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aivan3 [116]
4 years ago
8

One side of a rectangle is 3 inches shorter than the other side, and the perimeter is 54 inches. What are the dimensions

Mathematics
1 answer:
vodomira [7]4 years ago
8 0

Answer:

2(x-3)+2x=54

Step-by-step explanation:

Take the side length of the rectangle as x

For the perimeter we must have - as we also have 2 lots of a side that is 3 inches shorter than x.

2x + 2(x-3) = 54

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et f(x) = x + |2x − 3|. Find all solutions to the equation f(x) = 12. (Enter your answers as a comma-separated list. If an answe
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Answer:

1. {5,-9}

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Step-by-step explanation:

The equation f(x)=x+\lvert 2x-3 \rvert=12 can be solved as follows:

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Then, the solutions of the equation are x=5, x=-9.

Now, if g(x)=5x-3+\lvert x+4\rvert, we can solve the equation g(a)=4a+9 as follows:

5a-3+\lvert a+4 \rvert =4a+9

\lvert a+4\rvert =4a+9-5a+3

a+4 =-a+12\,\,\text{or}\,\,a+4=-(-a+12)

2a=8\,\,\text{or}\,\,4=12

So, the unique solution of this last equation is a=4

The last equation is h(x-1)=x-3, where h(x)=\lvert x \rvert -2x+5.. To solve this equation we can proceed as follows:

h(x-1)=x-3

\lvert x-1\rvert -2(x-1)+5=x-3

\lvert x-1 \rvert -2x+2+5=x-3

\lvert x-1\rvert =3x-10

x-1=3x-10\,\,\text{or}\,\,x-1=-(3x-10)

-2x=-9\,\,\text{or}\,\,4x=11

x=9/2\,\,\text{or}\,\,x=11/4

But, x=11/4 is not a solution of this equation. So the unique solution is x=9/2.

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