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kari74 [83]
3 years ago
9

El costo total en pesos para producir calcomanías,es el monto del alquiler del local más 1.5 veces el número de calcomanías prod

ucidas por día
Mathematics
1 answer:
Nonamiya [84]3 years ago
5 0

Answer:

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The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.
Ratling [72]
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x

The equation to represent the perimeter of the triangle would be:
y = 3x - 6

The solutions to the system would be (12, 30) or (1, -3).  The only viable solution is (12, 30).

Explanation
The area of a triangle is found using the formula
A = 1/2bh

For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x

We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x

The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)

Combining like terms we get:
P = 3x - 6

We will replace P with y, so we have:
y = 3x - 6

Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:

3x - 6 = 1/2(x²) - (7/2)x

It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x

We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x

When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12

This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)

Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.

Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)

We cannot have a negative perimeter, so the only viable solution is (12, 30).
8 0
2 years ago
How do you figure perimeter
marta [7]

Answer:

You add up all the sides of the shape

8 0
3 years ago
Read 2 more answers
What is the simplified expression for:
kari74 [83]
81=3^4 
I hope this helps! Good luck!
5 0
3 years ago
Which fraction is equivalent to 50%? (in simplest fraction form) A) 1 2 B) 1 4 C) 2 5 D) 4 5
Tatiana [17]

Answer:

1/2 is equivalent to 50%

Step-by-step explanation:

In order to convert a fraction to a percentage you divide the numerator (Top number of a fraction) by the denominator (Bottom number of a fraction), multiply by 100, and add a percentage sign.

So lets try that with our first answer option A) 1/2:

1 divided by 2 = 0.5

0.5 x 100 = 50

50%

So we know that 1/2 is equivalent to 50%

8 0
2 years ago
Multiply: 68.1 x 0.8 ___________________ explain it plz
MArishka [77]

Answer:

54.48

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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