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3 years ago

2x+6>2and 5x< 6 + 2x

Mathematics

1 answer:

LiRa [457]3 years ago

8 0

Answer:

-2 > x < 2

Step-by-step explanation:

Given that:

2x + 6 > 2

Subtracting 6 from both sides:

2x + 6 -6 > 2-6

2x > -4

Dividing by 2 on both sides:

x > -2

For second equation:

5x< 6 + 2x

Subtracting 2x from both sides:

5x - 2x < 6 + 2x -2x

3x < 6

Dividing by 3 on both sides:

x < 2

Result: -2 > x < 2

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The area of a right triangle is given by the expression:

lorasvet [3.4K]

The expression that models the length of the second leg of the triangle is 2x - 3.

Recall:

The area of a triangle = $\frac{1}{2} bh$

Given:

Area of triangle = $\frac{1}{2} (6x^2 - 7x - 3)$

Length of one of the legs = 3x + 1

Therefore, it means that multiplying both legs should give us:

$6x^2 - 7x - 3$

To find the expression that models the other leg, divide $6x^2 - 7x - 3$ by 3x + 1:

Thus:

$\frac{6x^2 - 7x - 3}{3x - 1}$

Factorize the numerator

$\frac{6x^2 - 2x - 9x - 3}{3x - 1}\\\\\frac{2x(3x - 1) - 3(3x - 1)}{3x - 1}\\\\\frac{(2x- 3)(3x - 1)}{3x - 1}$

Simplify

$\frac{(2x- 3)(3x - 1)}{3x - 1} = 2x- 3$

Therefore, the expression that models the length of the second leg of the triangle is 2x - 3.

Learn more here:

brainly.com/question/20712284

6 0

2 years ago

Drag the values to order them from least to greatest, with the least at the top.

GuDViN [60]

$\bf 4\pi \qquad \approx \qquad 12.57 \\\\[-0.35em] ~\dotfill\\\\ \sqrt{79}+\sqrt{63}\qquad \approx \qquad 8.89 + 7.94\implies 16.83 \\\\[-0.35em] ~\dotfill\\\\ \sqrt{143}\qquad \approx \qquad 11.96 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{11.96}{\sqrt{143}}\qquad \stackrel{12.57}{4\pi }\qquad \stackrel{16.83}{\sqrt{79}+\sqrt{63}}~\hfill$