The value of b^2-4ac is known as the discriminant of a quadratic function, and can tell you how many roots exist of this function depending on what it is equal to.
Start by moving the -1 to the other side, as we need this function to equal zero.
2x^2 + 3x + 1 = 0
This is now the standard form ax^2 + bx + c = 0. Plug each value that corresponds into the discriminant equation.
b^2-4ac
(3)^2 - 4(2)(1)
9 - 8
1
The value of the discriminant is 1, meaning that two real roots exist for the function described.
Answer:
A. 
Step-by-step explanation:
I am joyous to assist you anytime.
Actually, when you know 2 sides and an included angle, you use the Law of Cosines. (and we don't know if theta is an included angle).
Solving for side c
c^2 = a^2 + b^2 -2ab * cos(C)
c^2 = 36 + 16 - 2*6*4 * cos(60)
c^2 = 52 -48*.5
c^2 = 28
c = 5.2915
Using the Law of Sines
side c / sin(C) = side b / sin (B)
5.2915 / sin(60) = 4 / sin (B)
sin(B) = sin(60) * 4 / 5.2915
sin(B) = 0.86603 * 4 / 5.2915
<span><span>sin(B) = 3.46412
</span>
/ 5.2915
</span>
<span><span><span>sin(B) = 0.6546571451
</span>
</span>
</span>
Angle B = 40.894 Degrees
sin (A) / side a = sin (B) / side b
sin (A) = 6 * sin (40.894) / 4
sin (A) = 6 * 0.65466 / 4
sin (A) = .98199
angle A = 79.109 Degrees
angle C = 60 Degrees
Answer:
<u>a = 13</u>
Step-by-step explanation:
We should know that: The sum of the interior angles of the triangle = 180°
Given the measure of the angles: (6a - 2) , (5a - 13) and (5a - 13)
So,
(6a - 2) + (5a - 13) + (5a - 13) = 180°
16 a - 28= 180 ⇒ Add 28 to both sides
16 a = 180 + 28 = 208 ⇒ Divide both sides by 16
a = 208/16 = 13
There are 4 quarts in a gallon. If you’re asking how many quarts are in the aquarium you’re answer is 80, but if you’re just asking how many quarts in a gallon it’s 4.
