Which is the independent and which is the dependent?
2 answers:
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<h2>Steps:</h2>
(Let x = greater number and y = lesser number)
So this question is asking us for a system of equations. Using the info they provide, we can form these two equations:
So for this, we will be using the substitution method. Since we know that x = y + 7, substitute x with (y + 7) in the second equation as such:
From here we can solve for y. Firstly, distribute 3 so that it multiplies with y and 7:
Next, subtract 3y on both sides of the equation:
Lastly, subtract 5 on both sides of the equation:
Now that we know the value of y, we can substitute it into either equation to solve for x:
<u>In short, 16 is the lesser number and 23 is the greater number.</u>
begin by pulling 2 out of the numerator using the distributive property.
numerator: 2(16x^4 - 25) and now factor
numerator: 2(4x^2 - 5)(4x^2 + 5)
Now go to the denominator. It looks messy but it will break down.
Pull out 4x^2 for the first two terms and 5 for the last 2 terms. Use the distributive property.
denominator: 4x^2(x - 3) - 5(x - 3) now x - 3 is the common term.
denominator: (x - 3)(4x^2 - 5)
Put the two results together.
After canceling out 4x^2 - 5 on both the numerator and the denominator, you are left with.