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2 years ago

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PLEASE HELP !!!!! (40 POINTS!!!!)

1 answer:

AfilCa [17]2 years ago

7 0

Answer:

you gayyy

Step-by-step explanation:

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For what values of $x$ is $$\frac{x^2 + x + 3}{2x^2 + x - 6} \ge 0?$$ note: be thorough and explain why all points in your answe

Rus_ich [418]

To solve the inequality $\frac{x^2+x+3}{2x^2+x-6}\ge \:0$

$\mathrm{Factor\:the\:left\:hand\:side\:}\frac{x^2+x+3}{2x^2+x-6}:$

The numerator $x^2+x+3$ is not factorizable.

so factor the denominator $2x^2+x-6$ :

$2x^2+x-6=\left(2x^2-3x\right)+\left(4x-6\right)=x\left(2x-3\right)+2\left(2x-3\right)\\ \mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-3x\mathrm{:\quad }x\left(2x-3\right)\\ \mathrm{Factor\:out\:}2\mathrm{\:from\:}4x-6\mathrm{:\quad }2\left(2x-3\right)\\$

Now take $\mathrm{Factor\:out\:common\:term\:}\left(2x-3\right)$

Then we get factor of the denominator as $\left(2x-3\right)\left(x+2\right)$

Thus $\frac{x^2+x+3}{2x^2+x-6}=\frac{x^2+x+3}{\left(x+2\right)\left(2x-3\right)}$

Now $\mathrm{Compute\:the\:signs\:of\:the\:factors\:of\:}\frac{x^2+x+3}{\left(x+2\right)\left(2x-3\right)}\\$

Signs of $x^2+x+3>0$

$\mathrm{Choosing\:ranges\:that\:satisfy\:the\:required\:condition:}\:\ge \:\:0$

$x\frac{3}{2}$ is the required solution of the given inequality.

5 0

3 years ago

Read 2 more answers

Write an expression that has three terms and simplifies to 4x-7.

nikklg [1K]

You get 3x + 4x, +4- -3,and +3 + 4

4 0

3 years ago

Increase £2193.67 by 8.5%

HACTEHA [7]

Answer:

£2380.23

Step-by-step explanation:

The increase will be 8.5% of £2193.76 added to £2193.76

That’s

8.5% of £2193.76

8.5% /100% x £2193.76

0.085 x £2193.76

£186.47

Increase = £2193.76 + £186.47

= £2380.23

6 0

3 years ago

If L||M, find x and y<br><br> i need help asap plis

klasskru [66]

(18x-44) + (8x-10) = 180

26x-54 = 180

26x = 234

x = 9

8(9)-10 + (13y-38) = 180

72-10+13y-38 = 180

13y+24 = 180

13y=156

y=12

8 0

2 years ago

I need help on these questions

lilavasa [31]

Answer:

9. m = -3

11. m = 1

13. m = $\frac{3}{5}$

3 0

3 years ago