Complete the square to rewrite the equation in the form (x−h)2=p.

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

4 0

Answer:

second option

Step-by-step explanation:

Given

x² - 6x - 33 = 0 ( add 33 to both sides )

x² - 6x = 33

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 33 + 9

(x - 3)² = 42 → second option

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Find the area of the shaded region. Round to the nearest tenth.

AURORKA [14]

Answer:

3.5 square cm

Step-by-step explanation:

$Area \: of \: both \: squares \\ = {2}^{2} + {3}^{2} \\ = 4 + 9 \\ = 13 \: {cm}^{2} \\ \\ Area \: of \: both \: right \: \triangle s \\ = \frac{1}{2} \times (2 + 3) \times 2 + \frac{1}{2} \times3 \times 3 \\ = 5 \times 1+ 1.5 \times 3 \\ = 5 + 4.5 \\ = 9.5 \: {cm}^{2} \\ \\ Area \: of \:shaded \: region \\ = Area \: of \: both \: squares\\ - Area \: of \: both \: right \: \triangle s \\ = 13 - 9.5 \\ \purple { \boxed{ \bold{Area \: of \:shaded \: region = 3.5 \: {cm}^{2} }}}$