3 years ago

True or False: b^2 - 4ac > 0 means the root is real.

Mathematics

1 answer:

slamgirl [31]3 years ago

8 0

It is true that b^2 - 4ac > 0 means the root is real.

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How do I solve this question?

asambeis [7]

This is a perfect square trnomial
(a+b)²=a²+2ab+b²
we see that a=5x and b=2

(5x)²+2(5x)(2)+2²=0
factor
(5x+2)²=0
set equal to zero
5x+2=0
5x=-2
x=-2/5

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Which best describes the graphs of the line that passes through (−12, 15) and (4, −5), and the line that passes through (−8, −9)

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Answer:

C) They are perpendicular lines.

Step-by-step explanation:

We first need to find the slope of the graph of the lines passing through these points using:

$m = \frac{y_2-y_1}{x_2-x_1}$

The slope of the line that passes through (−12, 15) and (4, −5) is

$m_{1} = \frac{ - 5 - 15}{4 - - 12}$

$m_{1} = \frac{ - 20}{16} = - \frac{5}{4}$

The slope of the line going through (−8, −9) and (16, 21) is

$m_{2} = \frac{21 - - 9}{16 - - 8}$

$m_{2} = \frac{21 + 9}{16 + 8}$

$m_{2} = \frac{30}{24} = \frac{5}{4}$

The product of the two slopes is

$m_{1} \times m_{2} = - \frac{4}{5} \times \frac{5}{4} = - 1$

Since

$m_{1} \times m_{2} = - 1$

the two lines are perpendicular.

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