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(3x + 4)2 = 14
(3x + 4)2 means that 2 will multiply both 3x and 4
2 * 3x = 6x 2 * 4 = 8
6x + 8 = 14
Move +8 to the other side of the equation
6x = 14 - 8 Note : Moving +8 to the other side will change the sign in front of it, that is from + to -
6x = 14 - 8
6x = 6
Divide both sides by 6 because of the 6 beside the x : 6x
6x/6 = 6/6
x = 1
d) Alternate interior angle to angle 3 is angle 6.
e) Alternate exterior angle of angle 7 is angle 2
In probability problems, look out for the word OR and AND.
OR means adding the probability
AND means multiplying the probability
P(a) = P(jack) + P(queen) + P(king) = (4/52) + (4/52) + (4/52) = 12/52 = 3/13
P(b) = [P(9) + P(10) + P(jack)] × P(red) = [(4/52) + (4/52) + (4/52)] × (26/52)
P(b) = (12/52) × (26/52) = 3/26
P(c) = 13/52 = 1/4
P(d) = P(a diamond) + P(a heart) + P(a spade) = (13/52) + (13/52) + (13/52) = 3/4
<span>How did the equation 2t + 16 ≤ 30 came about?
The left side of the equation, 2t + 16, represents Alex's expenses. 16 stands for the admission and lunch ( 8+8 = 16) and 2t stands for 't' tickets times 2, since each costs $2. The right side of the equation is the limit expense which is equal to 30. Lastly, the inequality stands for 'less than or equal to'. Solving the equation,
2t </= 30 - 16
2t </= 14
t </= 7
This means that Alex should only get less than or equal to 7 tickets. Particularly, Alex is only limited to 7 tickets. The answer is letter B.</span>
