Evaluate the algebraic expressions below (no decimal answers)
1. N^2 - 25 a) when n=-10 b) when n=-5 c) when n=1/2 d) when n=9
2. (-7d + 14)/2 a) when d=2 b) when d=-2 c) when d= 6/7 d) when d=4
3. 2x^-2 - x a) when x=2 b) when x=-1 c) when x= 1/4
+2440 Evaluating these algebraid expressions just requires you to substitute in the values given for the variable. Let's do the first one together:
1. \(N^2-25\)
a) When n=-10
| \(N^2-25\) | Replace N, the variable, with -10 and evaluate from there. |
| \((-10)^2-25\) | Do \((-10)^2=-10*-10=100\) first so to adhere to the order of operations. |
| \(100-25\) | |
| \(75\) | |
The process repeats for the other values for N.
b) n=-5
| \(N^2-25\) | |
| \((-5)^2-25\) | |
| \(25-25\) | |
| \(0\) | |
c) n=1/2
| \(N^2-25\) | |
| \((\frac{1}{2})^2-25\) | Remember that squaring a fraction follows the rule that \((\frac{a}{b})^2=\frac{a^2}{b^2}\) |
| \(\frac{1^2}{2^2}-25\) | Simplify the fraction. |
| \(\frac{1}{4}-25\) | Change 25 to an improper fraction so that you can subtract it from 1/4. |
| \(\frac{25}{1}*\frac{4}{4}=\frac{100}{4}\) | Now that we have changed 25 to a fraction with a common denominator, reinsert it back into the equation. |
| \(\frac{1}{4}-\frac{100}{4}\) | Subtract the fractions. |
| \(-\frac{99}{4}=-24\frac{3}{4}\) | The fraction is already in simplest form. I've provided both versions of the answer. |
d) n=9
| \(N^2-25\) | |
| \(9^2-25\) | |
| \(81-25\) | |
| \(56\) | |
I'll do half of the next one and the rest are up to you to complete:
2. \(\frac{-7d+14}{2}\)
a) d=2
| \(\frac{-7d+14}{2}\) | Substitute the given value for d, 2. |
| \(\frac{-7*2+14}{2}\) | Do -7*2 first. |
| \(\frac{-14+14}{2}\) | Simplify the numerator by calculating -14+14. |
| \(\frac{0}{2}=0\) | |
b) d=-2
| \(\frac{-7d+14}{2}\) | |
| \(\frac{-7*-2+14}{2}\) | A negative times a negative always results in a positive. |
| \(\frac{14+14}{2}\) | |
| \(\frac{28}{2}\) | Divide 28 by 2. |
| \(14\) | |
+2440 Evaluating these algebraid expressions just requires you to substitute in the values given for the variable. Let's do the first one together:
1. \(N^2-25\)
a) When n=-10
| \(N^2-25\) | Replace N, the variable, with -10 and evaluate from there. |
| \((-10)^2-25\) | Do \((-10)^2=-10*-10=100\) first so to adhere to the order of operations. |
| \(100-25\) | |
| \(75\) | |
The process repeats for the other values for N.
b) n=-5
| \(N^2-25\) | |
| \((-5)^2-25\) | |
| \(25-25\) | |
| \(0\) | |
c) n=1/2
| \(N^2-25\) | |
| \((\frac{1}{2})^2-25\) | Remember that squaring a fraction follows the rule that \((\frac{a}{b})^2=\frac{a^2}{b^2}\) |
| \(\frac{1^2}{2^2}-25\) | Simplify the fraction. |
| \(\frac{1}{4}-25\) | Change 25 to an improper fraction so that you can subtract it from 1/4. |
| \(\frac{25}{1}*\frac{4}{4}=\frac{100}{4}\) | Now that we have changed 25 to a fraction with a common denominator, reinsert it back into the equation. |
| \(\frac{1}{4}-\frac{100}{4}\) | Subtract the fractions. |
| \(-\frac{99}{4}=-24\frac{3}{4}\) | The fraction is already in simplest form. I've provided both versions of the answer. |
d) n=9
| \(N^2-25\) | |
| \(9^2-25\) | |
| \(81-25\) | |
| \(56\) | |
I'll do half of the next one and the rest are up to you to complete:
2. \(\frac{-7d+14}{2}\)
a) d=2
| \(\frac{-7d+14}{2}\) | Substitute the given value for d, 2. |
| \(\frac{-7*2+14}{2}\) | Do -7*2 first. |
| \(\frac{-14+14}{2}\) | Simplify the numerator by calculating -14+14. |
| \(\frac{0}{2}=0\) | |
b) d=-2
| \(\frac{-7d+14}{2}\) | |
| \(\frac{-7*-2+14}{2}\) | A negative times a negative always results in a positive. |
| \(\frac{14+14}{2}\) | |
| \(\frac{28}{2}\) | Divide 28 by 2. |
| \(14\) | |
