Answer: q = 40
Step-by-step explanation:
Given the quadratic formula as
x = [-b +/-√(b^2 -4ac)]/2a
b = -14
a = 1
c = q
Difference d between the two roots.
d = [-b + √(b^2 -4ac)]/2a - [-b -√(b^2 -4ac)]/2a
d = 2√(b^2 -4ac)/2a
d = √(b^2 -4ac)/a
And d = 6
Substituting the values of a,b and c. We have;
6 = √[(-14^2) - (4×1×q)]
Square both sides
6^2 = 196 - 4q
4q = 196 - 36
q = 160/4
q = 40
The equation becomes
x^2 - 14x + 40 = 0
Answer:
Let a be the width and b the length
a+3=b
a*b=54
a(a+3)=54
a^2+3a-54=0
a=6
Answer:
1350
units²
Step-by-step explanation:
The regular hexagon consists of 6 equiangular triangles
The area (A) of a equilateral triangle is calculated as
A = 
( s is the side length )
Here s = 30 , then
A = 
= 
= 225 units²
Thus the area of the regular hexagon is
area = 6 × 225
= 1350 units² ← exact value
≈ 2338.3 units² ( to 1 dec. place )
Let's write an inequality, such as follows: x < sqrt(50) < y. Square both sides of the equation. We get x^2 < 50 < y^2. Obviously, x is between 7 and 8. Also notice, that for integers a,b, (ab)^2/b^2, equals a^2. So let's try values, like 7.1. Using the previous fact, (7.1)^2, equals (71)^2/100. So, (7.1)^2, equals 50.41. Thus, our number is between 7 and 7.1. We find, with a bit of experimentation, that the square root of 50, is 7.07.
