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Answer:
3×5×53
Step-by-step explanation:
You can use divisibility rules to find the small prime factors.
The number ends in 5, so is divisible by 5.
795/5 = 159
The sum of digits is 1+5+9 = 15; 1+5 = 6, a number divisible by 3, so 3 is a factor.
159/3 = 53 . . . . . a prime number,* so we're done.
795 = 3×5×53
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* If this were not prime, it would be divisible by a prime less than its square root. √53 ≈ 7.3. We know it is not divisible by 2, 3, or 5. We also know the closest multiples of 7 are 49 and 56, so it is not divisible by 7. Hence 53 is prime.
Answer: (5,3)
Step-by-step explanation:
the formula used for a reflection across the x-axis is (x,-y)
Answer:
a) SPAZ is equilateral.
b) Diagonals SA and PZ are perpendicular to each other.
c) Diagonals SA and PZ bisect each other.
Step-by-step explanation:
At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.
a) If figure is equilateral, then SP = PA = AZ = ZS:
![SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}](https://tex.z-dn.net/?f=SP%20%3D%20%5Csqrt%7B%5B4-%28-4%29%5D%5E%7B2%7D%2B%5B%28-2%29-%28-4%29%5D%5E%7B2%7D%7D)

![PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}](https://tex.z-dn.net/?f=PA%20%3D%20%5Csqrt%7B%286-4%29%5E%7B2%7D%2B%5B6-%28-2%29%5D%5E%7B2%7D%7D)



![ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}](https://tex.z-dn.net/?f=ZS%20%3D%20%5Csqrt%7B%5B-4-%28-2%29%5D%5E%7B2%7D%2B%28-4-4%29%5E%7B2%7D%7D)

Therefore, SPAZ is equilateral.
b) We use the slope formula to determine the inclination of diagonals SA and PZ:




Since
, diagonals SA and PZ are perpendicular to each other.
c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:








Then, the diagonals SA and PZ bisect each other.