Answer:
A counterexample for a conjecture is the statement that disproves a conjecture.
Step-by-step explanation:
To find : What is a counterexample for the conjecture?
Solution :
A conjecture is an educated guess but not yet proven. It is possible that next example shown the conjecture wrong.
A counterexample is an example that disproves or disagree a conjecture.
For example : Prime numbers - 3,7,11,23
Conjecture - All prime numbers are odd
Counterexample - 2
→ 2 is a prime number but not odd, it is an even number.
A linear equation is an equation with two variables whose graph is a line. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.
If you want to graph a linear equation you have to have at least two points, but it's usually a good idea to use more than two points. When choosing your points try to include both positive and negative values as well as zero.
Example
Graft the function y = x + 2
Begin by choosing a couple of values for x e.g. -2, -1, 0, 1 and 2 and calculate the corresponding y values.
X Y = x + 2 Ordered pair
-2 -2 + 2 = 0 (-2, 0)
-1 -1 + 2 = 1 (-1, 1)
0 0 + 2 = 2 (0, 2)
1 1 + 2 = 3 (1, 3)
2 2 + 2 = 4 (2, 4)
Now you can just plot the five ordered pairs in the coordinate plane
picture13
At the moment this is an example of a discrete function. A discrete function consists of isolated points.
By drawing a line through all points and while extending the line in both directions we get the opposite of a discrete function, a continuous function, which has an unbroken graph.
picture14
If you only want to use two points to determine your line you can use the two points where the graph crosses the axes. The point in which the graph crosses the x-axis is called the x-intercept and the point in which the graph crosses the y-axis is called the y-intercept. The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).
picture15
The standard form of a linear equation is
Ax+By=C,A,B≠0
Before you can graph a linear equation in its standard form you first have to solve the equation for y.
2y−4x=8
2y−4x+4x=8+4x
2y=4x+8
2y2=4x2+82
y=2x+4
From here you can graph the equation as we did in the example above.
The graph of y = a is a horizontal line where the line passes through the point (0, a)
picture16
Whereas the graph of x = a is a vertical line that passes through the point (a, 0)
picture17
Answer:
The answer to your question is x = 17.32; y = 8.67
Step-by-step explanation:
Process
1.- Use trigonometric functions to find x and y
a) sin Ф = ![\frac{opposite side}{hypotenuse}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%20side%7D%7Bhypotenuse%7D)
Ф = 60°
opposite side = 15
hypotenuse = ?
![hypotenuse = \frac{opposite side}{sin \alpha }](https://tex.z-dn.net/?f=hypotenuse%20%3D%20%5Cfrac%7Bopposite%20side%7D%7Bsin%20%5Calpha%20%7D)
![hypotenuse = \frac{15}{sin 60}](https://tex.z-dn.net/?f=hypotenuse%20%3D%20%5Cfrac%7B15%7D%7Bsin%2060%7D)
![hypotenuse = \frac{15}{0.87}](https://tex.z-dn.net/?f=hypotenuse%20%3D%20%5Cfrac%7B15%7D%7B0.87%7D)
hypotenuse = 17.32
b) cosФ = ![\frac{y}{hypotenuse}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Bhypotenuse%7D)
![y = hypotenuse x cos 60](https://tex.z-dn.net/?f=y%20%3D%20hypotenuse%20x%20cos%2060)
![y = 17.32 x 0.5](https://tex.z-dn.net/?f=y%20%3D%2017.32%20x%200.5)
y = 8.67
Hey there! I’m happy to help!
NUMBER 15
To solve this problem we want to round to the nearest millionth. We cannot actually write out the entire number because it goes on forever, but we can expand long enough so we can round it the millions place.
One million has six zeroes. This means that a millionth is six decimal places over (0.000001 is one millionth). Same goes for other base ten numbers (100 has two zeroes, one hundredth is two decimal places over)
We see that there is a line over the 45 in our decimal. This means that after this 45 it is going to go 4545454545.... forever. We want to round to the nearest millionth. However, when you round, you need the next digit over. Let’s expand our to the ten millionth (seven digits.)
6.2145454............
Now, we look at our millionths place. The next place over is four. Therefore, we round down. Therefore, the answer is D) 6.214545
QUESTION 18
Solving questions like this is very simple. With proportions (two equal ratios of fractions) the product of the diagonal sides are equal. So, you just multiply the two numbers that are diagonal from each other and then divide it by the other number and you have your x. If you want, I can explain to you more why this works.
7(2/7)=2
2/2 1/4= 8/9
Therefore, the answer is 8/9.
I hope this has been helpful! If you need anymore help please ask! :D