X=width of a coccer pitch
2x-20=length of a soccer pitch
Area (rectangule)=length x width
We suggest this equation:
x(2x-20)=6000
2x²-20x=6000
2x²-20x-6000=0
x²-10x-3000=0
We solve this quadratic equation:
x=[10⁺₋√(100-4*1*-3000)]/2=[10⁺₋√(100+12000)]/2=
=(10⁺₋110)/2
we have two solutions:
x₁=(10-110)/2=-50, invalid solution.
x₂=(10+110)/2=60
x=60
2x-20=2(60)-20=120-20=100
Solution: the length is 100 m, and the width is 60 m.
To check:
Area=100 m*60 m=6000 m²
The twice of width is =2(60 m)=120 m,
20 m less than twice its width is: 120 m-20 m=100 m=the length.
The complex solution of a quadratic equation are (- 2 + i ) and
(- 2 - i ).
What is Quadratic equation?
An algebraic equation of the second degree is called a quadratic equation.
Given that;
A quadratic equation is;
3x² = -12x - 15
Now, The equation is written as;
3x² + 12x + 15 = 0
Take 3 common, we get;
3 (x² + 4x + 5) = 0
x² + 4x + 5 = 0
Factorize the equation by using Sridharacharya Formula;
x = - 4 ± √4² - 4*1*5 / 2*1
x = -4 ± √16 - 20 / 2
x = - 4 ± √-4 / 2
Since, √-1 = i
x = -4 ± 2i / 2
x = - 2 ± i
It gives two values of x as;
x = - 2 + i
And, x = - 2 - i
Hence, The complex solution of a quadratic equation are (- 2 + i ) and
(- 2 - i ).
Learn more about the quadratic equation visit:
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61 because you always multiply first 60 x 0= 0 so now we have 60+1 which is 61
In order to do mean you have to add all of the numbers in the list together. then divide them by the total amount of numbers (ex. 7,9,3,2,5. you would add all of these up 7+9+3+2+5=26 then you would divide that by 5 because there are five numbers in the list.
Answer: Length of AB is 16 cm
Step-by-step explanation:
Given: Diameter of a circle is 20 cm and CE = 4 cm
Now as shown in figure AO, BO, CO are radii
Therefore
AO=BO=CO= 10 cm
Now
Now in Δ OEB
∠OEB =90°
Therefore by Pythagoras theorem : In a right angle triangle the square of hypotenuse is equal to the sum of square of other two sides.
So we have
Now as we know perpendicular to the chord from the center of a circle bisect the chord.
Therefore
Hence , the length of AB is 16 cm .
