Eliminate x's
multiply 2nd equation by -2 ad add to first
2x+3y=9
<u>-2x-10y=-16 +</u>
0x-7y=-7
-7y=-7
divide by -7
y=1
sub back
2x+3y=9
2x+3(1)=9
2x+3=9
minus 3
2x=6
divide 2
x=3
x=3
y=1
(x,y)
(3,1)
D
Answer:
home inventory
Step-by-step explanation:
the insurance company wants to know what they are going to be insuring
L1: 2x+4y-3=0 ..........(1)
P: (2,0)
The point on the line L1 closest to the given point P is at the intersection of L1 with L2, which is the perpendicular passing through P.
Slope of L1=-2/4=-1/2
Slope of L2=-1/(-1/2)=2
Since it passes throug P(2,0), we can use the point-slope formula:
(y-0)=2(x-2) =>
L2: 2x-y-4=0.............(2)
Solve for x & y using (1) and (2) to get intersection point required:
(1)-(2)
2x-2x + 4y-(-y) -3 -(-4) =0
5y=-1, y=-1/5
Substitute y=1/5 in equation (1)
2x+4(-1/5)-3=0 =>
2x-19/5=0
x=19/10
=> the point on L1 closest to (2,0) is (19/10, -1/5)
Circle formula
(x-h)^2+(y-k)^2=r^2 where (h,k) is the center
and r=radius
to find the radius
we are given one of the points and the center
distnace from them is the radius
distance formula
D=

points (-3,2) and (1,5)
D=

D=

D=

D=

D=5
center is -3,2
r=5
input
(x-(-3))^2+(y-2)^2=5^2
(x+3)^2+(y-2)^2=25 is equation
radius =5
input -7 for x and solve for y
(-7+3)^2+(y-2)^2=25
(-4)^2+(y-2)^2=25
16+(y-2)^2=25
minus 16
(y-2)^2=9
sqqrt
y-2=+/-3
add 2
y=2+/-3
y=5 or -1
the point (-7,5) and (7,-1) lie on this circle
radius=5 units
the points (-7,5) and (-7,1) lie on this circle