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STALIN [3.7K]
3 years ago
12

The perimeter of an airplane ticket is 30 centimeters. The area is 50 square centimeters. What are the dimensions of the ticket?

Mathematics
1 answer:
marishachu [46]3 years ago
8 0

Answer:

The length can be 5 and the width 10.

Step-by-step explanation:

perimeter is equal to 2L + 2W

area is equal to L * W

you get 2 equations:

30 = 2L + 2W

50 = L*W

we'll solve by substitution.

you can use either equation to solve for either variable.

we'll use the second equation to solve for L.

second equation is:

50 = L*W

divide both sides of this equation by W to get:

L = 50/W

we now have a value of L that we can substitute in the first equation which we can then use to solve for W.

the first equation is:

30 = 2L + 2W

replace L with 50/W to get:

30 = 2*(50/W) + 2W

simplify to get:

30 = 100/W + 2W

multiply both sides of this equation by W to get:

30W = 100 + 2W^2

subtract 30W from both sides of this equation to get:

2W^2 - 30W + 100 = 0

factor this equation to get:

(2W - 20) * (W - 5) = 0

solve for W to get:

W = 10 or W = 5

if W = 10, then use the equation of 50 = L*W to get L = 5

if W = 5, then use the equation of 50 = L*W to get L = 10

you have 2 possible solutions.

L = 5 and W = 10 or:

L = 10 and W = 5

both are plausible so we'll test them both out.

when L = 5 and W = 10:

the first equation becomes 2*5 + 2*10 = 10 + 20 = 30

the second equation becomes 5*10 = 50

both equations confirm that the solution of L = 5 and W = 10 is good.

when L = 10 andW = 5:

the first equation becomes 2*10 + 2*5 = 20 + 10 = 30

the second equation becomes 10*5 = 5

both equations confirm that the solution of L = 10 and W = 5 is good.

the ticket can have either:

a length of 5 and a width of 10 or:

a length of 10 and a width of 5.

since the length is usually longer than the width, you are free to choose that the ticket most likely has a length of 10 and a width of 5.

alternatively, you can simply say that the dimensions are 5 by 10 and let the recipient of that information determine which is the length and which is the width.

mathematically, the length can be 10 and the width 5 or the length can be 5 and the width 10.

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Dmitry [639]
X = 89

41 + 50 = 91 which is 89 away from 180
5 0
3 years ago
K= 35.50x + 42<br> k=991x + 27
SSSSS [86.1K]

Answer:

k=42.5573 and x=0.015699

Step-by-step explanation:

Step: Solve k=35.5x+42for k:

k=35.5x+42

Step: Substitute 35.5x+42 for k in k=991x+27:

k=991x+27

35.5x+42=991x+27

35.5x+42+−991x=991x+27+−991x(Add -991x to both sides)

−955.5x+42=27

−955.5x+42+−42=27+−42(Add -42 to both sides)

−955.5x=−15

−955.5x

−955.5

=

−15

−955.5

(Divide both sides by -955.5)

x=0.015699

Step: Substitute0.015699 for x in k=35.5x+42:

k=35.5x+42

k=(35.5)(0.015699)+42

k=42.5573(Simplify both sides of the equation)

Hope this helps!

:)

6 0
2 years ago
15 points. Please answer as soon as possible.
abruzzese [7]

Answer:

A. \frac{(a-b)^{2} +b^{2} }{a^{2}}

Step-by-step explanation:

So to get the area of a square, we need to find the length of one side.  

We know the length of the larger square is a, so the area of the larger cube is a^{2}

We can find the length of a side of the smaller square by using pythagoreans theorem to find the hypotenuse of the triangle formed in the bottom left corner.  The length of one side along the x axis is a - b, and the length of the other side, along the y-axis, is b.

We can plug it into pythagoreans theorem to get

(a-b)^{2} +b^{2} = C^{2} (C represents the length of one side of the smaller square, and the hypotenuse of the triangle)

C = \sqrt{ (a-b)^{2} +b^{2}}

The area of the smaller triangle is C squared to the area of the smaller triangle is

(a-b)^{2} +b^{2}

To get the ratio of the smaller square in comparison to the larger square we divide the area of the smaller square by the area of the larger square.

So the ratio should be

\frac{(a-b)^{2} +b^{2} }{a^{2}}

8 0
3 years ago
An artist used 6 tubes of red paint, 2 tubes of yellow paint, 13 tubes of white paint, and 9 tubes of blue paint for a mural. Wh
dmitriy555 [2]
Since there are 6 tubes of red paint and 13 tubes of red paint the ratio of red to white would be 6:13
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Simplify 3xy+5yz-2xy +3yz
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Answer:

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