Expand the polynomials and simplify. (2x+3y)^2

Mathematics

1 answer:

astra-53 [7]3 years ago

6 0

Answer:

4x^2+12xy+9y^2

Step-by-step explanation:

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At a pizzeria, a medium pizza which has diameter of 12 inches sells for $6.00 and a large pizza which has a diameter of 16 inche

Sidana [21]

We are comparing areas, so square of the linear dimension
Relative cost per unit area
12^2/6=24
16^2/10=256/10=25.6
Since 24<25.6, the 12" pizza is a better deal.

Note: we could compare exact area by calculating A=pi (d^2)/4, but since it is a relative comparison, the result will be the same, albeit more work.

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3 years ago

Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

bonufazy [111]

Answer:

Using the rule of 72, the doubling time is 9.35 years.

The exact answer is that the doubling time is 8.89 years.

Step-by-step explanation:

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 7.7%. So, by the rule of 72:

$D = \frac{72}{7.7} = 9.35$ .

Exact answer:

The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

$A = 2P$