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Tatiana [17]
3 years ago
9

Please select the best answer from the choices provided.

Mathematics
1 answer:
Basile [38]3 years ago
8 0

Answer: 34

Step-by-step explanation:

SOH-CAH-TOA

To find the angle, find the inverse cosine of the adjacent side over the hypotenuse. ArcCos(72/87)=34

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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
0.8 is 10 times as great as what decimal
Aleks04 [339]
0.08.
0.8/10 is 0.08
the answer is 0.08
3 0
3 years ago
ABC ~ DEF and the scale factor from ABC to DEF is 1/2, what are the lengths of DE
Likurg_2 [28]

Answer:

13

Step-by-step explanation:

ABC ~ DEF means that ABC and DEF are the same triangle either expanded or contracted.

In this case the scale factor is 1/2. That means DEF is half ABC.

Since AB = 26 then DE must be 26/2 = 13

6 0
3 years ago
Y = 2 - 6x<br>17 y - x=1 solve the system​
Bond [772]

Answer:

(33/103,8/103)

In point form it is (33/103,8/103)

In equation form it is x = 33/103, y = 8/103

Hope this helps!

Consider giving brainliest. I only have 4 brainliest left and then my rank will go up.

7 0
3 years ago
What is the value of x if 7-9x=10 plz help
NeX [460]
The value of x is 12
7 0
3 years ago
Read 2 more answers
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