If the 9th term of an A.P is 0, prove that its 29th term is twice its 19th term
Answers
Let the first term, common difference and number of terms of an AP are a, d and n respectively.
Given that, 9th term of an AP, T9 = 0 [∵ nth term of an AP, Tn = a + (n-1)d]
⇒ a + (9-1)d = 0
⇒ a + 8d = 0 ⇒ a = -8d ...(i)
Now, its 19th term , T19 = a + (19-1)d
= - 8d + 18d [from Eq.(i)]
= 10d ...(ii)
and its 29th term, T29 = a+(29-1)d
= -8d + 28d [from Eq.(i)]
= 20d = 2 × T19
Hence, its 29th term is twice its 19th term
Answer:
Proved below.
Step-by-step explanation:
a9 = a1 + 8d = 0 where a1 = first term and d = common difference.
we need to prove that
a1 + 28d = 2(a1 + 18d
simplifying:-
a1 + 36d - 28d = 0
a1 + 8d = 0 which is what we are given.
Therefore the proposition is true.
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Answers
For seven months it is less expensive to have a monthly membership.
What is the arithmetic expression?
When evaluating arithmetic expressions, the stack organization is extremely efficient. We employ a number of techniques, including PEMDAS, to simplify the issue. In addition to the value, the variables also need to be made easier.
Given, A full-year membership to a gym costs $325 upfront with no monthly charge. A monthly membership costs $100 upfront and $30 per month. For calculating the number of months is it less expensive to have a monthly membership we need to create an expression where the number of months will be variable. Hence,
100 + 30x < 325
subtract 100 on both sides
30x < 225
divide 30 into both sides
x < 225/30
x < 7.21
Therefore, it is less expensive to have a monthly membership if we take it for seven months.
Learn more about arithmetic expressions here:
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Answers
25.60 minus 8.96 is 16.64
the amount of the discount is 16.64
35*25.60=8.96
25.60-8.96=16.64
Discount=$16.64
I hope this helps;)
384,400
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2. 3 hundred thousand value 300,000
Part one: Arif and Keisha go to a restaurant. their meal cost 13.75. The sales tax is 5%
I got $0.69.
Part two: They want to leave a 15% tip based on the bill and tax combined. I got $2.17
Now the part 3 I need help with says Arif ordered a more expensive meal than Keisha after tax and tip are figured he decides he should pay $3.00 more than Keisha. How much should he pay?
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(13.75 + 5%) + 15% on top of that.
(13.75) + (0.69) + (2.17) = $16.60 .
If they split the bill equally, each would pay (1/2) (16.60) = $8.30 .
But Arif wants to pay $3 more than Keisha.
Just take $1.50 away from Keisha's half (leave $6.80),
and add it on to Arif's half (make it $9.80). Then their
total is the same, but his share is $3 more than her share.
$9.80 + $6.80 = $16.60
$ 9.80 - $6.80 = $ 3.00 .
Answers
The easiest way is to write down the length of each side, and then add up
the three numbers.
In fact, that's the ONLY way to find the perimeter. If anything else needs to
be done, that's usually because you don't know all three lengths yet, and
you have to find a missing length. Once you accomplish that, you ALWAYS
find the perimeter by adding them up.
side 1+ side 2+side 3= perimeter of the triangle