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Elenna [48]
2 years ago
12

What is the slope of the line (9,1) and (-3,-7)

Mathematics
2 answers:
Grace [21]2 years ago
8 0
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.

kifflom [539]2 years ago
6 0

Answer:

2/3

Step-by-step explanation:

A-P-E-X

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Evaluate how organizations can use one-sample hypothesis testing to determine if there are performance issues in the organizatio
Margarita [4]

Answer:

Organizations can use one-sample hypothesis test to determine if there are performance issues in many ways.

It can be applied to the performance of a sector, a machine, a product, an advertising campaing, etc.

For example, we can take the example of a machine. It may be claimed that a specific machine performs significantly worse than the average.

This average would be the population mean: the average performance of the machines of the same type or process.

Then, a sample of the performance of the machine in study is taken and the hypothesis test can be performed to test the claim that this machine performs significantly worse.

Step-by-step explanation:

For example, we have an historic performance for this type of machine of 100 units a day. The machine A in study is sampled 14 days and have a performance of 92 units a day, with a sample standard deviation of 12 units/day. We have to test the claim that the machine A makes less units per day than the average.

Then, the null and alternative hypothesis are:

H_0: \mu=100\\\\H_a:\mu< 100

The significance level is 0.05.

The sample has a size n=14.

The sample mean is M=92.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{14}}=3.2071

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{92-100}{3.2071}=\dfrac{-8}{3.2071}=-2.4944

The degrees of freedom for this sample size are:

df=n-1=14-1=13

This test is a left-tailed test, with 13 degrees of freedom and t=-2.4944, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0.0134) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that machine A produces significantly less units per day than the average.

3 0
3 years ago
PLEASE HELP ME WITH THIS QUESTION <br> 6
nata0808 [166]

Answer:

45

Step-by-step explanation:

Assuming this is a trapezoid,

\frac{29+WZ}{2}=37 \\ \\ 29+WZ=74 \\ \\ WZ=45

5 0
2 years ago
How do I divide 2 divided 898
nalin [4]
Probably with division
4 0
3 years ago
Read 2 more answers
I need help with fractions :(
bearhunter [10]

Answer:

x = 0, Need the steps?

STEPS:

9x - 7 = -7 (Original Problem)

9x = 0 (Add 7 to both sides)

x = 0 (Divide both sides by 9)

8 0
3 years ago
Read 2 more answers
Please help me now plz <br> I will mark you brainliest
EastWind [94]

Answer:

  1229 km

Step-by-step explanation:

The missing angle is ...

  180° -60° -75° = 45°

Knowing that, the Law of Sines can be used to find the side opposite the 75° angle.

  ?/sin(75°) = 900 km/sin(45°)

  ? = (900 km)sin(75°)/sin(45°) ≈ 1229.423 km

The UFO is about 1229 km from KA-12.

5 0
3 years ago
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