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ziro4ka [17]
2 years ago
8

If angle 6 is 25 degrees how much is 7

Mathematics
1 answer:
Sindrei [870]2 years ago
5 0

Given:

Angle 6 = 25 degrees

To Find:

The value of Angle 7

Solution:

We know that,

the value of Angle 6 is equal to 25 Degrees

Since Angle 6 and Angle 7 together comprise of a Straight Line, this means that they are Supplementary Angles.

Therefore,

Angle 6 + Angle 7 = 180 degrees

This implies that,

25 degrees + Angle 7 = 180 degrees.     (since Angle 6 = 25 Degrees)  

Angle 7 = (180-25) degrees

Thus ,

Angle 7 = 155 degrees

Hence, Angle 7 is  155 degrees (Option 1)

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Parabolas. Please help me
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  1. x² = 16 y
  2. x = 0
  3. (x + 4)² = 2/3 (y - 2)
  4. Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>
  5. (y - 6)² = 4p (x - 3)

Step-by-step explanation:

1. First figure

We plot the parabola as given in the attached diagram.

As it is facing upwards, the equation goes as x² = 4py

where, p = 4 (refer the attached diagram)

x² = 4py

x² = 4 (4) y

∴, standard form of parabola is x² = 16 y

2. Second figure

(y + 3)² = 4 (x - 1)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

h = 1

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Directrix is x = (h - p)

So, x = 0

3. Third figure

3x² + 24x - 2y + 52 = 0

3x² + 24x = 2y - 52

3 (x² + 8x) = 2 (y - 26)

(x² + 8x) = 2 (y - 26) / 3

Adding 16 on both sides,

x² + 8x + 16 = 2 (y - 26) / 3 + 16

(x + 4)² = 2/3 y - 52/3 + 16

(x + 4)² = 2/3 y - 4/3

(x + 4)² = 2/3 (y - 2)

4. Fourth figure

(y + 1)² = 12 (x - 3)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

k = -1

h = 3

p = 3

Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>

5. Fifth figure

Focus = (2, 6)

Directrix is x = 4

Therefore, it follows the standard form

(y - k)² = 4p (x - h)

Directrix is given by x = h-p = 4

Focus is given by (h + p, k) = (2, 6)

Solving for (h - p) = 4, (h + p) = 2

2 - p - p = 4

-2p = 2

p = -1

Hence, h = 3

Therefore, the standard form can be written as

(y - 6)² = 4p (x - 3)

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