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3 years ago

Suppose that the area of a square lawn is 4x^2 + 16x + 16. What is the length of one side of the lawn?

Mathematics

1 answer:

bogdanovich [222]3 years ago

7 0

Answer:

2x+4

Step-by-step explanation:

remember the formula (a+b)^2=a^2+b^2+2ab

in this case, 4x^2 would be a^2, 16 would be b^2, and 16x would be 2ab

so, the variable a would be 2x and the variable b would be 4

so, you can turn 4x^2+16x+16 into (2x+4)^2

and since the area of a square is (one of its sides)^2, or in this case (2x+4)^2, the length of one side of the lawn will be 2x+4

problems where you have to use the (a+b)^2=a^2+b^2+2ab formula to turn trinomials into binomials squared are very common, so make sure to look out for questions like these and be ready to use this formula

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4 years ago

Select the correct answer. Consider these three numbers written in scientific notation: 6. 5 × 103, 5. 5 × 105, and 1. 1 × 103.

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Scientific notation uses expression which gives easy access of order. The greatest number is $5.5 \times 10^5$ .It is greater by smallest number by 500 times.

<h3>How to convert a number to scientific notation?</h3>

It is usually of the form $a.bc.. \times 10^k$ exponent of 10 starts)

(we have 1 ≤ |a| < 10 ) (where |a| is magnitude of a without sign)

This notation is used to get some idea of how large or small a number is in terms of power of 10.

<h3>What are some basic properties of exponentiation?</h3>

If we have $a^b$ base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

$a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\ a^b \times a^c = a^{b+c}$

The given numbers are:

First number = $6.5 \times 10^3 = 6500$
Second number = $5.5 \times 10^5 = 550000$
Third number = $1.1 \times 10^3 = 1100$

The smallest number is 1,100 and greatest is 550,000

Getting the division to get to know how many times the greatest number is larger than the smallest number, we get:

$\dfrac{5.5 \times 10^5}{1.1 \times 10^3} = \dfrac{5.5 \times 10^{5-3}}{1.1} = \dfrac{5.5}{1.1} \times 10^2 = 5 \times 10^2 = 500$

Thus, it is found that greatest number is $5.5 \times 10^5$ . It is greater by smallest number by 500 times.

Learn more about scientific notation here:
brainly.com/question/3112062

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Oduvanchick [21]

Answer:

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Step-by-step explanation:

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Answer:

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