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3 years ago

10

The radius of a circle is 5 feet. What is the circumference?

1 answer:

givi [52]3 years ago

7 0

The answer is 31.42ft

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For an arithmetic sequence, a35=57. If the common difference is 5. Find a1 and the sum of the first 61 terms.

Flauer [41]

$\displaystyle\bf\\a_{35}=57\\r=5\\----\\a_1=?\\S_{61}=?\\----\\Solve:\\1)\\a_1=a_{35}-(35-1)\times r=57-34\times 5=57-170=-113\\\boxed{\bf a_1=-113}\\\\$

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$\displaystyle\bf\\2)\\A_{61}=a_1+(61-1)\times r=-113+60\times5=-113+300=187\\\\S_{61}=(-113)+(-108)+(-103)+...+(-8)+(-3)+2+7+12+...+187\\\\S_{61}=SA+SB\\\\SA=(-113)+(-108)+(-103)+...+(-8)+(-3)=-(3+8+103+108+113)\\\\n=\frac{113-8}{5}+1=\frac{105}{5}+1=21+1=22~terms\\SA=-\Big( \frac{n(113+3)}{2} \Big)=-\Big( \frac{22\times116}{2} \Big)=-11\times116 =-1276$

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$\displaystyle\bf\\SB=2+7+12+...+187\\\\n=\frac{187-2}{5}+1=\frac{185}{5}+1=37+1=38~terms\\\\SB=\frac{n(187+2)}{2}=\frac{38\times189}{2}=19\times189=3591\\\\S_{61}=SA+SB=-1276+3591=2315\\\\\boxed{\bf S_{61}=2315}$

8 0

3 years ago

What is Mary's location if she travels 3 units left and 4 units up from (5, 0)?

Novosadov [1.4K]

Answer:

here is the right answer

C- (2,4)

7 0

2 years ago

Salvatore attends class every 4 weeks, chess club every 2 weeks, and fencing lessons every 3 weeks. If he attended all three thi

Amiraneli [1.4K]

Answer:

12

Step-by-step explanation:

Listing the weeks he will attend each item

Class 4,8,12,16

Chess 2,4,6,8,10,12

Fencing 3,6,9,12

Starting today at week 0, he will attend all 3 again at week 12

6 0

3 years ago

Read 2 more answers

4/5 divided 8/7 HELP ASAP !!!

Leno4ka [110]

Answer:

7/10

Step-by-step explanation:

You can either use a calculator, or make both fractions have the denominator of 35 and change the two fractions to be,

$\frac{28}{35}$ and $\frac{40}{35}$ then divide.

Hope that helps and have a great day!

6 0

3 years ago

Read 2 more answers

Eric has $25 to purchase magazines and to pay for his lunch. Each

faust18 [17]

Answer:

B

Step-by-step explanation:

The maximum amount Eric can spend on magazines is $25 less the cost of lunch, $15.

The appropriate inequality sign would be less than since he cannot spend more than $25.

Also, the amount he can spend on magazines would be what is left after paying for lunch.

So the correct inequality is 4m - 15 < 25

8 0

3 years ago