2 years ago

Complete the missing factors

Mathematics

1 answer:

natita [175]2 years ago

4 0

(3a-5b)•(2a+7b)
That’s the answer

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3 years ago

18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

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3 years ago

Please show your work please

Nadusha1986 [10]

The correct answer is 4.

5 0

3 years ago

. Curt is installing a picket fence around his garden which is 45.45 ft by 14.63 ft. When he gets to the hardware store he finds

Dmitriy789 [7]

The fence must have two sides of length 45.45 ft and two sides of length 14.63

To cover each of 45.45 ft long side, he will need 45.45 / 2 = 22.7 slats which approximates to 23. So, they are 2 * 23 = 46 slats.

To cover each of 14.63 ft sides, he will need 14.63 / 2 = 7.3 which approximates to 8 (to not leave any spaces between each slat). So, they are 2 * 8 = 16 slats.

That makes 46 + 16 = 62 slats.

Answer: around 62 slats.

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3 years ago