Answer:
The numbers are 18 and 91
Step-by-step explanation:
You can translate the information to two equations:
<em>a value 5 times a smaller number is 1 less than a larger number</em>
5a = b - 1
<em>their difference is 73</em>
b - a = 73
Then you should merge one equation into the other, thereby eliminating one variable. You can do this any way you want. I choose to rewrite the first equation as:
b = 5a + 1
Now I can write 5a+1 in the second equation at the place where b was:
5a + 1 - a = 73
It is now an equation with only one variable, solve by simplifying
4a = 72
a = 18
Now b can be found using b = 5a + 1
b = 91
The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.
Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.
As p is a prime number, and 2 is the smallest prime number, so, p2
So, the positive divisors of the integer n are: 1,p,p².
As σ(n) represents the sum of all positive divisors of the integer n.
σ(n)=1+p+p²
In order to prove that σ(n) < 2n,for all n of the form n = p².
1+p+p²<2p²
p²-p-1>0
It is know that, p2.
So, p²-p-11
Thus, σ(n) < 2n holds true for all n of the form n = p².
Learn more about prime numbers here:
brainly.com/question/145452
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Answer:
B. (-3,1)
Step-by-step explanation:
From the graph, point P is 3 units to the left of x-axis and 1 unit to the positive side of y-axis
Let's solve your equation step-by-step.
−3x2−4x−4=0
Step 1: Use quadratic formula with a=-3, b=-4, c=-4.
x=
−b±√b2−4ac
2a
x=
−(−4)±√(−4)2−4(−3)(−4)
2(−3)
x=
4±√−32
−6
Answer:
No real solutions.
D.6x^2+3x+3, to find your answer combine like terms. ex: x^2 and 5x^2 have ^2 in common so combine to get 6x^2.