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:
C) a = 10√3, b = 5√3, c = 15 , d = 5
Step-by-step explanation:
Here we use the ratio of 30, 60, 90 degree triangle.
The ratio of sides, 1:√3:2
2x = 10
x = 5
d = 5
b = 5√3
c = 5√3√3
c = 5*3 = 15
c = 15
a = 2(5√3)
a = 10√3
Therefore, a = 10√3, b = 5√3, c = 15 and d = 5
Thank you.
Answer:
do you understand it
Step-by-step explanation:
do you understand it
Functions cannot have different values of y for the same value of x. Now let us check each case one at a time.
<u>First Case:</u> For the same value of x=-1, y has two different values of 7 and 1, which is not allowed in a function. Therefore, the first case is not a function.
<u>Second Case:</u> For the same value of x=-1, y has two different values of -5 and 1, which is not allowed in a function. Therefore, the second case is not a function.
<u>Third Case:</u> For the same value of x=3, y has two different values of 2 and 4, which is not allowed in a function. Therefore, third case is not a function.
<u>Fourth Case:</u> In this case no value of x is same. So, this is a function.
Answer:
AI = 3.25in
IH = 4.2in
Area = 23.025in
Step-by-step explanation: