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3 years ago

X — 5 < 3 OR x – 5 > 8

Mathematics

2 answers:

Vlad1618 [11]3 years ago

8 0

Answer:

x<8 or x>13

Step-by-step explanation:

x-5 < 3

x < 3 + 5

x <8

x – 5 > 8

x > 8 +5

x >13

combining the two, the combined answer for x is

x<8 or x>13

inessss [21]3 years ago

6 0

Answer:

Step-by-step explanation:

Isolate x on one side of the equation.

x-5<3 and x-5>8

x-5<3

x-5+5<3+5 (First, add 5 from both sides.)

3+5 (Solve.)

3+5=8

x<8

x-5>8

x-5+5>8+5 (Add 5 from both sides.)

8+5 (Solve.)

8+5=13

x>13

The correct answer is x<8 and x>13.

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$\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad 
radius=\stackrel{}{ r}\\\\
-------------------------------\\\\
(x+1)^2+y^2=36\implies [x-(\stackrel{h}{-1})]^2+[y-\stackrel{k}{0}]^2=\stackrel{r}{6^2}~~~~
\begin{cases}
\stackrel{center}{(-1,0)}\\
\stackrel{radius}{6}
\end{cases}$

so, that's the equation of the circle, and that's its center, any point "ON" the circle, namely on its circumference, will have a distance to the center of 6 units, since that's the radius.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
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\\\\\\
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$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\\\\\\
\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(6-0)^2}\implies d=\sqrt{(-1+1)^2+6^2}
\\\\\\
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$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})
\\\\\\
\stackrel{distance}{d}=\sqrt{[4-(-1)]^2+[-8-0]^2}\implies d=\sqrt{(4+1)^2+(-8)^2}
\\\\\\
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notice, C is farther than the radius 6, meaning is outside the circle, hiking about on the plane.

3 0

3 years ago

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