Find the interval in which the function is positive x^2-x-6=y

Mathematics

2 answers:

Alenkinab [10]3 years ago

7 0

9514 1404 393

Answer:

(-∞, -2) ∪ (3, ∞)

Step-by-step explanation:

The function can be factored as ...

(x +2)(x -3) = y

The leading coefficient is positive, so the parabola opens upward. It will be positive up to the left-most zero, and positive again to the right of the right-most zero. That is, the function is positive everywhere outside the interval [-2, 3], where it is not.

The function is positive on (-∞, -2) ∪ (3, ∞).

Semmy [17]3 years ago

6 0

Answer:

(-INFINITY , -2) (3 , INFINITY)

Function is positive when above the x axis

Function is below the x axis between -2 and 3

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3 years ago

Eugene walked all the way to school at 3 mph then realized she forgot her math book (how could she?!), so she ran back at 7 mph.

Fynjy0 [20]

$\text{Answer: }1\frac{23}{40}\ miles\text{ far she live from school.}$

Explanation:

Since we have given that

Speed at which Eugene walked all the way to school = 3 mph

After realizing that she forgot her math book, she ran back

Speed at which Eugene walked back to her house = 7 mph

Let the distance between her house and her school be x

According to question,

$\frac{x}{3}+\frac{x}{7}=\frac{45}{60}\\\\\frac{7x+3x}{21}=\frac{3}{4}\\\\\frac{10x}{21}=\frac{3}{4}\\\\x=\frac{3\times 63}{4\times 10}=\frac{63}{40}=1\frac{23}{40}\ miles.$