confused

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Write the inverse function for the function, ƒ(x) = 1/2x + 4. Then, find the value of ƒ -1(4). Type your answers in the box
anastassius [24]
F(x) = (1/2)x + 4
Plug y in for f(x).
y = (1/2)x + 4
Swap x and y.
x = (1/2)y + 4
Solve the equation for y =.
Subtract 4 from both sides.
x - 4 = (1/2)y
Multiply each term 2.
2x - 8 = y
Plug f^-1(x) in for y.
f^-1(x) = 2x - 8

f^-1(4) = 2(4) - 8
f^-1(4) = 0
3 0
3 years ago
Use the given information to write the equation of the parabola.
m_a_m_a [10]

Answer:

x² = -2y

Step-by-step explanation:

The focus is p away from the vertex, and so is the directrix.

To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.

  • Horizontal parabola [Standard form]: (y – k)² = 4p(x – h)
  • Vertical parabola [Standard form]: (x – h)² = 4p(y – k)

If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).

Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).

For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).

You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).

If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.

Now we can just plug in our known information to derive the equation!

h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →

(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →

x² = -2y.

Also p = 1/4a, if you are wondering.

So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.

8 0
3 years ago
Read 2 more answers
How many different ways can the line be named? What are those names?
boyakko [2]

Answer: A. 3 ways: k, DE, ED (both DE and ED have line markers over top)

To name a line, we just need two points on the line. We list them in any order because the line extends forever in both directions. Contrast this with a ray where order does matter. The little k is another way to name a line, potentially simplifying things.

Choice B is close, but it mentions ray DE instead of line DE. Choice C is missing line ED. Choice D is a similar story as choice B. These facts allow us to rule out B through D.

5 0
3 years ago
Read 2 more answers
Compute the perimeter of the figure given below. All angles are right angles.
Mashcka [7]

Answer:44

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
The sum of two numbers is 18 and the difference is 8
Andrews [41]

Answer:

x = 13 and y = 5

Step-by-step explanation:

x + y = 18

x - y = 8

<u>Step 1:  Find y</u>

x = 18 - y

(18 - y) - y = 8

18 - y - y - 18 = 8 - 18

-2y / -2 = -10 / -2

<em>y = 5</em>

<em />

<u>Step 2:  Plug into x + y = 18 to get x</u>

x + 5 - 5 = 18 - 5

<em>x = 13</em>

<em />

Answer:  x = 13 and y = 5

3 0
3 years ago
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