Find a polynomial function that has the given zeros. (there are many correct answers.) −9, 5

Okay the question is simple provided you understand what these 4 terms mean. I imagine that must be the sticking point here.

In the geometric sense, similarity means one thing scales to another. This doesn't make a huge amount of sense with regards to a single length. But if you have a triangle of lengths 3,4,5 and another of lengths 6,8,10, these are similar because it is all in the same proportion. The only difference is one is twice as large in the length sense.

Collinear means on the same line. Again this doesn't make a huge amount of sense in this context, usually we refer to points being collinear, for example (1,1), (2,2) and (3,3) are all on the same line y = x. In this context, it is saying that both diagonals are exactly the same line, which doesn't make sense.

Congruence, in the geometric sense, means the same. A 3,4,5 triangle can only be congruent to another 3,4,5 triangle. This then is saying that the lengths of the two diagonals are the same in a rhombus. This is indeed true, a property that can be proved using elementary vector geometry.

Finally we have perpendicularity, the property in two dimensions whereby two lines have an angle of 90 degrees between them. In fact only a very special rhombus will have this property, a square. Hence this isn't likely to be the answer to the question because it is not true for all rhombi.

The answer is congruent. I hope this helps :)

8 0

4 years ago

A person invests 3000 dollars in a bank. The bank pays 4.25% interest compounded semi-annually. To the nearest tenth of a year,

3241004551 [841]

Answer:

The person must leave the money for approximately 14.8 years.

Step-by-step explanation:

This can be calculated using the formula for calculating the future value as follows:

FV = PV * (1 + r)^n …………………………………. (1)

Where;

FV = Future value of the investment = 5600

PV = Present value of the investment = 3000

r = semiannual interest rate = 4.25% / 2 = 0.0425 / 2 = 0.02125

n = number of semiannuals = ?

Substitute the values into equation (1) and solve for n, we have:

5600 = 3000 * (1 + 0.02125)^n

5600 / 3000 = 1.02125^n

1.02125^n = 1.86666666666667

Loglinearizing both sides, we have:

nlog1.02125 = log1.86666666666667

n = log1.86666666666667 / log1.02125

n = 0.271066772286539 / 0.0091320695404719

n = 29.6829509548973

Since n is number of semiannuals, we divide the answer by 2 obtain the number of years as follows:

Number of years = 29.6829509548973 / 2 = 14.8414754774487

Rounding to the nearest tenth of year, we have:

Number of years = 14.8

Therefore, the person must leave the money for approximately 14.8 years.

5 0

3 years ago