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 ![\rm [-2,2]](https://tex.z-dn.net/?f=%5Crm%20%5B-2%2C2%5D)
where you can clearly observe how the graph does not cross the x-axis in the interval.
Answer:
$12
Step-by-step explanation:
36÷3=12
Each ticket costs $12
Answer:
The square root of six hundred and eighty-three √683 = 26.13426869074
The statements which are correct are-
- The number of miles increases as time increases.
- The number of hours causes a change in the number of miles ridden.
- The variable h is the independent variable.
Step-by-step explanation
The above table displays the relationship between the time taken in hours ("h") by Mayon to cover the distance (miles "m").
It means that the distance is dependent on time in hours. Hence, the variable "m" is a dependent variable since it depends on time "h" for which bicycle is being ridden.
Similarly, the variable "h" is an independent variable.
As seen from the table, the value of "m" continuously increases for the value of "h" and thus the number of hours causes a change in the distance ridden.
The equation of a line given the slope and y-intercept is given as;
m(x-x₁) = (y-y₁)
∴equation of line with m = 2 and y-intercept = (0,3) =
2(x - 0) = (y - 3)
= 2x - 0 = y - 3
making y the subject obtains y = 2x + 3.
so, equation of the line: y = 2x + 3.
