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
$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$
$\mathrm{Combine\:the\:intervals}$
$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$
Answer:
-8+5√2 and -8-5√2
Step-by-step explanation:
Given the expression x² + 16x + 14 = 0
USing the general formulas
x = -16±√16²-4(14)/2
x = -16±√256-56/2
x = -16±√200/2
x = -16±10√2/2
x = -8±5√2
Hence the required solutions are -8+5√2 and -8-5√2
Answer: Summary: 1. Frequency is the number of times a result occurs, while “relative frequency” is the number of times the result occurs divided by the number of times the experiment is repeated. ... On the other hand, relative frequency is determined by using simple division
Step-by-step explanation:
Answer:
I guess that you want to know the transformations:
We start with:
f(x) = y = 4*x + 3
a)the transformed function is:
f(x) = y = -4*x - 3
So the sign changed.
This means that we go from (x, y) to (x, - y)
This is a reflection over the x-axis which changes the sin of the y component.
b) Now we go to f(x) = 4*x + 3
So the coefficient in the leading term changed.
This is a horizontal contraction:
A horizontal contraction of factor K for the function g(x) is: g(K*x)
In our case, we have:
f(K*x) = 4*(k*x) + 3 = x + 3
4*k*x = x
4*k = 1
k = 1/4
Then the transformation is an horizontal contraction of scale factor 1/4.
