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12345 [234]
2 years ago
11

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

Mathematics
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
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Write an expression that has three terms and simplifies to 4x-7.
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You get 3x + 4x, +4- -3,and +3 + 4
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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

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3 years ago
If L||M, find x and y<br><br> i need help asap plis
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(18x-44) + (8x-10) = 180

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