2 1/4 - 1 2/3 as a mixed number?
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Question: An aquarium is on sale for $59.50. If this price represents a 15% discount from the original price, what is the original price?
First, you multiply the sale price and the 15% discount
![$59.50*.15 = [tex]$8.92](https://tex.z-dn.net/?f=%2459.50%2A.15%20%3D%20%5Btex%5D%248.92)
[/tex] (To change the percent to a decimal, you take out the percentage sign and divide by 100)
Now add $59.50 to $8.92
Answer:
$68.43 (when rounded to the nearest cent)
or
$68 (when rounded to the nearest dollar)
or
$70 (when rounded to the nearest ten dollar)
First, you multiply the sale price and the 15% discount
Now add $59.50 to $8.92
Answer:
$68.43 (when rounded to the nearest cent)
or
$68 (when rounded to the nearest dollar)
or
$70 (when rounded to the nearest ten dollar)
Consider the contrapositive of the statement you want to prove.
The contrapositive of the logical statement
<em>p</em> ⇒ <em>q</em>
is
¬<em>q</em> ⇒ ¬<em>p</em>
In this case, the contrapositive claims that
"If there are no scalars <em>α</em> and <em>β</em> such that <em>c</em> = <em>α</em><em>a</em> + <em>β</em><em>b</em>, then <em>a₁b₂</em> - <em>a₂b₁</em> = 0."
The first equation is captured by a system of linear equations,
or in matrix form,
If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be
and this is what we wanted to prove. QED