Answer:
a. 3 times the sum of a number and 3 equals 9
b. 5 less than the product of 4 times a number equals 11
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Answer: There were 10 students in the class on the first day.
Step-by-step explanation:
Let x be the number of students of the first day.
Given: A college writing seminar increased its size by 50 percent from the first to the second day.
i.e. Number of students on second day = (Number of students on first day)+(50% of Number of students on first day)
= x +50% of x
= x+0.50x
= (1.50)x
=1.50x
Since, it is given that the total number of students in the seminar on the second day was 15.
i.e. 

Hence, there were 10 students in the class on the first day.
Answer:
Solution
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m
2
−3m−1=0
m
2
−3m=1 → (1)
Third term =(
2
1
coeeficientofm)
2
(
2
1
×(−3))
2
=(
2
−3
)
2
=
4
9
Adding
4
9
to both sides of equation (1), we get
m
2
−3m+
4
9
=1+
4
9
∴ m
2
−3m+
4
9
=
4
4+9
∴ (m−
2
3
)
2
=
4
13
Taking square roots on both sides
∴ m−
2
3
=±
2
13
∴ m=
2
3
+
2
13
or m=
2
3
−
2
13
m=
2
3+
13
,
2
3−
13
are the roots of the given quadratic equation.