A rectangle with sides 7 and #x+2# has a perimeter of 40 units. What is the value of #x#?
Using our perimeter equation:
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The perimeter (( P )) of a rectangle is given by the formula:
[ P = 2 \times (\text{length} + \text{width}) ]
Given that the length of the rectangle is 7 units and the width is ( x + 2 ) units, we can write the equation for the perimeter as:
[ 40 = 2 \times (7 + x + 2) ]
Simplify and solve for ( x ):
[ 40 = 2 \times (9 + x) ]
[ 20 = 9 + x ]
[ x = 20 - 9 ]
[ x = 11 ]
Therefore, the value of ( x ) is 11 units.
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To find the value of ( x ), we use the formula for the perimeter of a rectangle, which is given by:
[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) ]
Given that one side of the rectangle is ( 7 ) units and the other side is ( x + 2 ) units, we can set up the equation:
[ 40 = 2 \times (7 + x + 2) ]
Simplify the expression inside the parentheses:
[ 40 = 2 \times (9 + x) ]
Now, distribute ( 2 ) across ( 9 + x ):
[ 40 = 18 + 2x ]
Subtract ( 18 ) from both sides of the equation:
[ 40 - 18 = 18 + 2x - 18 ] [ 22 = 2x ]
Finally, divide both sides by ( 2 ):
[ \frac{22}{2} = \frac{2x}{2} ] [ 11 = x ]
So, the value of ( x ) is ( 11 ) units.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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