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Musya8 [376]
3 years ago
7

What is the solution to the equation 1/2x+3 = 2/3+1?

Mathematics
1 answer:
Alex3 years ago
7 0

Answer:

x = -8/3

Step-by-step explanation:

1/2x+3 = 2/3+1

Combine like terms

1/2x+3 = 2/3 + 3/3

1/2x + 3 = 5/3

Subtract 3 from each side

1/2x + 3-3 = 5/3 - 3

1/2x = 5/3 - 9/3

1/2x = -4/3

Multiply each side by 2

1/2x *2 = -4/3*2

x = -8/3

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So hmm notice the graph below

based on where the focus point is at, and the directrix, then, the parabola is opening upwards, meaning the squared variable is the "x"

\bf \begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
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now, keep in mind, the vertex is at coordinates h,k
the vertex itself is half-way between the focus and directrix
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so, half-way will then be \bf \cfrac{17}{8}-\cfrac{15}{8}=\cfrac{2}{8}\iff \cfrac{1}{4}

well, so is 1/4 between the focus point and the directrix, half of that is 1/8
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what's the "p" distance? well, we just found it, is just 1/8

so, the x-coordinate is obviously -4, get the y-coordinate by 17/8 - 1/8   or 15/8 + 1/8

and plug your values (x-h)² = 4p(y-k)   and then solve for "y", that's the equation of the quadratic

4 0
3 years ago
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Step-by-step explanation:

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