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Charra [1.4K]
3 years ago
7

Determine whether the following scenario represents a direct variation and describe why or why not: It takes 4 painters 8 hours

to paint a house and 12 painters 6 hours to paint the same house.
Mathematics
1 answer:
marysya [2.9K]3 years ago
4 0

Answer:

No

Step-by-step explanation:

It would take 1 painter 32 hours to paint a house (because 4*8=32). If we divide 32 by 12 we get 3, so no, it is not a direct variation because if it was it would only take 3 hours for the 12 painters to paint the house.

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In parallelogram ABCD, AD = 12 in, m∠C = 46º, m∠DBA = 72º. Find the area of ABCD
dmitriy555 [2]

Answer:

The area of   parallelogram ABCD  is78.42 \mathrm{in}^{2}

Explanation:

Given:

AD = 12 in

m \angle C=46^{\circ}

m \angle D B A=72^{\circ}

To Find:

The area of   parallelogram ABCD=?  

Solution:

When we construct the parallelogram with the given data, we get a parallelogram formed by 12 cm as one side and an angle with 46 degrees.  

The area of the parallelogram can be calculated by a b * \sin (a n g l e)

Substituting the value of a=12  we have

\text { Area of parallelogram }=12 * \text { bsin } 46

<u>To find  the value of b, </u>

We know that area of a triangle can be expressed as,

\text { Area of triangle }=(A b / 2) \sin (\text {angle})

So,

(12 * B D / 2) * \sin 46=(A B * B D / 2) * \sin 72

Cancelling BD and 2 on both sides we get,  

12 * \sin 46=A B * \sin 72

A B=12 * \frac{\sin 46}{\sin 72}

Therefore,

b=\frac{12 \sin 46}{\sin 72}

Substituting the value of b,

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Given

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So,

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Given

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Hence,

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Keywords: Speed, unit rate

Learn more about speed at:

  • brainly.com/question/9801816
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