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Studentka2010 [4]
3 years ago
8

Graph the solution to the following system of inequalities in the coordinate plane.

Mathematics
1 answer:
Goshia [24]3 years ago
4 0

Answer:

see below

Step-by-step explanation:

The first equation is in slope-intercept form, so you can see that the boundary line has a slope of -2 and goes through the point (x, y) = (0, -4). Since the comparison is "<", the line is dashed and shading is below it.

The second equation is that of a vertical boundary line at x=-3. It is solid, because the comparison includes the "equal" case. Shading is to the right of it, where x values are greater than -3.

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A function f is​ _____ on an open interval I​ if, for any choice of x1 and x2 in​ I, with 1 less than
Zepler [3.9K]

Answer:

If f(x_1)\leq f(x_2) whenever x_1\leq x_2 f is <em>increasing</em> on I.

If f(x_1)\geq f(x_2) whenever x_1\leq x_2 f is <em>decreasing</em> on I.

Step-by-step explanation:

These are definitions for real-valued functions f:I→R. To help you remember the definitions, you can interpret them in the following way:

When you choose any two numbers x_1\leq x_2 on I and compare their image under f, the following can happen.

  • f(x_1)\leq f(x_2). Because x2 is bigger than x1, you can think of f also becoming bigger, that is, f is increasing. The bigger the number x2, the bigger f becomes.
  • f(x_1)\geq f(x_2). The bigger the number x2, the smaller f becomes so f is "going down", that is, f is decreasing.

Note that this must hold for ALL choices of x1, x2. There exist many functions that are neither increasing nor decreasing, but usually some definition applies for continuous functions on a small enough interval I.

3 0
2 years ago
Factor the trinomial by grouping.<br> 9x^3 - 3x^2 -30x
katen-ka-za [31]

Answer:

3x(3x+5)(x-2)

Step-by-step explanation:

9x^3-3x^2-30x= \\\\3x(3x^2-x-10)= \\\\3x(3x^2+5x-6x-10)= \\\\3x(x(3x+5)-2(3x+5))= \\\\3x(3x+5)(x-2)

Hope this helps!

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2 years ago
0401) Which unitrate is equivalent to 17 miles per gallon
Dimas [21]

51 is the answer

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6 0
2 years ago
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2 years ago
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What is the slope of a line that passes through the points (5,0) and (10,0)?
disa [49]

Answer:

0

Step-by-step explanation:

Use two-point form to find the slope.

m=y2-y1/x2-x1

m=0-0/10-5

m=0/5

4 0
3 years ago
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