Hello from MrBillDoesMath!
Answer:
31a. 2 real roots
31b 2 complex roots
Discussion:
31a.
2x^2 + 3x - 6 = 0
Using standard quadratic notation, the above equation has a = 2, b = 3 and c = -6. The discriminant is given by b^2 - 4ac, which is
3^2 - 4*2*(-6) = 9 + 48 = 57 > 0, so the quadratic has 2 real roots
31b.
The equation is equivalent to 16x^2 + 10x +3 = 0. Its discriminant is
10^2 - 4 * (16) * (3) = 100 - 192 = -92 so this equation has two complex roots
Regards,
MrB
Answer:
D
Step-by-step explanation:
Starts with 2
2 x 2 = 4
4 x 2 = 8
8 x 2 = 16
and so on
Answer:
35° and 55°
Step-by-step explanation:
The sum of the angles of a right rectagle is 180°, with a right angle of 90°.
The tell us that A = 2B-15, so:
180° = 90° + A + B
180° = 90° + 2B - 15 + B
180° - 90° + 15 = 2B + B
105° = 3B
B = 105°/3 = 35°
Now, let's find A:
A = 180° - 90° - 35° = 55°
Beginning with the function y = sin x, which would have range from -1 to 1 and period of 2pi:
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
Answer:
9
Step-by-step explanation:
4/6 = 1.5, 1.5(6)= 9
