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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

Guest Jul 1, 2017

Best Answer 

 #1
avatar+1088 
+2

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.
\(14\)  
   
TheXSquaredFactor  Jul 2, 2017
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1+0 Answers

 #1
avatar+1088 
+2
Best Answer

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.
\(14\)  
   
TheXSquaredFactor  Jul 2, 2017

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