Answer:
Infinite series equals 4/5
Step-by-step explanation:
Notice that the series can be written as a combination of two geometric series, that can be found independently:
The first one: 
is a geometric sequence of first term (
) "1" and common ratio (r) " 
", so since the common ratio is smaller than one, we can find an answer for the infinite addition of its terms, given by: 
The second one: 
is a geometric sequence of first term "1", and common ratio (r) " 
". Again, since the common ratio is smaller than one, we can find its infinite sum:
now we simply combine the results making sure we do the indicated difference: Infinite total sum= 
Answer:
1. AB ~= DF
2. Definition of Congruent
3. Reflexive Property of Congruency
4 BD=BD
6. AB+BD=AD; DF+BD=BF
7. Substitution Property of Equality
8. Definition of Congruent
Step-by-step explanation:
1. The given always goes first, and that's the first reason, so AB ~= DF must be the first statement (that should be the congruency symbol).
2. The definition of congruent is that if they are congruent then they are equal. Since that statement made two congruent lines equal, it must be the definition.
3. The reflexive property means something is congruent to itself, and BDis BD, therefore it is the reflexive property.
4. Remember if something is congruent then it is equal.
6. The segment addition postulate states that if we are given two points on a line segment, then AB+AC=AC.
7. In this statement AD was substituted for DF+BD. This can be done because of AB=DF and BD=BD as aforementioned.
8. If two things are congruent then they are equal by definition of congruency.
9514 1404 393
Answer:
18
Step-by-step explanation:
90 = 18·5
126 = 18·7
180 = 18·10
990 = 18·55
The greatest common factor of these numbers is 18.
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<em>Comment on the GCF</em>
It can be useful to know Euclid's algorithm for finding the GCF:
- Determine the remainder from dividing the larger number by the smaller.
- If the remainder is zero, the smaller number is the GCF. If the remainder is non-zero, use it to replace the larger number and repeat from step 1.
For example, 126 mod 90 = 36; 90 mod 36 = 18; 36 mod 18 = 0, so 18 is the GCF of 126 and 90. (The modulo function 'mod' returns the remainder from division.)
Answer:
4.5 > 4.420
0.67 < 0.8
0.82 = 0.820
62.4 > 6.24
0.13, 0.3, 0.303, 0.32
0.08, 0.8, 0.82, 8.2
24.54, 24.4, 24.304, 24.24
6.5, 6.25, 6.05, 6.007
Step-by-step explanation:
The most useful way to compare fractions is to add extra zeros at the end.
For example, 0.67 ___ 0.80.
0.80 is obviously bigger than 0.67.
In 24.4, 24.54, 24.304, 24.24, you can add extra zeros as well.
24.400, 24.540, 24.304, 24.240 (This makes it much easier to group the numbers, whether from largest to smallest or smallest to larger).
**REMEMBER TO REMOVE THOSE ZEROS AFTER FINDING YOUR FINAL ANSWER**
A+b is less than or equal to 50
