A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]
B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)
<h3>A. How to determine the mid point</h3>
- Coordinate of C = (4, 5)
- Coordinate of D = (p, q)
- Mid point =?
Mid point = (X , Y)
X = (x₁ + x₂) / 2
X = (4 + p) / 2
Y = (y₁ + y₂) / 2
Y = (5 + q) / 2
Thus,
Mid point = (X , Y)
Mid point = [(4 + p) / 2 , (5 + q) / 2]
<h3>B. How to determine the coordinates of D</h3>
- Mid point = (7, 1)
- Coordinates of D =?
Mid point = (7, 1) = (X , Y)
X = (4 + p) / 2
7 = (4 + p) / 2
Cross multiply
7 × 2 = 4 + p
14 = 4 + p
Collect like terms
p = 14 - 4
p = 10
Y = (5 + q) / 2
1 = (5 + q) / 2
Cross multiply
1 × 2 = 5 + q
2 = 5 + q
Collect like terms
q = 2 - 5
q = -3
Coordinates of D = (p, q)
Coordinates of D = (10 , -3)
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Answer:
8
Step-by-step explanation:
x is 8
Answer:
Step-by-step explanation:
Given expression:
Expand following:
Distribute inside parenthesis:
Multiply/Simplify following:
Answer:
(a) 3 years FV=$4,221.80
(b) 6 years FV=$5,092.46
(c) 9 years FV=$6,142.69
Step-by-step explanation:
The formula for continuously compounded interest is
FV = PV x e^(i x t)
where,
FV=future value of the investment,
PV= present value,
i = stated interest rate,
t = time in years,
e= mathematical constant approximated as 2.7183.
In this case,
PV=$3,500
i = 6.25%
(a) 3 years
FV = PV x e^(i x t)
FV = $3,500 x e^(6.25%x3)
FV=$4,221.80
(b) 6 years
FV = $3,500 x e^(6.25%x6)
FV=$5,092.46
(c) 9 years
FV = $3,500 x e^(6.25%x9)
FV=$6,142.69
