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Free_Kalibri [48]
3 years ago
12

What expression is equivalent to 5(1/3x+7)-3(1/2x-4)

Mathematics
2 answers:
Anna11 [10]3 years ago
5 0

Step-by-step explanation:

5/3x +35-3/2x+12=0

5/3x -3/2x+35+12=0

1/6x+47=0

1/6x=-47

divide through by 6x

×=1/282

Leto [7]3 years ago
4 0
5 (1/3x + 7) - 3 (1/2x - 4)

1/3x = x/3

1/2x = x/2

5 (x/3 + 7) - 3 (x/2 - 4)

Expand with the multiplier 5

= 5x/3 + 35 - 3 (x/2 - 4)

Expand with the multiplier -3

= 5x/3 + 35 - 3x/2 + 12

Simplify the problem

= x/6 + 47

Therefore 5 (1/3x + 7) - 3 (1/2x - 4) is equivalent to x/6 + 47
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Answer:

  See attached for graphs

  g(x) -- domain: -∞ < x < ∞; range: 0 < y < ∞

  g^-1(x) -- domain: 0 < x < ∞; range: -∞ < y < ∞

Step-by-step explanation:

g(x) is an exponential decay function. Its base is 1/3, so each increase of 1 unit in x will multiply the y-value by a factor of 1/3. The graph will rapidly approach its horizontal asymptote of y=0 as x gets large. The y-intercept is (0, 1). Just as y gets smaller as x increases, so it gets larger as x decreases. Each decrease of x by 1 unit causes the y-value to be multiplied by 3.

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The graph of g^-1(x) is the graph of g(x) reflected across the line y=x. That is, each coordinate pair (x, y) on the graph of g(x) becomes a point (y, x) on the graph of the inverse function. In order to graph g^-1(x), you don't need to write down the function, you only need to know the relationship between the graphs.

Just as x- and y- are interchanged on the graph, so the domain, range, and intercepts are interchanged. g^-1(x) will have a vertical asymptote of x=0, and an x-intercept of (1, 0). The domain of g^-1(x) is the range of g(x): 0 < x < ∞; and the range of g^-1(x) is the domain of g(x): -∞ < y < ∞.

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The attached graph shows g(x) in red and g^-1(x) in blue. As you can see, we created the graph simply by interchanging x and y. The line y=x is shown for reference, so you can see that each curve is a reflection of the other across that line.

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<em>Additional comment</em>

The explicit expression for g^-1(x) can be found by solving for y:

  x = g(y)

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If you're familiar with the log function, you know it has an x-intercept of 1 and a vertical asymptote at x=0. The base of the log function is simply a vertical scale factor. The minus sign reflects it across the x-axis.

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Answer:

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