9514 1404 393
Answer:
(2, 3)
Step-by-step explanation:
Compare the given equation ...
y = (x -2)^2 +3
to the vertex form ...
y = (x -h)^2 +k
You can see that h=2 and k=3.
The vertex of the parabola is (h, k) = (2, 3).
Answer:
The budget line will remain unchanged.
Step-by-step explanation:
A budget line helps in showing the possible combinations of two commodities.
We can find the slope of the budget line that is also called the price ratio between two things. If we get a straight line, we say the slope is constant.
Here in the question its given that the initial constraints are (3,15) with initial income of $60. Then the price increases and constraints become (6,30) with an increase in income up to $120.
Therefore, the budget line will not be affected and remain unchanged as each constraint is doubling and the slope will be constant.
Last answer for the first question and in not sure about the second one
P=1560000
APR=5.6%
monthly interest, i=5.6%/12=7/1500 [fractions keep exact values]
R=1+i=1+7/1500
# of periods, n=30 years = 360 periods
monthly payment, A
A=PR^n(i)/(R^n-1)
=1560000*(1+7/1500)^360*(7/1500)/((1+7/1500)^360-1)
=$8955.632
At the end of eight years,
number of periods, n1 = 8*12 = 96
If paid off at the end of 8 years, value of loan then
future value of principal
F1=PR^n1=1560000*(1+7/1500)^96=2439135.635
future value of payments
F2=A(R^n1-1)/i=8955.632*(1+7/1500)^96-1)/(7/1500)=1081485.620
Therefore the balloon payment
= future value of principal (owing) - future value of payments (paid)
=F1-F2
=2439135.635-1081485.620
=1357650.0152
Round to two places after decimal to get final answer.
Step-by-step explanation:
(2, 4), (4, 8) and (5, 10) are on the line y = 2x.
Hence they line on a straight line,
The line passes through the origin, and
it shows a proportional relationship.
