We know that
the law of cosines establish
c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b]
in this problem
a=11 units
b=11 units
c=14 units
C=angle A
cos C=[11²+11²-14²]/[2*11*11]-----> cos C=0.19008
C=arc cos (0.19008)------> C=79.04°
the answer is
the measure of angle A is 79°
X 2 +y 2 +4x−2y=−1space, x, start superscript, 2, end superscript, plus, y, start superscript, 2, end superscript, plus, 4, x, m
stepan [7]
The radius is 2.
We will rewrite this equation in center-radius form,
(x-h)²+(y-k²)=r²
where (h, k) is the center of the circle and r is the radius.
In order to do this, we will need to complete the square. We will first rewrite this with the x terms grouped together and the y terms grouped together:
x²+4x+y²-2y = -1
To complete the square for the x terms, we divide the coefficient b (as in bx) by 2:
4/2 = 2
Now we square this:
2²=4
We will add this to both sides of the equation (in order to maintain balance, we must add it to both sides):
x²+4x+4+y²-2y=-1+4
x²+4x+4+y²-2y=3
We have completed the square for the x terms. When we divided b by 2, that gave us the number we need, 2:
(x+2)²+y²-2y=3
Now we will do the same thing for the y terms. The b for our y terms is -2:
-2/2 = -1
(-1)²=1
So we will add 1 to both sides, and use -1 in the finalized form:
(x+2)²+y²-2y+1=3+1
(x+2)²+(y-1)²=4
We can see that the center would be located at (-2, 1) and the radius is √4=2.
Answer:
The answer is 8.
Step-by-step explanation:
We need to use the quadratic formula, that is ax2+bx+c=0
Where
For the given equation x2+5x-104=0 we have
a=1, b=5, c= -104
If you solve that, we will have x=-13. x=8, two answers,
The first one, by being negative does not have physical sense (there are no negatives quantities when you measure the length of something)
So we use the anwser x=8
Step-by-step explanation:
multiple height by width
