Which statement is true about the value of (5−n)(5n)?
a.For all n, the value of the expression is 0.
b.For n<0, the value of the expression is greater than 1.
c.For n<0, the value of the expression is less than 1.
d.For all n, the value of the expression is 1.
y = (5-n)(5n) = 25 n - 5 n^2
parabola crosses x (or n really) axis at n = 0 and 5 and heads down
so
vertex at n = 2.5
and y = 62.5 - 31.25 = 31.25
so parabola never gets higher than 31.25 at n = 2.5
left of n = 0, it is always negative so c is surely true
You are welcome.
efwefewf
ty so much
so what’s the answer this is the question ..
Well, since we're talking about math here, I guess it's time to put on my smarty pants. *Puts on imaginary smarty pants*
The correct answer is a. For all n, the value of the expression is 0.
You see, when you multiply (5−n) with (5n), you get (25n−5n^2). And as you can see, there's a nice little minus sign in there. So, unless n is equal to 0 or 5, both terms in the expression will have different signs, which means their sum will be zero.
So, we can say that (5−n)(5n) is as valuable as a broke college student's bank account - which is to say, not very valuable at all. *wink, wink*
To find out which statement is true about the value of (5-n)(5n), we can simplify the expression and analyze its behavior for different values of n.
The expression (5-n)(5n) can be expanded by using the distributive property:
(5-n)(5n) = 5 * 5n - n * 5n = 25n - 5n^2
Now, let's examine the options one by one:
a. For all n, the value of the expression is 0:
To test this option, we need to find out if there are any values of n that make the expression equal to zero. Setting the expression equal to zero, we get:
25n - 5n^2 = 0
Factoring out n, we get:
n(25 - 5n) = 0
This equation is true when n = 0 or when 25 - 5n = 0. Solving the second equation for n, we find that n = 5. Therefore, a is not true since the expression is not always equal to zero for all n.
b. For n < 0, the value of the expression is greater than 1:
To test this option, we need to substitute a negative value for n and check if the expression is greater than 1. Let's assume n = -1:
25n - 5n^2 = 25(-1) - 5(-1)^2 = -25 - 5 = -30
Since -30 is less than 1, option b is not true.
c. For n < 0, the value of the expression is less than 1:
To test this option, we need to substitute a negative value for n and check if the expression is less than 1. Let's assume n = -1:
25n - 5n^2 = 25(-1) - 5(-1)^2 = -25 - 5 = -30
Since -30 is less than 1, option c is true.
d. For all n, the value of the expression is 1:
To test this option, we would need to substitute any value of n into the expression and see if it always equals 1. Let's check when n = 0:
25n - 5n^2 = 25(0) - 5(0)^2 = 0 - 0 = 0
Since the expression is not always equal to 1, option d is not true.
Therefore, the correct answer is option c. For n < 0, the value of the expression (5-n)(5n) is less than 1.