Answer:
- 891 = 3^4 · 11
- 23 = 23
- 504 = 2^3 · 3^2 · 7
- 230 = 2 · 5 · 23
Step-by-step explanation:
23 is a prime number. That fact informs the factorization of 23 and 230.
The sums of digits of the other two numbers are multiples of 9, so each is divisible by 9 = 3^2. Dividing 9 from each number puts the result in the range where your familiarity with multiplication tables comes into play.
891 = 9 · 99 = 9 · 9 · 11 = 3^4 · 11
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504 = 9 · 56 = 9 · 8 · 7 = 2^3 · 3^2 · 7
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230 = 10 · 23 = 2 · 5 · 23
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<em>Comment on divisibility rules</em>
Perhaps the easiest divisibility rule to remember is that a number is divisible by 9 if the sum of its digits is divisible by 9. That is also true for 3: if the sum of digits is divisible by 3, the number is divisible by 3. Another divisibility rule fall out from these: if an even number is divisible by 3, it is also divisible by 6. Of course any number ending in 0 or 5 is divisible by 5, and any number ending in 0 is divisible by 10.
Since 2, 3, and 5 are the first three primes, these rules can go a ways toward prime factorization if any of these primes are factors. That is, it can be helpful to remember these divisibility rules.
Hello!
1) A and D
The radius is the distance from the center of a circle to any part of the edge. Both A and D have a radius of three, regardless of what direction they go.
2) 5"
In circle C we see that there is a line segment that is 5" that goes from the center to the edge, or the radius.
3) C
The different variables are representing different points on the circles. The circle that contains a line connecting C and L is circle C.
4) BN
Circle B contains a radius that is the distance from B to N, or BN.
5) EF
The diameter is the distance of a straight line that was pass through the middle of a circle, or its width. The diameter is double the radius. In circle A we see that line EF passes through the center put goes all the way across the circle.
6)IJ
Line IJ isn't even linear, so it could not be the radius. Both AG and BH are straight lines that represent the radius.
7) 6"
The diameter is always twice the radius. In circle A the radius is 3, so the diameter is 6.
8) A and D
Just as we said in the first answer, A and D both have a radius that measures 3 inches.
I hope this helps!
The difference between the highest and lowest temperature is 85°F.
