If 3/x=5/y then what is the value of y/x? plss help

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

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Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

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Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

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Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

2 years ago

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A carpenter has 10 1/2 feet of wooden plank. He cuts off 4 1/4 feet to replace the slat of a deck and 3 2/3 to repair a Banniste

aalyn [17]

10 1/2-4 1/4= 6 1/4. 6 1/4-3 2/3= 2 7/12. They used 2 7/12 ft or 2ft 7in of wood to fix the stairs.

8 0

2 years ago

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Recipe ingredients remain in a constant ratio no matter how many servings are prepared. Which table shows a possible

Tpy6a [65]

Answer:

Table N 4

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

Verify the table 4

For x=1, y=2

so

y/x=2/1=2

For x=2, y=4

so

y/x=4/2=2

For x=3, y=6

so

y/x=6/3=2

therefore

The constant of proportionality k is equal to 2 and the equation is equal to

y=2x

The table 4 represent a direct variation, therefore is a possible ratio table for ingredients X and Y

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2 years ago

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Consider the graphs of f (x) = StartAbsoluteValue x EndAbsoluteValue + 1 and g (x) = StartFraction 1 Over x cubed EndFraction. T

Westkost [7]

Answer:

We have the functions:

f(x) = IxI + 1

g(x) = 1/x^3.

Now, we know that the composite functions do not permute.

How we can prove this?

First, two composite functions are commutative if:

f(g(x)) = g(f(x))

Well, you could use brute force (just replace the values and see if the composite functions are commutative or not)

But i will use a more elegant way.

We can notice two things:

g(x) has a discontinuity at x = 0.

so:

f(g(x)) = I 1/x^3 I + 1

still has a discontinuty at x = 0, but:

g(f(x)) = 1/( IxI + 1)^3

here the denominator is IxI + 1, is never equal to zero.

So now we do not have a discontinuity.

Then the composite functions can not be commutative.

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2 years ago

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Landon babysits and works part time at tge water park over the summer. onw week, he babysat for 3 hours and worked at the water

Tems11 [23]

B = hourly rate for babysitting and w = hourly rate for working at water park

3b + 10w = 109...multiply by -8
8b + 12w = 177...multiply by 3
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-24b - 80w = - 872 (result of multiplying by -8)
24b + 36w = 531 (result of multiplying by 3)
---------------------add
- 44w = - 341
w = -341/-44
w = 7.75 <=== hourly rate for working at water park

3b + 10w = 109
3b + 10(7.75) = 109
3b + 77.50 = 109
3b = 109 - 77.50
3b = 31.50
b = 31.50/3
b = 10.50 <== hourly rate for babysitting

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2 years ago

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