You have the following inequality given in the problem shown above:

(x^2-1)/(x^2+5x+4)≤0

1. To solve it, you must factor it and then you must make the study of the signs.

2. Once you do the proccedure mentioned above, you obtain the following solutions:

-4<x<-1

-1<x≤1

3. You can graph the inaquality given in the problem, as you can see in the figure attached.

6 0

2 years ago

The table below represents the displacement of a turtle from its nest as a function of time: Time (hours) x Displacement from ne

andriy [413]

Part A: The y-intercept is 5. If you look to the data, when x=0, y=5. This means that the turtle started off 5 miles away from its nest. (at 0 hours, the distance away from his nest was 5 miles)

Part B:Answer=22. Remember, if you take any two distinct points on a line, the slope of the line will be equal to the average rate of change. In short, we're just looking for the slope between the ordered pairs (1,27) and (4,93). The formula for slope is:

$slope= \frac{y_{2}- y_{1} }{ x_{2} - x_{1} } = \frac{93-27}{4-1}= \frac{66}{3}=22$

The average rate of change between x=1 and x=4 is 22. The average rate of changed describes the rate at which miles is changing with respect the the change in hour.

Part C: Answer=10hours. Since by now we know both the slope and the y-intercept, lets write the equation in slope intercept form and then solve for 225 miles.

y=mx+b
y=22x+5
225=22x+5
subtract 5 from both sides
220=22x
divide both sides by 22
10=x
It would take 10 hours for the turtle to travel 225miles from it's nest.

4 0

2 years ago

How do i put 250 to 1000 as a fraction in its simplest form

shusha [124]

Divide 250 from 250 and 1000 to get 1/4.

4 0

2 years ago

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