<em>Answer:</em>
Complete proof is written below.
Facts and explanation about the segments shown in question :
- As BC = EF is a given statement in the question
- AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
- AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
- AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.
Below is the complete proof of the observation given in the question:
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<em>STATEMENT REASON </em>
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1. BC = EF 1. Given
2. AB + BC = AC 2. Betweenness
3. AC > BC 3. Def. of segment inequality
4. AC > EF 4. Def. of congruent segments
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<em>Keywords: statement, length, reason, proof</em>
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Answer:
Area of shape B = 312.5 cm²
Step-by-step explanation:
Ratio of Area of A : Area of B = 12² : 15²
Given that area of A is 200 cm², let the area of shape B = x
Therefore:
200:x = 12²:15²
200/x = 144/225
Cross multiply
144x = 200*225
144x = 45,000
x = 45,000/144
x = 312.5 cm²
Area of shape B = 312.5 cm²
Answer: x= -2/3
Step-by-step explanation:
Answer:
657kg
Step-by-step explanation:
405 ÷ 45 = 9
9 x 73 = 657kg
I hope this helps!
Answer:
Frank has $22.34.
Step-by-step explanation:
24 pennies - 0.01 x 24 = 0.24
62 nickels - 0.05 x 62 = 3.10
55 dimes - 0.10 x 55 = 5.50
16 quarters - 0.25 x 16 = 4.00
19 half dollar (50cent) - 0.50 x 19 = 9.50
0.24 + 3.10 + 5.50 + 4.00 + 9.50 = 22.34
