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elena-s [515]
3 years ago
12

Figure VWYX is a kite.

Mathematics
2 answers:
Pachacha [2.7K]3 years ago
7 0

Answer:

∠VXY = 74°

Step-by-step explanation:

The sum of the 4 interior angles of a kite = 360°

Sum the 4 angles and equate to 360

90 + 18x - 2 + 90 + 12x + 2 = 360 ← simplify left side

30x + 180 = 360 ( subtract 180 from both sides )

30x = 180 ( divide both sides by 30 )

x = 6

Hence

∠VXY = 12x + 2 = (12 × 6) + 2 = 72 + 2 = 74°

Sladkaya [172]3 years ago
4 0
Your answer is the second option, 74.
You can find this by knowing that a kite is a quadrilateral, and angles in a quadrilateral add up to 360 degrees. Then, because two of the angles in the kite are right angles, you can say that the two angles left over add to 180 (360 - (90 + 90)).
This gives you the equation:
(12x + 2) + (18x - 2) = 180
30x = 180
x = 6

Then you substitute 6 into (12x + 2) because this is the expression for angle VXY, and you get 12(6) + 2 = 72 + 2 = 74.

I hope this helps! Let me know if you have any questions :)
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Solve x 2 - 4x - 7 = 0 by completing the square. What are the solutions?
Bingel [31]

Answer:

x = 2±sqrt(11)

Step-by-step explanation:

x^2 -4x - 7 =0

Add 7 to each side

x^2 -4x -7+7 =0+7

x^2 -4x =7

To complete the square take the coefficient of the x term and  divide by 2 and then square it.  Add it to both sides

-4 /2 = -2 then square

(-2)^2 = 4

Add 4 to both sides

x^2 -4x+4 =7+4

x^2 -4x+4 = 11

Factor the left side into (x-b/2)^2

(x-2)^2 =11

Take the square root of each side

sqrt((x-2)^2) =±sqrt(11)

x-2 = ±sqrt(11)

Add to to each side

x-2+2 = 2±sqrt(11)

x = 2±sqrt(11)

3 0
3 years ago
A 748-N man stands in the middle of a frozen pond of radius 4.0 m. He is unable to get to the other side because of a lack of fr
Ber [7]

Answer:

The man will take 64 seconds to reach to the south shore of the frozen pond.

Step-by-step explanation:

Given:

Weight of the man = 748 N      Mass of the man,(m)= \frac{W}{g} = \frac{748}{9.8} = 76.32 kg

Radius of the pond (r) = 4 m

Mass of the textbook = 1.2 kg

Velocity at which the textbook is thrown = 4 ms^1

We have to find the velocity of the man after the throw.

Let the velocity is V_m .

Now using law of conservation of momentum we can find the V_m value.

m_(_b_)V_b_(_i_) +m_(_m_)V_m_(_i_) =m_(_b_)V_b_(_f_)+m_(_m_) V_m_(_f_)

Considering V_m_(_f_)=V_m

And initial velocity of both the man and book i.e V_b_(_i_)=0,\ V_m_(i_)=0

So,

⇒ 0 =m_(_b_)V_b_(_f_)+m_(_m_) V_m

⇒ Plugging the values.

⇒ V_m=-\frac{m_(_b_)V_b_(_f_)}{m_(_m_)}

⇒ V_m=-\frac{1.2\times 4}{76.32}

⇒ V_m=-0.062 ms^-1

Here the negative velocity is meant for opposite direction of the throw.

Numerically we will write, V_m = 0.062

With this velocity the man will move towards south.

We have to calculate the time taken by the man to move to its south shore.

And we know velocity(v)\times time(t) = distance(d)

Let the time taken be t and v\times t = d and d=r then, V_m\times t=r

Then

⇒ t=\frac{radius\ (r)}{V_m}

⇒ Plugging the values.

⇒ t=\frac{4}{0.062}

⇒ t =64 sec

The man will take 64 seconds to reach to the south shore of the frozen pond (circular).

5 0
3 years ago
If the circumference of a circle is tripled, what happens to its area?
avanturin [10]
If the circumference of a circle is tripled, the area increases hugely. Hope this helps!
6 0
3 years ago
The ages of George and Genemy are in ratio 5:7 . Four years from now the ratio of their ages will be 3:4 .Find their present age
DedPeter [7]

Answer:

Below in bold.

Step-by-step explanation:

Let x be George's age and y be Genemy's age.

x/y = 5/7

(x + 4)/ (y + 4) = 3/4

From equation 1, y = 7x/5 = 1.4x so substituting in equation 2 :

(x + 4)/ (1.4x + 4) = 3/4

3(1.4x + 4) = 4(x + 4)

4.2x + 12 = 4x + 16

0.2x = 16 -12 = 4

x = 4/0.2 = 20 = George's age.

So y = 1.4x = 1.4 * 20 = 28 = Genemy's age.

3 0
3 years ago
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Answer:

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Step-by-step explanation:

8 0
3 years ago
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