Answer: 912
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Work Shown:
The starting term is a1 = 3. The common difference is d = 5 (since we add 5 to each term to get the next term). The nth term formula is
an = a1+d(n-1)
an = 3+5(n-1)
an = 3+5n-5
an = 5n-2
Plug n = 19 into the formula to find the 19th term
an = 5n-2
a19 = 5*19-2
a19 = 95-2
a19 = 93
Add the first and nineteenth terms (a1 = 3 and a19 = 93) to get a1+a19 = 3+93 = 96
Multiply this by n/2 = 19/2 = 9.5 to get the final answer
96*9.5 = 912
I used the formula
Sn = (n/2)*(a1 + an)
where you add the first term (a1) to the nth term (an), then multiply by n/2
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As a check, here are the 19 terms listed out and added up. We get 912 like expected.
3+8+13+18 +23+28+33+38 +43+48+53+58 +63+68+73+78 +83+88+93 = 912
There are 19 values being added up in that equation above. I used spaces to help group the values (groups of four; except the last group which is 3 values) so it's a bit more readable.
Answer:
x = 2/9 (or = 0.222)
Step-by-step explanation:
1/x + 1/(3x) =6 (multiply both sides by 3x)
(1/x) (3x) + [1/(3x)](3x) =6 (3x)
3 + 1 = 18x
4 = 18x
x = 4/18
x = 2/9 (or = 0.222)
Answer:
Some answers to the reducing fraction sheet
Q14 = 4/5 because divide 12 and 15 by 3
Q15=can't be reduced because 11 is a prime number so it can't be divided by anything
Q17=can't be reduced because 17 is a prime number
Q18=can't be reduced because 13 is a prime number
Q19=38/9 because 114 and 27 would be divided by 3
Q20= -1/1 because you would divide both 14,529 by itself would equal to - 1/1
I can only help you with this sheet I can't help you with the other one hope this was helpful! :)
Answer:
= 2 1/4 feet
Step-by-step explanation:
Length of chain Jesse needs = 10 1/4 feet
Length of chain Jesse has:
Two small pieces each measuring 2 1/8 feet
= 2 × 2 1/8 feet
= 2 × 17/8
= 34/8 feet
Third piece measuring 3 3/4 feet
Total Length of chain Jesse has = 34/8 feet + 3 3/4 feet
= 34/8 + 15/4
= 34+30/8
= 64/8
= 8 feet
Total Length of chain Jesse has = 8 feet
Length of chain Jesse needs to purchase = Length of chain Jesse needs - Total Length of chain Jesse has
= 10 1/4 feet - 8 feet
= 2 1/4 feet
Length of chain Jesse needs to purchase = 2 1/4 feet
