Answer:
Step-by-step explanation:
Using the section formula, if a point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n, then
(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
The vertices of the triangle are given to be (x
1
,y
1
),(x
2
,y
2
) and (x
3
,y
3
). Let these vertices be A,B and C respectively.
Then the coordinates of the point P that divides AB in l:k will be
(
l+k
lx
2
+kx
1
,
l+k
ly
2
+ky
1
)
The coordinates of point which divides PC in m:k+l will be
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
m+k+l
mx
3
+(k+l)
(l+k)
lx
2
+kx
1
,
m+k+l
my
3
+(k+l)
(l+k)
ly
2
+ky
1
⎭
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎫
⇒(
m+k+l
kx
1
+lx
2
+mx
3
,
m+k+l
ky
1
+ly
2
+my
3
)
Answer:
The vertex is the point 
Step-by-step explanation:
we have
we know ow that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
Convert the equation into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Factor the leading coefficient
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
therefore
the vertex is the point
a) The cost for 10 mile taxi ride is $18
b) The cost for m mile taxi ride is 1.5 m + 3
Step-by-step explanation:
Step 1 :
The fixed charges for the pick up = $3
Charges per mile = $1.50
Let s denote the total miles driven and t be the total cost for the trip
This can be represented by the equation
t = 3 + 1.5s
Step 2:
Distance traveled by Jonathan in his trip = 10 miles
So cost for riding 10 miles is
t = 3 + 1.5(10) = 3 + 15 = $18
The cost for 10 mile taxi ride is $18
Step 3 :
If the distance traveled is m miles, then substituting s = m in the above equation we get the cost as 1.5 m + 3
Step 4 :
Answer :
a) The cost for 10 mile taxi ride is $18
b) The cost for m mile taxi ride is 1.5 m + 3
Answer:
rate- 6
distance fallen- 18
Step-by-step explanation:
