Answer:
The correct answer is
(x + 2) (x + 1) (x - 3)
Step-by-step explanation:
Answer:
The equation does not have a real root in the interval ![\rm [0,1]](https://tex.z-dn.net/?f=%5Crm%20%5B0%2C1%5D)
Step-by-step explanation:
We can make use of the intermediate value theorem.
The theorem states that if
is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:
- If a continuous function has values of opposite sign inside an interval, then it has a root in that interval. This is also known as Bolzano's theorem.
- The image of a continuous function over an interval is itself an interval.
Of course, in our case, we will make use of the first one.
First, we need to proof that our function is continues in
, which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval
, which means to evaluate the equation in 0 and 1:

Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval
. I attached a plot of the equation in the interval
where you can clearly observe how the graph does not cross the x-axis in the interval.
Answer:
= -4x + 7 is the correct answer
Step-by-step explanation:
The total area would be 9 1/4 multiplied by 8 4/5 which would equal 81.4 inches
Answer:
$ 9 each bottle
Step-by-step explanation:
1 crate = $45
1 crate = 25 bottles
if we want to earn $180 per crate , we have to add this value to the $45
45 + 180 = 225
if the value of the box to win $180 is $225, we have to divide the new value by 25 (number of bottles) and we will have what we will have to charge each bottle
225/25 = 9
we have to charge $ 9 each bottle to earn $ 180 per crate