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garri49 [273]
3 years ago
13

37+z≤54 37+z≤54 . Graph the solution.

Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer:

See attached picture.

Step-by-step explanation:

Solve the inequality:

37+z\leq 54\\z\leq 17

Graph the solution by placing a closed dot (or filled in dot) on 17 on the number line. This is closed or filled in since z is less than or equal to. Then for the less than part, shade to the left of 17.

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(3,-7) and (9,-5)<br> What is the equation
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5. Find the value(s) of x so that the line containing the points (2x + 3, x + 2) and (0, 2) is
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Answer:

  x = -2 or -9

Step-by-step explanation:

You want the values of x such that the line defined by the two points (2x+3, x+2) and (0, 2) is perpendicular to the line defined by the two points (x+2, -3-3x) and (8, -1).

<h3>Slope</h3>

The slope of a line is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

Using the formula, the slopes of the two lines are ...

  m1 = (2 -(x+2))/(0 -(2x+3)) = (-x)/(-2x-3) = x/(2x +3)

and

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<h3>Perpendicular lines</h3>

The slopes of perpendicular lines have product of -1:

  \dfrac{x}{2x+3}\cdot\dfrac{2+3x}{6-x}=-1\\\\x(3x+2)=(2x+3)(x-6)\qquad\text{multiply by $(2x+3)(6-x)$}\\\\3x^2+2x=2x^2-9x-18\qquad\text{eliminate parentheses}\\\\x^2+11x+18=0\qquad\text{put in standard form}\\\\(x+2)(x+9)=0\qquad\text{factor}

<h3>Solutions</h3>

The values of x that satisfy this equation are x = -2 and x = -9. The attached graphs show the lines for each of these cases.

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