Answer:
Explanation:
We must write this equation in the form
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
Where
(
a
,
b
)
are the co ordinates of the center of the circle and the radius is
r
.
So the equation is
x
2
+
y
2
−
10
x
+
6
y
+
18
=
0
Complete the squares so add 25 on both sides of the equation
x
2
+
y
2
−
10
x
+
25
+
6
y
+
18
=
0
+
25
=
(
x
−
5
)
2
+
y
2
+
6
y
+
18
=
0
+
25
Now add 9 on both sides
(
x
−
5
)
2
+
y
2
+
6
y
+
18
+
9
=
0
+
25
+
9
=
(
x
−
5
)
2
+
(
y
+
3
)
2
+
18
=
0
+
25
+
9
This becomes
(
x
−
5
)
2
+
(
y
+
3
)
2
=
16
So we can see that the centre is
(
5
,
−
3
)
and the radius is
√
16
or 4
600 mm of rain / 30 min = 50 mm of rain per minute
Answer:
4x-2y=2
Step-by-step explanation:
Line R is represented by the following equation:
x+y=2
We need to choose another system of equation of x+y=2
whose solution is (1,1)
The equation must be satisfy the point (1,1)
Option 1: 2x+y = 2
Put x=1 and y=1
2(1)+1 = 3
3 ≠ 2
False
Option 2: 4x-2y=2
Put x=1 and y=1
4(1) - 2(1) = 2
2 = 2
True
Option 3: 2x-2y=2
Put x=1 and y=1
2(1) - 2(1) = 0
0 ≠ 2
False
Option 4: x+y=4
Put x=1 and y=1
1+1 = 2
2 ≠ 4
False
Hence, The system of equation is 4x-2y=2
If you extend the line from 1 through the parallel line you create a transversal and a triangle.
Consecutive angles inside the parallel lines are supplementary therefor the exterior angle of the triangle on the left side measures 118 degrees. This angle creates a linear pair with the left base angle therefore that angle measures 62 degrees.
144 forms a linear pair with the right base angle of the triangle making its measure 36 degrees.
The third angle of the triangle would then measure 82 degrees. Finally this third angle forms a linear pair with angle 1 making angle 1 measure 98 degrees.
So the culture banner size has length x, width x (since it is square)
The sports banner has length x+12, width x.
The area of the sports banner is length x width = x(x+12) = x²+12x.
Now, lets look at the tiles.
- The monomial, x, a factor of the expression is the width of the sports banner.
- The binomial (x+12) is the length of the spots banner (this is given!)
- The second degree term of the expression x²+12 is x², the area of the culture banner
- The first degree term of the expression x²+12x is 12x, it represents the increase in area, since the area went from x² to x²+12x
