Add 1, then add 2, then add 3, then 4, then 5, then 6.
Answer:
Step-by-step explanation:
To solve, we need to find the y-intercept (b). In order to find the y-intercept, we can plug in the slope and the (x,y) coordinate pair given to us into the equation to solve for the y-intercept:
y=mx+b
4=(-7/-2)*-2+b
4=14/-2+b
4=-7+b
Add 7 to both sides
b=11
Therefore the equation is:
(note that the fraction is positive since the two negatives cancel out)
Answer:
The probability that the first die is a 2 or the second die is a prime = 1/12
Step-by-step explanation:
It is given that,a fair (6 sided) die is rolled TWO times.
The sample space for rolling 2 dies
(1, 1), (1, 2) .......... (1,6)
(2,1) ..........................
.
.
(6, 1) ..........................(6, 6)
There are total of 6^2 = 36 sample space
<u>To find the probability</u>
The prime numbers from 1 to 6 are 2, 3 and 5
the possible outcomes are(2,1), (2, 3) and (2, 5)
The probability that the first die is a 2 or the second die is a prime = 3/36 = 1/12
no number can have a positive and a negative at the same time. a negative number has a negative sign and a positive number has a plus sign.
Step-by-step explanation:
The equation of a circle can be the expanded form of
\large \text{$(x-a)^2+(y-b)^2=r^2$}(x−a)
2
+(y−b)
2
=r
2
where rr is the radius of the circle, (a,\ b)(a, b) is the center of the circle, and (x,\ y)(x, y) is a point on the circle.
Here, the equation of the circle is,
\begin{gathered}\begin{aligned}&x^2+y^2+10x-4y-20&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4-49&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &x^2+10x+25+y^2-4y+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &(x+5)^2+(y-2)^2&=&\ \ 7^2\end{aligned}\end{gathered}
⟹
⟹
⟹
⟹
x
2
+y
2
+10x−4y−20
x
2
+y
2
+10x−4y+25+4−49
x
2
+y
2
+10x−4y+25+4
x
2
+10x+25+y
2
−4y+4
(x+5)
2
+(y−2)
2
=
=
=
=
=
0
0
49
49
7
2
From this, we get two things:
\begin{gathered}\begin{aligned}1.&\ \ \textsf{Center of the circle is $(-5,\ 2)$.}\\ \\ 2.&\ \ \textsf{Radius of the circle is $\bold{7}$ units. }\end{aligned}\end{gathered}
1.
2.
Center of the circle is (−5, 2).
Radius of the circle is 7 units.
Hence the radius is 7 units.
