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3 years ago

Find the 59th term of the following arithmetic sequence. 15, 23, 31, 39

1 answer:

4 0

$15~~,~~\stackrel{15+8}{23}~~,~~\stackrel{23+8}{31}~~,~~\stackrel{31+8}{39}~~,~~...~\hspace{10em}\stackrel{common~difference}{d=8} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{59}\\ a_1=\stackrel{\textit{first term}}{15}\\ d=\stackrel{\textit{common difference}}{8} \end{cases} \\\\\\ a_{59}=15+(59-1)8\implies a_{59}=15+472-8\implies a_{59}=479$

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Determine if triangle OPQ and triangle RST are or are not similar, and, if they are, state which triangle similarity shortcut (A

murzikaleks [220]

Answer:

SAS Similarity

Step-by-step explanation:

ΔOPQ similar to ΔRST

∠Q = ∠T

OQ : RT = 28 : 84 = 1 : 3

QP : TS = 16 : 48 = 1 : 3

The measures of two sides of ΔOPQ are proportional to the measure of two side of ΔRST and their included angles are congruent. The triangles are similar by SAS Similarity.

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3 years ago

Suppose the weights of farmer carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1

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Given that <span>the weights of farmer carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1 ounces.

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3 years ago

Rewrite the fractions 2/5 and 4/15 as fractions with a least common denominator

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2/5 is equal to 4/10 and 6/15, 6/15 has a common denominator with 4/15.

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3 years ago

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3 years ago

What is the greatest area of a rectangle with a perimeter of 60cm? What is the length and width of this rectangle?

erastovalidia [21]

The length and width of this rectangle are 15 cm respectively

<h3>How to determine the greatest area?</h3>

The perimeter is given as:

Perimeter, P = 60

The greatest area is calculated as:

Greatest = (P/4)^2

Substitute 60 for P

Greatest = (60/4)^2

Evaluate the quotient

Greatest = 15^2

Evaluate the exponent

Greatest = 225 square centimeters

Hence, the greatest area is 225 square centimeters

<h3>How to determine the length and width</h3>

We understand that the area is the greatest.

In such a scenario;

Length = Width

This means that:

Area =Length^2 =Width^2

So, we have:

Length^2 =Width^2 = 225

Take the square root

Length =Width = 15

Hence, the length and width of this rectangle are 15 cm respectively