Please help!!! Will mark brainlist

Mathematics

1 answer:

Naddika [18.5K]3 years ago

5 0

Answer:

Not a Solution

Step-by-step explanation:

We are given two inequalities which are

y ≤ x -4 .............(i)

-x+3y>-4 ............(ii)

Also we are given an ordered pair which is (5, 1/3)

Now from this order pair we see that

x = 5 and y = 1/3

Because in an ordered pair the first element represents the x value while the second value represent the y value

Now to find whether this order pair satisfies the given inequality or not we have to plugin the values of x and y in both inequalities separately and see whether it satisfies the in equality or not

Taking First inequality:

which is

y ≤ x -4

Putting x = 5 and y = 1/3 in inequality

it becomes

$\frac{1}{3}$ ≤ 5 -4

$\frac{1}{3}$ ≤ 1 ∵ which is true

So this inequality holds the order pair

Taking second inequality:

which is

-x+3y> -4

Putting x = 5 and y = 1/3 in inequality

it becomes

-5+ $\frac{1*3}{3}$ > -4

-5+1 >-4

-4>-4 ∵ which is false because - 4 = - 4

So this inequality does not holds the order pair

So the order pair is not solution of the given inequalities because of the reason that second inequality is not satisfied

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$\bf \textit{using the pythagorean theorem}
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c^2=a^2+b^2
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
-------\\
c=2a\\
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b=5
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\\\\\\
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\\\\\\
\textit{and then we can \underline{rationalize the denominator} }
\\\\\\
a=\cfrac{5}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies a=\cfrac{5\sqrt{3}}{\sqrt{3^2}}\implies a=\cfrac{5\sqrt{3}}{3}$