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nadya68 [22]
3 years ago
15

A (n) ?graph consists of distinct, isolated points

Mathematics
1 answer:
Alex_Xolod [135]3 years ago
5 0

The answer is discrete graph

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What is 12^3-9x^2-4x+3 in factored form
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Answer:

(3x^2 + 1) (4x – 3)

Step-by-step explanation:

 12x³– 9x² + 4x – 3 in factored terms;

First, find the GCF of  12x³– 9x² + 4x – 3

3x²is a common factor in 12x³ and 9x²

we have 3x² (4x – 3) + 4x – 3

 Splitting the expression into 2 groups 3x² (4x – 3) + ( 4x – 3)

4x – 3 is a common factor in both groups

 Factoring 4x – 3, we have

3x² (4x – 3) + (4x – 3)

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Answer:

The equation of the line passes through (3, -2) and parallel to the given line:

  • y = 3x-11

The equation of the line passes through (3, -2) and perpendicular to the given line:

  • y=-\frac{1}{3}x-1

Step-by-step explanation:

Given the points on the graph line

(2, -1)

(1, -4)

Finding the slope between (2, -1) and (1, -4)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:-4\right)

m=\frac{-4-\left(-1\right)}{1-2}

m=3

Equation of the line passes through (3, -2) and parallel to the given line.

We know that parallel lines have the same slope.

so the equation of the line parallel to the given line = 3

Thus, using the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 3 and the point (3, -2)

y - (-2) = 3(x-3)

y+2 = 3x-9

y = 3x-9-2

y = 3x-11

Therefore, the equation of the line passes through (3, -2) and parallel to the given line:

y = 3x-11

The equation of the line passes through (3, -2) and perpendicular to the given line

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = 3

perpendicular slope = – 1/m = -1/3 = -1/3

Therefore, substituting the values of perpendicular slope = -1/3 and the point (3, -2) in the point-slope form of the line equation

y-\left(-2\right)=-\frac{1}{3}\left(x-3\right)

y+2=-\frac{1}{3}\left(x-3\right)

subtract 2 from both sides

y+2-2=-\frac{1}{3}\left(x-3\right)-2

y=-\frac{1}{3}x-1

Therefore, the equation of the line passes through (3, -2) and perpendicular to the given line:

y=-\frac{1}{3}x-1

Conclusion:

The equation of the line passes through (3, -2) and parallel to the given line:

  • y = 3x-11

The equation of the line passes through (3, -2) and perpendicular to the given line:

  • y=-\frac{1}{3}x-1

8 0
3 years ago
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