I'll give brainliest to the correct answer! (Picture below)

Mathematics

1 answer:

Lina20 [59]2 years ago

6 0

9514 1404 393

Answer:

D. 7

Step-by-step explanation:

The equation is ...

x = a(y +1)² -3

For the point (x, y) = (4, 0), we have ...

4 = a(0 -1)² -3

7 = a . . . . . . . . . . . . add 3, simplify

The leading coefficient is 7.

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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 $2x^2+x-6$ :

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