Step-by-step explanation:
the lowest common denominator (LCD) is the lowest common multiple (LCM) of the denominator numbers (the ones at the bottom of the fractions).
finding the LCM of 9 and 12 using the prime factor method :
9 = 3×3
12 = 2×2×3
the LCM is the combination of the longest chains per prime factor. which means we have 2×2 and 3×3 as longest chains for 2 and 3.
LCD = LCM = 2×2×3×3 = 36
2/9 turns into x/36 by multiplying by 4/4 :
2/9 × 4/4 = 8/36
5/12 turns into x/36 by multiplying by 3/3 :
5/12 × 3/3 = 15/36
so, the third answer option is correct.
Answer:
see explanation
Step-by-step explanation:
The measure of arc MP = 360° - measure of arc PM, that is
arc MP = 360° - 210° = 150°
x is half the measure of the intercepted arc MP, thus
x = 0.5 × 150 = 75
Answer: C) similar, SAS similarity, triangle LQR
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Explanation:
The vertical angles KLJ and QLR are congruent. This forms the "A" in "SAS". The angles in question are between the marked sides.
KL = 18 is twice that of QL = 9, or put another way, KL/QL = 18/9 = 2. The ratio of the sides is 2. Also, JL/RL = 16/8 = 2 is the same ratio. Because both pairs of sides have the same ratio, the sides are in proportion. This helps form the two "S" letters of "SAS".
The original triangle has LKJ mentioned at the top. Note the order as its important. We start with L and move to K, so LK is the first segment mentioned. LK = 18 pairs up with LQ = 9, meaning that LQ must be the first segment mentioned of the answer triangle. Therefore LQR is the correct letter sequence if we start with point L. Writing QLR is not correct because Q is the first letter here but Q does not pair up with L.
6+7+3 =16
7+9+7 =23
9+6+7=22
6+8+1=15
