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sergejj [24]
2 years ago
8

.The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 s

quare feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.
What is the constant of variation?



What is the equation representing the direct variation?
Mathematics
1 answer:
Citrus2011 [14]2 years ago
5 0

Answer:

The constant of variation is 1/9

The equation representing the direct variation is y/x= 1/9

Step-by-step explanation:

In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get

y/x = k

3 / 27 = k

(3/27) / (3/3) = 1/9* = k

Therefore, the constant of variation is 1/9

Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation

* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both

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Two ships leave a harbor together, traveling on courses that have an angle of 135°40' between them. If they each travel 402 mile
mario62 [17]

Answer:

Therefore they are 734.106 miles apart.

Step-by-step explanation:

Given that ,

Two ships have a harbor together. The angle between two ships  is  135°40'. Each of two ships travel 402 miles.

It forms a isosceles triangle whose two sides are 402 miles and one angle is 135°40'. Since it is isosceles triangle then other two angles of the triangle is equal.

Let ∠B= 135°40', and AB = 402 miles , BC =  402 miles

Then the distance between the ships = AC

We know

The sum of all angles = 180°

⇒∠A+∠B+∠C=180°

⇒∠A+135°40'+∠C=180°

⇒2∠A= 180°- 135°40'      [ since ∠A=∠C]

⇒2∠A=44°60'

⇒∠A= 22°30'

Again we know that,

\frac{AB}{sin\angle C}=\frac{BC}{sin \angle A}=\frac{AC}{sin \angle B}

Taking last two ratio,

\frac{BC}{sin \angle A}=\frac{AC}{sin \angle B}

Putting the value of BC , AC ,∠A,∠B

\frac{402}{sin 22^\circ30'}=\frac{AC}{sin 135^\circ40'}

\Rightarrow AC=\frac{402 \times sin135^\circ40'}{sin 22^\circ30'}

         ≈734.106 miles

Therefore they are 734.106 miles apart.

3 0
3 years ago
Hiro and his co-workers had lunch at a restaurant near their work. An 18% tip on their bill was $10.08. How much was the bill, n
Ghella [55]

Answer:

$8.27

Step-by-step explanation:

First we need to find the tip.  We know it was 18% of the total. So...

x (the variable we need to find)         18%

__                                                   =     ___

10.08 (the total bill including tip)        100%

cross multiply

100x = 181.44

--------------------   (divide by 100 to get x by itself)

100

x = 1.81 (The 18% tip that was given)

So now we know how much the tip was, we subtract it from the bill

10.08 - 1.81 = $8.27

5 0
3 years ago
Abdul is working on a project and has cut a number of wooden blocks of equal size that are represented by this right rectangular
Valentin [98]

The amount of fabric needed to cover 8 blocks is 192cm.

<h3>How much fabric is needed to cover 8 blocks?</h3>

In order to determine the amount of fabric needed, the total surface area of the rectangular prism has to be determined. The total surface area of the rectangular prism is the sum of the areas its faces.

Total surface area of a rectangular prism = 2 (lw + wh + lh)

where:

  • l = length
  • w = width
  • h = height

2 x [(4 x 1/2) + (1/2 x 2) + (4 x2)] = 24cm

Fabric needed fo 8 blocks = 24 x 8 = 192cm

To learn more about rectangular prisms, please check: brainly.com/question/8890358

3 0
2 years ago
Read 2 more answers
А<br> D<br> 11x+8<br> 950<br> B<br> с<br> Find the value of X
Ivenika [448]

Answer:

write your question properly...

4 0
2 years ago
NEED HELP ASAP. BEST ANSWER GETS BRAINLIEST.
Verizon [17]

Answer:

d = 12800/f

Step-by-step explanation:

variation of proportion is 256(50) = 12,800

d = 12800/f

7 0
3 years ago
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