PLEASE HELP ASAP

Mathematics

1 answer:

Ganezh [65]3 years ago

4 0

The answer is (C). We want to use reasoning to show that AD is perpendicular to BC, so we have to use something else in the “if” part of the “if-then” statementto say that the statement is true. You can’t use what you want to prove as your reasoning, which is what it is using for (D). So, the answer is (C).

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F(x) = -4x(2)+ 12x – 9

kenny6666 [7]

For this case we have the following function:

$f (x) = - 4x ^ 2 + 12x-9$

$y = 0$ we have:

$-4x ^ 2 + 12x-9 = 0$

Where:

$a = -4\\b = 12\\c = -9$

By definition, the discriminant of a quadratic equation is given by:

$d = b ^ 2-4 (a) (c)$

$d> 0:$ Two different real roots

$d = 0:$ Two equal real roots

$d$ : Two different complex roots

Substituting the values we have:

$d = (12) ^ 2-4 (-4) (- 9)\\d = 144-144$

$d = 0$

We have two equal real roots.

To find the intersections with the x axis, we do $y = 0:$

$-4x ^ 2 + 12x-9 = 0$

We apply the quadratic formula:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

Substituting the values we have:

$x = \frac {-12 \pm \sqrt {12 ^ 2-4 (-4) (- 9)}} {2 (-4)}\\x = \frac {-12 \pm \sqrt {144-144}} {- 8}\\x = \frac {-12 \pm0} {- 8}\\x = \frac {-12} {- 8}\\x = \frac {3} {2}$