The graph shown is only a small part of a larger graph. The table shows two additional points that are part of the function but
are not shown on the graph.
Do either of the points prevent the function from being a linear function?
A. No, both points indicate this function is linear because the x and yvalues can be substituted into the equation y=mx+b to create a true equation.
B. Yes; Point A prevents this function from being linear because (-12, 16) would only satisfy the function if the function was exponential.
C. Yes; Point B prevents this function from being linear because (12, -16) would only satisfy a function with a variable rate of change.
D. No; both points indicate this function is linear because they both follow the pattern of the line.
Do either of the points prevent the function from being a linear function?
A. No, both points indicate this function is linear because the x and yvalues can be substituted into the equation y=mx+b to create a true equation.
B. Yes; Point A prevents this function from being linear because (-12, 16) would only satisfy the function if the function was exponential.
C. Yes; Point B prevents this function from being linear because (12, -16) would only satisfy a function with a variable rate of change.
D. No; both points indicate this function is linear because they both follow the pattern of the line.
1 answer:
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A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or
ancestors.
In the third generation we have 8 ancestors ot
ancestors.
We can see that each succesive generation has two times more members. The sum is:
To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
</span>
<span>Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements
For this question:
a1 = 2
r = 2
n = 40
</span>
<span>
b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years
c.
Total number of people who have ever lived = </span>
Number of ancestors in 40 generations =
The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or
In the third generation we have 8 ancestors ot
We can see that each succesive generation has two times more members. The sum is:
To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
</span>
<span>Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements
For this question:
a1 = 2
r = 2
n = 40
</span>
<span>
b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years
c.
Total number of people who have ever lived = </span>
Number of ancestors in 40 generations =
The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.
The necessary formulas to get the area of a circle’s segment are the area of the circle’s sector and the triangle it is bounded by.
Hence the formula for the segment’s area is:Area of Segment = Area of sector – area of the triangle.
The formula of the area of a circle’s sector is:Area of Sector =
x (radius of circle)²
While the formula for the area of a triangle is:Area of Triangle =
x base of triangle x height of triangle
Hence the formula for the segment’s area is:Area of Segment = Area of sector – area of the triangle.
The formula of the area of a circle’s sector is:Area of Sector =
While the formula for the area of a triangle is:Area of Triangle =
The possible ordered pairs whose product will be negative (less than zero) are,
That is all these products will give us,
The point must be in the second quadrant where x is negative and y is positive.
Or in the fourth quadrant, where y is negative and x is positive.
That is all these products will give us,
The point must be in the second quadrant where x is negative and y is positive.
Or in the fourth quadrant, where y is negative and x is positive.