All these equations are in the form of ax^2 + bx + c = 0, where a, b, and c are some numbers. the discriminants of equations like this are equal to b^2 - 4ac. if the discriminant is negative, there are two imaginary solutions. if the discriminant is positive, there are two real solutions. if the discriminant is 0, there is one real solution.
<span>x^2 + 4x + 5 = 0
</span>b^2 - 4ac
4^2 - 4(1)(5)
16-20
-4, two imaginary solutions.
<span>x^2 - 4x - 5 = 0
</span>b^2 - 4ac
(-4)^2 - 4(1)(-5)
16 + 20
36, two real solutions.
<span>4x^2 + 20x + 25 = 0
</span>b^2 - 4ac
20^2 - 4(4)(25)
400 - 400
0, one real solution.
8 pieces of fruit and 3 pears
means she bought 4 apples and 1 cantaluope
Step-by-step explanation:
It is given that,
The height of the sail on a boat is 7 feet less than 3 times the length of its base.
Let the length of the base is x.
ATQ,
Height = (3x-7)
Area of the sail is 68 square feet.
Formula for area is given by :
x = 8 feet and x = -3.73 feet
So, length is 8 feet
Height is 3(8)-7 = 17 feet.
So, its height and the length of the base is 17 feet and 8 feet respectively.
Distance between A and B
= Distance between C and D
= sqrt((4 - 1)^2 + (5 - 2)^2)
= sqrt(3^2 + 3^2)
= sqrt(2 * 3^2)
= sqrt(3^2) * sqrt(2)
= 3sqrt(2)
Distance between B and C
= Distance between A and D
= sqrt((4 - 3)^2 + (5 - 0)^2)
= sqrt(1^2 + 5^2)
= sqrt(26)
Since sqrt(26) is more than 3sqrt(2), the length must be sqrt(26).
Hope this helps you.
