Answer:
Step-by-step explanation:
General form of quadratic equation:
ax^2+bx+c=0
ax^2+bx=-c
To complete the square, we will divide the coefficient of x in the general quadratic equation as written above and divide by 2
I'm the question;
x^2-20x+13=0
x^2-20x=-13
The coefficient of x =-20
Divide the coefficient by 2 and square the result afterwards
-20/2= - 10
(-10)^2= 100
Add 100 to both sides of the equation
x^2-20x+100=-13+100
x^2-20x+100=87
x^2-10x-10x+100=87
x(x-10)-10(x-10)=87
(x-10)(x-10)=87
(x-10)^2=87
Answer is 10,87
This is the associative property of addition
Explanation:
The Law of Cosines specifies the relationship between the three sides of a triangle and any one of the angles. If the sides are designated a, b, and c, and the angle opposite side c is C, then it tells you ...
c² = a² + b² -2ab·cos(C)
This relationship can be used to find any and all angles, given the three sides of a triangle. Or, having found one angle using the Law of Cosines, the others can be found using the Law of Sines:
sin(A)/a = sin(B)/b = sin(C)/c
_____
Typically, inverse functions are required. That is, from the Law of Cosines, ...
C = arccos((a² +b² -c²)/(2ab))
And from the Law of Sines, ...
A = arcsin(a/c·sin(C))
B = arcsin(b/c·sin(C))
_____
<em>Note on solving triangles</em>
It often works best to make use of exact values where possible. It is also a good idea to start with the longest side/largest angle. Of course, once you have two angles the other can be found as the supplement of their sum.
Answer:
x = 9/25
y = 7/25
z = 4/25
Step-by-step explanation:
2x + y = 1 .......(1)
3y + z = 1 ........(2)
x + 4z = 1 ........(3)
Elimination 1 and 2
2x + y = 1 | ×3 |
3y + z = 1 | ×1 |
6x + 3y = 3
3y + z = 1
___________--
6x - z = 2 .............. (4)
Elimination 3 and 4
x + 4z = 1 | ×6 |
6x - z = 2 | ×1 |
6x + 24z = 6
6x - z = 2
___________--
25z = 4
z = 4/25
Elimination 3 and 4
x + 4z = 1 | ×1 |
6x - z = 2 | ×4 |
x + 4z = 1
24x - 4z = 8
___________+
25x = 9
x = 9/25
Subsitution 1
2x + y = 1
2(9/25) + y = 1
18/25 + y = 1
y = 1 - 18/25
y = 25/25 - 18/25
y = 7/25
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