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snow_tiger [21]
3 years ago
12

I need help on this, picture is attached below

Mathematics
1 answer:
Paladinen [302]3 years ago
4 0
<h3>Answer:  37 degrees</h3>

=====================================

Explanation:

Refer to the diagram below. I've marked angles FBD and ECG in red. We can see that they are alternate exterior angles because they are

Outside (aka exterior) of the parallel lines

On alternating sides of the transversal cut

Because JD is parallel to EK, this means the alternate exterior angles are congruent. Therefore, angle ECG is also 37 degrees.

Ignore angle ABG and ignore line AH. In my opinion, this is filler added as a distraction.

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<u>Discriminant</u>

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\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}

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Answer:

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3 {x}^{2}  - 4x =  - 2 \\ 3 {x}^{2}  - 4x + 2 = 0 \\ equating \: it \: with  \\ a {x}^{2}  + bx + c = 0 \\ a = 3 \:  \: b =  - 4 \:  \: c = 2 \\  {b}^{2}  - 4ac \\  =  {( - 4)}^{2}  - 4 \times 3 \times 2 \\  = 16 - 24 \\  =  - 8  \\  \ {b}^{2}  - 4ac < 0  \\  \therefore \: given \: quadratic \: equation \: have \:  \\ imaginary \: solutios. \\  \\ x =  \frac{ - b \pm \sqrt{{b}^{2}  - 4ac } }{2a}  \\ =  \frac{ - ( - 4) \pm \sqrt{ - 8} }{2 \times 3} \\ =  \frac{ 4 \pm 2\sqrt{2} \: i }{2 \times 3}  \\  =  \frac{ 2 \pm \sqrt{2} \: i }{3} \\  \therefore \: x  = \frac{ 2   - \sqrt{2} \: i }{3}  \: or \: x  = \frac{ 2   +  \sqrt{2} \: i }{3} \:  \\  \\ x =   \bigg \{\frac{ 2   - \sqrt{2} \: i }{3}, \:  \: \frac{ 2    +  \sqrt{2} \: i }{3} \bigg \}

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