Answer:
x<6/5, x>14/5
Step-by-step explanation:
Steps
$5\left|x-2\right|+4>8$
$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$
$5\left|x-2\right|+4-4>8-4$
$\mathrm{Simplify}$
$5\left|x-2\right|>4$
$\mathrm{Divide\:both\:sides\:by\:}5$
$\frac{5\left|x-2\right|}{5}>\frac{4}{5}$
$\mathrm{Simplify}$
$\left|x-2\right|>\frac{4}{5}$
$\mathrm{Apply\:absolute\:rule}:\quad\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad\mathrm{or}\quad\:u\:>\:a$
$x-2<-\frac{4}{5}\quad\mathrm{or}\quad\:x-2>\frac{4}{5}$
Show Steps
$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$
Show Steps
$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$
$\mathrm{Combine\:the\:intervals}$
$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$
We know that the price of all the fabrics is the same. However, the length of the fabrics is different. We have to determine which fabric is the longest.
Option A:
= 8.6
Option B:
= 8.25
Option C:
= 8.6667
Option D:
= 7.33....
Hence, the longest fabric is the one given in option C, and its length is 8.6667
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
Answer:
1.45 m
Step-by-step explanation:
Convert 1.5 metre into cm
1.5 metre =150 center meters
150 cm -5=145
145 into metres is 1.45 m
Answer:
Slope = 5/3
Step-by-step explanation:
See attached image