Question
A class of 45 students has a total weight of 1080 kg.
Two students with weights 22 kg and ‘z’ kg leave the class, and a new student with weight (3z + 12) kg joins. The average weight of the class rises by 1 kg. What is the weight of the new student?Solution
ATQ,
Initial average = 1080 / 45 = 24 kg Final average = 24 + 1 = 25 kg Final number of students = 45 – 2 + 1 = 44 Final total weight = 25 × 44 = 1100 kg According to the question, 1080 – 22 – z + (3z + 12) = 1100 ⇒ 1058 + 2z + 12 = 1100 ⇒ 1070 + 2z = 1100 ⇒ 2z = 1100 – 1070 = 30 ⇒ z = 30 / 2 = 15 Weight of new student = 3z + 12 = 3 × 15 + 12 = 45 + 12 = 57 kg
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 37x² - 172x + 135 = 0
Equation 2: 29y² - 132y + ...
I. p2 - 19p + 88 = 0
II. q2 - 48q + 576 = 0
For what real value(s) of k does the quadratic equation - x² − (k + 3)x + 2k = 0, have equal real roots?
I. x2 – 12x + 32 = 0
II. y2 + y - 20 = 0
I. 195x² - 46x - 21 = 0
II. 209y² + 13y - 12 = 0
I. x² - (16)2 = 0
II. 2y - 14 = 0
Solve for x: |2x − 5| + |x + 1| ≤ 10.
I. 9x2 + 45x + 26 = 0
II. 7y2 – 59y − 36 = 0
Roots of the quadratic equation 2x2 + x – 528 = 0 is
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