The table below shows selected points from a function.
1 answer:
Answer:
<em>True </em>
Step-by-step explanation:
<em>Rate Of Change Of Functions </em>
Given a function y=f(x), the rate of change of f can be computed as the slope of the tangent line in a specific point (by using derivatives), or an approximation by computing the slope of a secant line between two points (a,b) (c,d) that belong to the function. The slope can be calculated with the formula
If this value is calculated with any pair of points and it always results in the same, then the function is linear. If they are different, the function is non-linear.
Let's take the first two points from the table (1,1)(2,4)
Now, we use the second and the third point (2,4) (3,9)
This difference in values of the slope is enough to state the function is non-linear
Answer: True
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The solution of the equation is x = 2
Step-by-step explanation:
The original equation is
We solve it using the following steps:
1) We apply the addition property of equality: by adding the same factor on both sides of the equation, the equation does not change.
In this case, we add +10 on both sides, and we get:
2) We apply the division property of equality: by dividing both sides of the equation by the same number (different from zero), the equation does not change.
In this case, we divide both sides of the equation by 5, and we get:
Therefore, the solution of the equation is .
Learn more about solving equations:
#LearnwithBrainly
Answer:
Step-by-step explanation:
This is not nearly as threatening and scary as I first thought it was. You must be in the section in Geometry where you are taught that perimeter of similar figures exist in a one-to-one relationship while areas of similar figures exist in a squared-to-squared relationship. We will use that here.
The area formula for a regular polygon is
where a is the apothem and p is the perimeter. We are first asked for the area of the polygon, but it would make more sense to find the perimeter first, since we need it to find the area.
P = 5(8) so
P = 40
We are given that the area of the triangle inside that polygon is 22.022 units squared. Knowing that the area formula for a triangle is
we can sub in what we know and solve to find the height:
and
22.022 = 4h so
h = 5.5055 units
It just so happens that the height of that triangle is also the apothem of the polygon, so now we have what we need to find the area of the polygon:
which gives us an area of
A = 110.11 units squared.
Here is where we can use what we know about similar figures and the relationships between perimeters and areas. We will set up a proportion with the smaller polygon info on top and the larger info on bottom. We know that the larger is 3 times the smaller, so the ratio of smaller to larger is
Since perimeter is one-to-one and we know the perimeter of the smaller, we can create a proportion to solve for the perimeter of the larger:
Cross multiply to get that the perimeter is 120 units. You could also have done this by knowing that if the larger is 3 times the size of the smaller, then the side measure of the larger is 24, and 24 * 5 = 120. But we used the way we used because now we have a means to find the area of the larger since we know the area of the smaller.
Area exists in a squared-to-squared relationship of the perimeter which is one-to-one. If the perimeter ratio is 1:3, then the area relationship is
which is, simplified:
Since we know the area for the smaller, we can sub it into a proportion and cross multiply to solve for the area of the larger.
A of the larger is 990.99 units squared