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zhannawk [14.2K]
3 years ago
14

Helpppp plzzz The frequency histogram shows the lengths of trails in a large park.

Mathematics
1 answer:
Rus_ich [418]3 years ago
8 0

Answer:

13 trails

Step-by-step explanation:

The histogram shows following numbers of trails:

  • <u>0 - 6 km long</u> - 5 trails;
  • 6 - 12 km long - 9 trails;
  • 12 - 18 km long - 7 trails;
  • 18 - 24 km long - 3 trails;
  • <u>24 - 30 km long</u> - 4 trails;
  • <u>30 - 36 km long</u> - 1 trail;
  • <u>36 - 42 km long</u> - 3 trails.

So, there are 5 trails with length less than 6 km and 4 + 1 + 3 = 8 trails that are at least 24 km long.

In total, 5 + 8 = 13 trails

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Step-by-step explanation:

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5) Your stock investments went from $450 in 2013 to $350 ir
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The most appropriate choice for percentage will be given by Percentage decrease in the investment is 22.22%

<h3>What Does Percent Mean?</h3>

Using a percentage of 100, we may express a ratio as a %.

Stock investments in this case decreased from $450 in 2013 to $350 in 2014.

Decrease in stock equals $100 ($450 - $355)

Decrease in percentage: 100/450 100 = 22.22%

<h3>What format does a percentage use?</h3>

The definition of percentage is "out of 100." In mathematics, percentages are used to represent parts of a whole, much as fractions and decimals. A total is considered to be made up of 100 equal parts when expressed as a percentage. The symbol % or, less commonly, the abbreviation 'pct' can be used to represent a percentage.

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3 0
1 year ago
Ayuda necesito resolver este problema con procedimiento ;)
Paraphin [41]

x^3-2x^2+x-1 is one of the prime factors of the polynomial

<h3>How to factor the expression?</h3>

The question implies that we determine one of the prime factors of the polynomial.

The polynomial is given as:

x^8 - 3x^6 + x^4 - 2x^3 - 1

Expand the polynomial by adding 0's in the form of +a - a

x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^7 - 4x^6 +x^6 + 2x^5 -2x^5- 3x^4 + 4x^4 + 2x^3 -6x^3+2x^3- x^2  -3x^2 +4x^2-2x+2x-1

Rearrange the terms

x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^5 - 3x^4 + 2x^3 - x^2 + 2x^7 - 4x^6 + 4x^4 -6x^3+4x^2-2x+x^6-2x^5+2x^3-3x^2+2x-1

Factorize the expression

x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^2(x^6-2x^5+2x^3-3x^2+2x-1) + 2x(x^6-2x^5+2x^3-3x^2+2x-1) + 1(x^6-2x^5+2x^3-3x^2+2x-1)

Factor out x^6-2x^5+2x^3-3x^2+2x-1

x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x^2+2x + 1)(x^6-2x^5+2x^3-3x^2+2x-1)

Express x^2 + 2x + 1 as a perfect square

x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6-2x^5+2x^3-3x^2+2x-1)

Expand the polynomial by adding 0's in the form of +a - a

x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^4-x^3 +x^3-2x^3-x^2 -2x^2 +x+x - 1)

Rearrange the terms

x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^3-x^4-2x^3-x^2+x+x^3-2x^2 +x - 1)

Factorize the expression

x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3(x^3-2x^2+x-1) -x(x^3-2x^2+x-1)+1(x^3-2x^2+x-1))

Factor out x^3-2x^2+x-1

x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3 -x+1)(x^3-2x^2+x-1)

One of the factors of the above polynomial is x^3-2x^2+x-1.

This is the same as the option (c)

Hence, x^3-2x^2+x-1 is one of the prime factors of the polynomial

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