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Least Common Denominator

Math 70 Final Exam Solutions

 (e) Note the order of operations :

5 − 2(7 − 4)^2 = 5 − 2(3)^2 ( Operations inside parenthesis first)
= 5 − 2(9) ( Exponents )
= 5 − 18 ( Multiplication )
= −13 (Subtraction)


2. Gas Mileage = 157.2 รท 6 = 26.2 So, the gas mileage is 26.2 miles per gallon.

3. Here’s a diagram with variables

Unknowns :
  Width = w
  Length = 4 + 3w 

Equation:

(w) + (w) + (4 + 3w) + (4 + 3w) = 40 (Perimeter = Sum of all sides )
-> 8w + 8 = 40 (Combining like terms )
8w = 32 ( Subtracting 8 from both sides)
w = 4 ( Dividing both sides by 8)

 So, the width of the chocolate bar is 4 feet and the length is 4 + 3(4) = 16 feet.
4. (a)

5x − 5.1 = 3x − 2.3 -> 2x − 5.1 = −2.3 (Subtracting 3x from both sides)
2x = 2.8 (Adding 5.1 to both sides)
x = 1.4 (Dividing both sides by 2)


 Note that −2.3 + 5.1 = 2.8   since  5.1 − 2.3 = 2.8.

Check:
 Left-side of equation: 5(1.4) − 5.1 = 7 − 5.1 = 1.9
 Right- side of equation : 3(1.4) − 2.3 = 4.2 − 2.3 = 1.9

(b)

 y + 2y + 7 = 1 3y + 7 = 1 (Combining like terms on the left -side)
3y = −6 (Subtracting 7 from both sides)
y = −2 (Dividing both sides by 3)

Check:
Left-side of equation: −2 + 2(−2) + 7 = −2 − 4 + 7 = 1
Right-side of equation: 1 3

5. The tax on the hybrid car will be 22, 000(0.08) = 1760 dollars. So, the total bill will be 22, 000 + 1760 = 23, 760 dollars.

7. Moving the decimal in 4.498 by 9 digits to the right: Distance = 4,498,000,000 kilometers

8. (a)

(3x^2 − 2x) − (−x^2 + 5x) = (3x^2 − 2x) + (x^2 − 5x) ( Changing the problem into
addition by changing the signs of the 2nd polynomial)
= 3x^2 + x^2 − 2x − 5x  
= 4x^2 − 7x (Combining like terms)

   (b)

(FOIL)
(Combining like terms)

  (c)

( Distributing 3x)
 
(Combining like terms)

9.
The area of the sail is A =1/2 (8)(6) =1/2 (48) = 24 square feet .
  
So, the total cost will be 24(2.50) = 60 dollars.

10.
For the point (3,−1), move 3 units to the right and 1 unit down from the origin.

 For the point (−2, 0), move 2 units left from the origin.

 

For the point (0,3/2), move 1 and a half units up from the origin.

(Note:3/2 = 1+1/2 or 1.5)

11.(a)

 
 
(Subtracting 4 from each side.)
(Mult. both sides by 2 or div. by 1/2)

So, the complete ordered pair is (1 , 2).

  (b)

 
 
(Subtracting 3 from each side.)
(Dividing both sides by 4)

So, the complete ordered pair is ( 1/2 , 6).

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