What is the simplified form of each expression?
2 answers:
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Answer: The area of the parallelogram is:
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in² = 1174 ⅛ in² = 1174.125 in² .
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Explanation:
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Area of a parallelogram:
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A = base * height = b * h ;
From the figure (from the actual "question"):
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b = 50.5 in.
h = 23.25 in.
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Method 1) A = b * h =
= (50.5 in) * (23.25 in) = 1174.125 in² ; or, write as: 1174 <span>⅛ .
</span>____________________________________________________________
Method 2) A = b * h =
= (50 ½ in) * (23 <span>¼ in) =
= (</span>
in) * (
<span> in) ;
</span>___________________________________________________________
Note: "50 ½ " = [(50*2) + 1 ] / 2 = ;
Note: "23 ¼ " = [(23*4) + 1 ] / 4 = ;
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→ A = ( in) * ( in) ;
→ A =
in² = in² ;
→ A = (9393/8) in² =
→ A = in² = 1174 ⅛ in² = 1174.125 in² .
________________________________________________________
_______________________________________________________
_______________________________________________________
Explanation:
_______________________________________________________
Area of a parallelogram:
_______________________________________________________
A = base * height = b * h ;
From the figure (from the actual "question"):
_______________________________________
b = 50.5 in.
h = 23.25 in.
____________________________________________________________
Method 1) A = b * h =
= (50.5 in) * (23.25 in) = 1174.125 in² ; or, write as: 1174 <span>⅛ .
</span>____________________________________________________________
Method 2) A = b * h =
= (50 ½ in) * (23 <span>¼ in) =
= (</span>
</span>___________________________________________________________
Note: "50 ½ " = [(50*2) + 1 ] / 2 =
Note: "23 ¼ " = [(23*4) + 1 ] / 4 =
____________________________________________________________
→ A = (
→ A =
→ A = (9393/8) in² =
→ A =
________________________________________________________
Answers:
- Domain is (-4, 3]
- Range is (-5, 5]
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Explanation:
The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that . It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).
The interval then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.
It says: x is between -4 and 3. It can't equal -4 but it can equal 3.
So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.
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The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.
The range as a compound inequality is . This condenses into the shorthand of (-5, 5] which is the range in interval notation.
Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.