For this case we have that by definition, the discriminant of a quadratic expression is given by:
If the discriminant is less than zero then the expression has two different complex roots.
In this case we have the following expression:
So we have to:
The discriminant is given by:
Then, if we want two complex roots it must be fulfilled that:
Thus, the expression has two complex roots for all values greater than 4.
ANswer:
Answer:
(I assume you have to do this on some kind of online graphing program.)
Step-by-step explanation:
Plot a point at (0, -3) because that is the y-intercept. Plot the second point at (3, 1). Once you hit “done” your graph should look similar to the one I attached a picture of. *rotatre the picture so the grey is on the bottom*
Answer:
Step-by-step explanation:
The cosine and tangent functions are useful here. The relevant relations are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
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The distance from Maria to Ava (ma) is the hypotenuse of the triangle, so we have ...
cos(40°) = 12/ma
ma = 12/cos(40°) ≈ 12/0.76604 ≈ 15.7 . . . feet
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The distance from Lucas to Maria (ml) is the side opposite the given angle, so we have ...
tan(40°) = ml/12
ml = 12·tan(40°) ≈ 12·0.83910 ≈ 10.1 . . . feet
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The angle formed at Maria's position is the complement of the other acute angle in the right triangle:
M = 90° -40° = 50°
In summary, ...
