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Math Asked by a SnapAndSolve user · about 1 hour ago

2^x > 3x: Graph the solution on the number line. 2. 2^x = 3x: Solve the equation. 3. x^2 - 6x - 7 = 0:...

1. 2^x > 3x: Graph the solution on the number line.
2. 2^x = 3x: Solve the equation.
3. x^2 - 6x - 7 = 0: Solve by factoring.
4. (x^2 - 9)/(x - 3): Simplify the expression.
5. Graph the equation: y = 2.
6. Graph the equation: 3x + 2y = 12.

Answer

  1. The solution to 2^x > 3x is not straightforward to graph without numerical methods or graphing software. However, you can test values to approximate the solution. The graph will show where the curve of 2^x is above 3x.

  2. For 2^x = 3x, the solution can be found using numerical methods or graphing. The approximate solution is x ≈ 1.89.

  3. To solve x^2 - 6x - 7 = 0 by factoring, rewrite as (x - 7)(x + 1) = 0. The solutions are x = 7 and x = -1.

  4. To simplify (x^2 - 9)/(x - 3), factor the numerator: ((x - 3)(x + 3))/(x - 3). Cancel the (x - 3) terms, leaving x + 3, for x ≠ 3.

  5. The graph of y = 2 is a horizontal line crossing the y-axis at y = 2.

  6. For 3x + 2y = 12, rearrange to y = -3/2x + 6. The graph is a line with a y-intercept at (0, 6) and a slope of -3/2.

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