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ella [17]
3 years ago
8

Is 1/8-10(3/4-3/8x)+5/8x equivalent to -1/8(59-35x)

Mathematics
2 answers:
KatRina [158]3 years ago
5 0

Answer:

Yes. They're equivalent.

Step-by-step explanation:

1/8-10(3/4-3/8x)+5/8x

1/8-30/4+30/8x+5/8x

1/8-60/8+35/8x

-59/8+35/8x

factor out -1/8

-1/8(59-35x)

docker41 [41]3 years ago
4 0

Answer:

S 1/8 - 10 prentices 3/4 - 3/8 X parantheses plus 58X equivalent to negative 1/8 Brettices 59 - 35X print eighties? Explain your answer

Step-by-step explanation:

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36(x + 4) = 36

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x + 4 = 1

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m=\frac{y_2-y_1}{x_2-x_1}

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See the attached picture.

  • Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.

The resulting box has a volume

V(x)=x(8-x)(12-x)=x^3-20x^2+96x

because the volume of a box is the product of its width (12-x), length (8-x), and height (x).

  • find the zeroes

You know right away from the factored form of V(x) that the zeroes are x=0,8,12. (zero product property)

  • sketch the graph of the function

Easy to plot by hand. You know the zeroes, and you can check the sign of V(x) for any values of x between these zeros to get an idea of what the graph of V(x) looks like. See the second attached picture.

Here's what I mean by "check the sign" in case you don't follow. We know V(x)=0 when x=0 and x=8. So we pick some value of x between them, say x=1, and find that

V(1)=1(8-1)(12-1)=7\cdot11=77

which is positive, so V(x) will be positive for any other x between 0 and 8. Similarly we would find that V(x) for x between 8 and 12, and so on.

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It's impossible to answer this without knowing the volume of each marble...

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While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions

x\approx0.1284

x\approx7.6398

x\approx12.2318

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The box's dimensions are (x in) x (8-x in) x (12-x in).

If x\approx0.1284, then 8-x\approx7.8716 and 12-x\approx11.8716.

If x\approx7.6398, then 8-x\approx0.3602 and 12-x\approx4.3602.

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