Listed price = $1.4 million
Down payment = 20% of $1.4 million = 0.2 x 1,400,000 = 280,000
Amount left to pay = $1.4 million - 280,000 = $1,120,000
Present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) / r
where: PV = $1,120,000
r = 5% = 0.05
t = 12
n = 30 years.
1,120,000 = P(1 - (1 + 0.05/12)^-(12 x 30)) / 0.05
1,120,000 x 0.05 = P(1 - (1 + 1/240)^-360)
56,000 = P(1 - 0.2238)
P = 56,000 / 0.7761 = 72,148.83
Therefore, the monthly payment is $72,148.83
Answer:
B. y = -0.58x^2 -0.43x +15.75
Step-by-step explanation:
The data has a shape roughly that of a parabola opening downward. So, you'll be looking for a 2nd-degree equation with a negative coefficient of x^2. There is only one of those, and its y-intercept (15.75) is in about the right place.
The second choice is appropriate.
_____
The other choices are ...
A. a parabola opening upward
C. an exponential function decaying toward zero on the right and tending toward infinity on the left
D. a line with negative slope (This might be a good linear regression model, but the 2nd-degree model is a better fit.)
Given: AD ≅ BC and AD ∥ BC
Prove: ABCD is a parallelogram.
Statements Reasons
1. AD ≅ BC; AD ∥ BC 1. given
2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate interior angles
3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent
4. AC ≅ AC 4. reflexive property
5. △CAD ≅ △ACB 5. SAS congruency theorem
6. AB ≅ CD 6. Corresponding Parts of Congruent triangles are Congruent (CPCTC)
7. ABCD is a parallelogram 7. parallelogram side theorem
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Alice should pick the enlarged-photo with dimensions of 8-inch by 10-inch.
Step-by-step explanation:
Step 1:
In order for a part of the photo to not be cut off, the enlarged photo's dimensions should be of a constant ratio with the original photo's dimensions.
We divide the dimensions of the enlarged-photo with the dimensions of the original photo to check which has a constant ratio.
Step 2:
The original photo was a 4-inch by 5-inch photo.
Option 1 is 7-inch by 9-inch, so the ratios are
The ratios are different so this cannot be the enlarged photo's dimensions.
Option 2 is 8-inch by 10-inch, so the ratios are
The ratios are the same so this can be the enlarged photo's dimensions.
Option 3 is 12-inch by 16-inch, so the ratios are
The ratios are different so this cannot be the enlarged photo's dimensions.
So the enlarged-photo with dimensions of 8-inch by 10-inch should be picked.
