The sum of the two numbers is equal to 70.
- Let the first number be x.
- Let the second number be y.
In this exercise, you're required to find two numbers by translating the word problem into an algebraic expression and then solving for the unknown variables (x and y).
Translating the word problem into an algebraic expression, we have;
Two numbers differ by 8:
....equation 1.
The product of the two numbers is 713:
....equation 2.
To calculate the sum of the two numbers:
First of all, we would solve for each of the unknown variables (x and y).
From eqn. 1, we have:
....equation 3.
Substituting eqn. 3 into eqn. 2, we have:
![y(y+8)=713\\\\y^2+8y=713\\\\y^2+8y-713=0](https://tex.z-dn.net/?f=y%28y%2B8%29%3D713%5C%5C%5C%5Cy%5E2%2B8y%3D713%5C%5C%5C%5Cy%5E2%2B8y-713%3D0)
Solving the quadratic equation by factorization, we have:
![y^2-31y +23y-713=0\\\\y(y-31)+23(y-31)=0\\\\(y+23)(y-31)=0](https://tex.z-dn.net/?f=y%5E2-31y%20%2B23y-713%3D0%5C%5C%5C%5Cy%28y-31%29%2B23%28y-31%29%3D0%5C%5C%5C%5C%28y%2B23%29%28y-31%29%3D0)
y = -23 or 31.
For the value of x, when y = 31:
![x=8+31](https://tex.z-dn.net/?f=x%3D8%2B31)
x = 39
Now, we can calculate the sum of the two numbers:
![x+y=39+31=70](https://tex.z-dn.net/?f=x%2By%3D39%2B31%3D70)
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Nothing, because copper has an extremely weak magnetic field. So if you were to perhaps take a magnet and place it next to a magnet, it wouldn't work. Since copper isn't magnetic.
Answer:
my answer is A.................
5.2 gallons you multiply 20*.26
The property that must be used in all the proofs is: logb(b^y) =y
<h3>What are the proofs or rules of logarithms?</h3>
The proofs are statements that are used to validate or invalidate a logarithmic expression
There are several proofs of logarithms; some of them are:
- Product rule
- Quotient rule
- Power rule
- Change of base
The common property in the first three proofs (listed above) is:
![\log_b(b^y) =y](https://tex.z-dn.net/?f=%5Clog_b%28b%5Ey%29%20%3Dy)
This is so because, it links all the three proofs
Read more about equations at:
brainly.com/question/14323743