Answer:
4 adults and 6 children
Step-by-step explanation:
9 x 4 = 36
5 x 6 = 30
36 + 30 = 66
There was 4 adults and 6 children
It’s is 2/3 because Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m. The larger the value is, the steeper the line. Given m, it is possible to determine the direction of the line that m describes based on its sign and value:
A line is increasing, and goes upwards from left to right when m > 0
A line is decreasing, and goes downwards from left to right when m < 0
A line has a constant slope, and is horizontal when m = 0
A vertical line has an undefined slope, since it would result in a fraction with 0 as the denominator. Refer to the equation provided below.
Slope is essentially change in height over change in horizontal distance, and is often referred to as "rise over run." It has applications in gradients in geography as well as civil engineering, such as the building of roads. In the case of a road the "rise" is the change in altitude, while the "run" is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. The slope is represented mathematically as:
m =
y2 - y1
x2 - x1
In the equation above, y2 - y1 = Δy, or vertical change, while x2 - x1 = Δx, or horizontal change, as shown in the graph provided. It can also be seen that Δx and Δy are line segments that form a right triangle with hypotenuse d, with d being the distance between the points (x1, y1) and (x2, y2). Since Δx and Δy form a right triangle, it is possible to calculate d using the Pythagorean theorem. Refer to the Triangle Calculator for more detail on the Pythagorean theorem as well as how to calculate the angle of incline θ provided in the calculator above. Briefly:
d = √(x2 - x1)2 + (y2 - y1)2
The above equation is the Pythagorean theorem at its root, where the hypotenuse d has already been solved for, and the other two sides of the triangle are determined by subtracting the two x and y values given by two points. Given two points, it is possible to find θ using the following equation:
m = tan(θ)
Given the points (3,4) and (6,8) find the slope of the line, the distance between the two points, and the angle of incline:
m =
8 - 4
6 - 3
=
4
3
d = √(6 - 3)2 + (8 - 4)2 = 5
4
3
= tan(θ)
θ = tan-1(4/3) = 63.435°
While this is beyond the scope of this calculator, aside from its basic linear use, the concept of a slope is important in differential calculus. For non-linear functions, the rate of change of a curve varies, and the derivative of a function at a given point is the rate of change of the function, represented by the slope of the line tangent to the curve at that point.
Answer:
Step-by-step explanation:
Start by finding the slope of the given line.
Slope of given line
A perpendicular bisector cuts through the line at its midpoint perpendicularly.
The product of the slopes of two perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
, where c is the y-intercept.
To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.
Midpoint of given line
= (0, 2)
When x= 0, y= 2,
2= ⅔(0) +c
2= 0 +c
c= 2
Thus, the equation of the perpendicular bisector is .
Answer: <u>A. 35</u>
Step-by-step explanation: The largest prime number less than 50. The largest number less than 50 is 49, but it is not prime, because 49=7·7. The previous number is 48, but it is also composite, because 48=2·2·2·2·3. The previous number is 47, it is prime.
The smallest composite number greater than 10. The smallest number greater than 10 is 11, but it is prime. The next number is 12, it is composite, because 12=2·2·3.
The difference between the largest prime number less than 50 and the smallest composite number greater than 10 is<u> 47-12=35.</u>
