Answer:
3
Step-by-step explanation:
It's given that ΔDEF ∼ΔXYZ . So the corresponding sides of both triangles will be proportional to each other.
DE = 4 ; XY = 4(n + 1) ; EF = 5 ; YZ = 7n - 1
Putting all these values gives ,
<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:
<em />
<em>STATEMENT REASON </em>
___________________________________________________
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
<em />
<em>Keywords: statement, length, reason, proof</em>
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9y+7 + 7y-19 = 180
Y =12 degrees
Answer:
5
Step-by-step explanation:
∛144 = 5.24148278842
5 is in the ones digit of the cube root of 144.
Answer:
a) 952
b) 136
Step-by-step explanation:
<u>Ratio of b:g = 3:4, based on this we have:</u>
- Number of boys = 3x
- Number of girls = 4x
- Total number of pupils = 3x+4x = 7x
<u>Number of spectacle wearers:</u>
- 1/3*3x + 3/8*4x = x + 3/2x = 2.5x
<u>Number of those not wearing spectacles:</u>
<u>And this number equals to 612, then we can find the value of x:</u>
- 4.5 x = 612
- x= 612/4.5
- x= 136
a) T<u>otal number of pupils:</u>
b)<u> The difference in the number of boys and girls:</u>
