T(d)= 2(d-1) + 30
T(6)= 2(6-1) + 30
= 40 mins
6x² + 11x - 35 = (3x - 5)(2x + 7)
=> (3x - 5)(2x + 7)/(3x - 5)
i.e. 2x + 7...........as the 3x - 5 term cancels.
Answer: a. Area b. 4222.26
Answer:
83.15
Step-by-step explanation:
Joey's current grade can be determined by weighting his scores with the weights given and adding the results
Tests = 0.6 x 82 = 49.2
Quizzes = 0.25 x 77 = 19.25
homework = 0.15 x 98 = 14.7
49.2 + 19.25 + 14.7 = 83.15
<u>Hint </u><u>:</u><u>-</u>
- Break the given sequence into two parts .
- Notice the terms at gap of one term beginning from the first term .They are like
. Next term is obtained by multiplying half to the previous term . - Notice the terms beginning from 2nd term ,
. Next term is obtained by adding 3 to the previous term .
<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>
We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,
.
We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,
Notice the term
will be too small , so we can neglect it and take its approximation as 0 .

Now the second sequence is in Arithmetic Progression , with common difference = 3 .
![\implies S_2=\dfrac{n}{2}[2a + (n-1)d]](https://tex.z-dn.net/?f=%5Cimplies%20S_2%3D%5Cdfrac%7Bn%7D%7B2%7D%5B2a%20%2B%20%28n-1%29d%5D%20)
Substitute ,
![\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}](https://tex.z-dn.net/?f=%5Cimplies%20S_2%3D%5Cdfrac%7B25%7D%7B2%7D%5B2%284%29%20%2B%20%2825-1%293%5D%20%3D%5Cboxed%7B%20908%7D%20)
Hence sum = 908 + 1 = 909