1.) 4 - t = 3(t - 1) - 5
4 - t = 3t - 3 - 5
4 - t = 3t - 8
3t + t = 4 + 8
4t = 12
t = 12/4 = 3
2.) 8x - 2(x + 1) = 2(3x - 1)
8x - 2x - 2 = 6x - 2
6x - 2 = 6x - 2
0 = 0
solution is identity.
3.) 3(c - 2) = 2(c - 6)
3c - 6 = 2c - 12
3c - 2c = -12 + 6
c = -6
4.) 0.5(m + 4) = 3(m - 1)
0.5m + 2 = 3m - 3
3m - 0.5m = 2 + 3
2.5m = 5
m = 5/2.5 = 2
m = 2
Answer:
$637.95
Step-by-step explanation:
convert 8.5% to a decimal by dividing by 100:
8.5÷100= 0.085
then multiply.
587.98×(0.085)=49.97
now add.
587.98+49.97=<u>637.95</u>
65 sequences.
Lets solve the problem,
The last term is 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent
So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
Hence the number of sequences are 65.
Learn more about Sequences on:
brainly.com/question/12246947
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