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3 years ago

Which graph shows the correct representation of {x | x ≤ 5}?

Mathematics

1 answer:

Andrew [12]3 years ago

3 0

Answer:

third choice

Step-by-step explanation:

That would be the third one. It has to be a closed circle because it includes the sign, ≤ meaning that it also has the number 5 included. The numbers that go to the left of 5 are smaller, too.

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Step-by-step explanation:

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2 years ago

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Which ordered pair is a solution of linear equations?

Bingel [31]

Answer:

$\{\frac{2}{3}, \frac{1}{5}\}$

ordered pair is the Solution to the given System.

Step-by-step explanation:

Given:

$\frac{1}{2}x- \frac{3}{4}y= \frac{11}{60} ...........Equation( 1 )\\ \\\frac{2}{5}x+ \frac{1}{6}y= \frac{3}{10} ...........Equation( 2 )\\$

To Check:

Which ordered pair is the Solution to the given System. ?

Solution:

If $\{\frac{2}{3}, \frac{1}{5}\}$

is the Solution then it must satisfy the given equation. i.e .Left Hand Side (L.H.S) must be Equal to Right Hand Side (R.H.S) of both the given equation for

$\{x=\frac{2}{3}, y=\frac{1}{5}\}$

∴ For Equation ( 1 )

$L.H.S=\frac{1}{2}\times \frac{2}{3}- \frac{3}{4}\times \frac{1}{5}\\\\\\=\frac{1}{3} -\frac{3}{20} \\\\=\frac{20-9}{20\times 3}\\\\ =\frac{11}{60} \\= R.H.S$

∴ Left Hand Side = Right Hand Side

Hence,

$\{x=\frac{2}{3}, y=\frac{1}{5}\}$

The solution.

∴ For Equation ( 2 )

$L.H.S=\frac{2}{5}\times \frac{2}{3}+ \frac{1}{6}\times \frac{1}{5}\\\\\\=\frac{4}{15} -\frac{1}{30} \\\\=\frac{120+15}{15\times 30}\\\\= \frac{135}{450}\\ \\\\=\frac{3}{30}\\ \\= R.H.S$

∴ Left Hand Side = Right Hand Side

Hence ,

$\{x=\frac{2}{3}, y=\frac{1}{5}\}$

The solution.

For other Solutions we do not have Left Hand Side equal to Right Hand Side.

i.e Left Hand Side ≠ Right Hand Side

Hence Not a Solution.

5 0

3 years ago