In ΔCDE, the measure of ∠E=90°, the measure of ∠C=83°, and DE = 8.6 feet. Find the length of EC to the nearest tenth of a foot.

Which polynomial can be simplified to a difference of squares

Mrrafil [7]

<h2>Hello!</h2>

The answer is:

The polynomial that can be simplified to a difference of squares is the second polynomial:

$16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}=(4-1)(4+1)$

To solve this problem, we need to look for which of the given quadratic terms given for the different polynomials can be a result of squaring (elevating by two).

So,

Discarding, we have:

The quadratic terms of the given polynomials are:

$First=10a^{2}$

$Second=16a^{2}$

$Third=25a^{2}$

$Fourth=24a^{2}$

We have that the coefficients of the quadratic terms that can be obtained by squaring are:

$16a^{2} =(4a)^{2} \\\\25a^{2} =(5a)^{2}$

The other two coefficients are not perfect squares since they can not be obtained by square rooting whole numbers.

So, the first and the fourth polynomial are discarded and cannot be simplified to a difference of squares at least using whole numbers.

Therefore, we need to work with the second and the third polynomial.

For the second polynomial, we have:

$16a^{2} -4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2} =(4-1)(4+1)$

So, the second polynomial can be simplified to a difference of squares.

For the third polynomial, we have:

$25a^{2} +6a-6a+36=16a^{2}+36=(5a)^{2}+(6)^{2}$

So, the third polynomial cannot be simplified to a difference of squares since it's a sum of squares.

Hence, the polynomial that can be simplified to a difference of squares is the second polynomial:

$16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}$

7 0

3 years ago

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A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

Assoli18 [71]

Step-by-step explanation:

Rate of growth equals 420/100 = 4.2 times per hour

So after t=three hours,

size of culture = 100*(4.2)^t = 100*4.2^3=7408.8 bacteria,

round to nearest unit 7409 bacteria after three hours (after initial size of 100).

8 0

3 years ago

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What’s the answer I need helppp?!!? <br><br> Plz no files or links

nekit [7.7K]

About 13,992

Hope that helps have a good day and can I get brainlist

3 0

3 years ago

Brad earns $12.75/hr and works 40 hours a week. What is his gross annual income?

professor190 [17]

Answer:

Gross Annual Income: $26,520

Step-by-step explanation:

Gross annual income is the amount of money made without any taxes or deductions subtracted from the total. If Brad earns $12.75 per hour and works 40 hours per week, we can first find his weekly income by multiplying the rate by the number of hours per week:

$12.75 x 40 = $510.00

Since Brad earns $510 per week and there are 52 weeks in one year, we can find his gross annual income again by multiply the weekly rate ($510) by the number of weeks in a year (52):

$510 x 52 = $26,520

3 0

3 years ago

There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does t

mario62 [17]

The first one I think because a linear function is always going to have a constant rate of change in one direction going straight up

3 0

3 years ago

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