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3 years ago

What is the sum of the arithmetic sequence 6, 14, 22, if there are 26 terms

1 answer:

3 0

Sum of nth term of arithmetic sequence is given by Sn = n/2[2a + (n - 1)d]
Here, a = 6, n = 26 and d = 14 - 6 = 8
S26 = 26/2[2(6) + (26 - 1)8] = 13[12 + 25(8)] = 2,756

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The height of a cylindrical can is 4 7/16 inches and the radius is 3 inches. Which measurement is closest to the total surface a

-Dominant- [34]

Answer:

140.19

Step-by-step explanation:

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2 years ago

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Which is the height of the triangle?<br> ( PIC IS PROVIDE PLS HELP ME)

zysi [14]

<h3>Answer: 80 meters</h3>

This is an isosceles triangle. The dashed line is the height which is perpendicular to the base 120. The height is always perpendicular to the base. The dashed line cuts the base into two equal pieces (this only works for isosceles triangles when you cut at the vertex like this).

So we have two smaller triangles each with a base of 60 and a height of x. Focus on one of the right triangles and use the pythagorean theorem to solve for x.

a^2 + b^2 = c^2

x^2 + (60)^2 = (100)^2

x^2 + 3600 = 10000

x^2 = 10000 - 3600

x^2 = 6400

x = sqrt(6400)

x = 80

Each smaller right triangle has side lengths of 60, 80, 100

Note the ratio 60:80:100 reduces to 3:4:5. A 3-4-5 right triangle is a very common pythagorean primitive.

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3 years ago

Read 2 more answers

Find the quotient of 21x^2y^6+6xy^3-30xy/3xy.

kaheart [24]

$\bf ~~~~~~~~~~~~\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
\qquad \qquad
\cfrac{1}{a^n}\implies a^{-n}
\qquad \qquad 
a^n\implies \cfrac{1}{a^{-n}}
\\\\
-------------------------------$

$\bf \cfrac{21x^2y^6+6xy^3-30xy}{3xy}\implies \stackrel{\textit{distributing the denominator}}{\cfrac{21x^2y^6}{3xy}+\cfrac{6xy^3}{3xy}-\cfrac{30xy}{3xy}}
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\cfrac{21}{3}\cdot x^2x^{-1}y^6y^{-1}+\cfrac{6}{3}\cdot x^1x^{-1}y^3y^{-1}-\cfrac{30}{3}\cdot x^1x^{-1}y^1y^{-1}
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7x^{2-1}y^{6-1}+2x^{1-1}y^{3-1}-10x^{1-1}y^{1-1}\implies 7xy^5+2y^2-10$

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3 years ago

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Naoya read a book cover to cover in a single session, at a rate of 555555 pages per hour. After reading for 444 hours, he had 33

siniylev [52]

Answer:

<h3>The function formula for the number of pages left to read is given by P(t)=55(10-t).</h3>

Step-by-step explanation:

Given that "Naoya read a book at a rate of 55 pages per hour".

After reading book for 4 hours, he had 330 pages remaining to read.

In 4 hours, Naoya must read is given by

$\frac{55}{1hr}\times 4hr$ ( by given)

$=220$

<h3>∴ In 4 hours, Naoya must read 220 pages</h3>

From the given there were 330 pages remaining to read at the time,

The total number of pages is given by

=220+330

=550

<h3>∴ The total number of pages is 550 </h3>

For each hour of reading, Naoya reads 55 pages, so the number of pages he finished reading by the "t"th hour is given by 55t

Let P(t) be the number of pages to read where P is a function of time t (measured in hours)

So the number of pages left to read is given by

P(t)=550-55t

P(t)=55(10-t)

<h3>∴ the function formula for the number of pages left to read is given by P(t)=55(10-t).</h3>

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3 years ago

A wall of a building is 34 inches wide 16 inches is concrete and 4 inches is limestone what fraction of the wall is brick

Molodets [167]

Answer:

7/17

Step-by-step explanation:

16 inches of concrete plus 4 inches of limestone come to 20 inches of concrete and limestone combined. Subtracting 20 inches from 34 inches yields 14 inches. 14 inches of the total wall thickness (34 inches) is brick. This fraction is 14/34, or 7/17.

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3 years ago