The lengths, in centimeters, of nine earthworms are shown below. 3, 4, 5, 5, 6, 7, 8, 9, 10 What is the median of the data?
mel-nik [20]
The median of the problem is 6 because it is in the middle of the number set of the earthworm sizes.
Answer:
<h3>y = -32</h3>
Step-by-step explanation:
![y=-2x+8\\\\x=20](https://tex.z-dn.net/?f=y%3D-2x%2B8%5C%5C%5C%5Cx%3D20)
Substitute ; x =20 in given equation
![y =-2(20 )+8\\\\y = -40+8\\\\y = -32](https://tex.z-dn.net/?f=y%20%3D-2%2820%20%29%2B8%5C%5C%5C%5Cy%20%3D%20-40%2B8%5C%5C%5C%5Cy%20%3D%20-32)
How many facts does it take to make triangles congruent? Only 3 if they are the right three and the parts are located in the right place.
SAS where 2 sides make up one of the three angles of a triangle. The angle must between the 2 sides.
ASA where the S (side) is common to both the two given angles.
SSS where all three sides of one triangle are the same as all three sides of a second triangle. This one is my favorite. It has no exceptions.
In one very special case, you need only 2 facts, but that case is very special and it really is one of the cases above.
If you are working with a right angle triangle, you can get away with being given the hypotenuse and one of the sides. So you only need 2 facts. It is called the HL theorem. But that is a special case of SSS. The third side can be found from a^2 + b^2 = c^2.
You can also use the two sides making up the right angle but that is a special case of SAS.
Answer
There 6 parts to every triangle: 3 sides and 3 angles. If you show congruency, using any of the 3 facts above, you can conclude that the other 3 parts of the triangle are congruent as well as the three that you have.
Geometry is built on that wonderfully simple premise and it is your introduction to what makes a proof. So it's important that you understand how proving parts of congruent triangles work.
It looks like you have the domain confused for the range! You can think of the domain as the set of all "inputs" for a function (all of the x values which are allowed). In the given function, we have no explicit restrictions on the domain, and no situations like division by 0 or taking the square root of a negative number that would otherwise put limits on it, so our domain would simply be the set of all real numbers, R. Inequality notation doesn't really use ∞, so you could just put an R to represent the set. In set notation, we'd write
![\{x\in\re\mathbb{R}\}](https://tex.z-dn.net/?f=%20%5C%7Bx%5Cin%5Cre%5Cmathbb%7BR%7D%5C%7D%20)
and in interval notation,
![(-\infty,\infty)](https://tex.z-dn.net/?f=%20%28-%5Cinfty%2C%5Cinfty%29%20)
The <em>range</em>, on the other hand, is the set of all possible <em>outputs</em> of a function - here, it's the set of all values f(x) can be. In the case of quadratic equations (equations with an x² term), there will always be some minimum or maximum value limiting the range. Here, we see on the graph that the maximum value for f(x) is 3. The range of the function then includes all values less than or equal to 3. As in inequality, we can say that
,
in set notation:
![\{f(x)\in\mathbb{R}\ |\ f(x)\leq3\}](https://tex.z-dn.net/?f=%20%5C%7Bf%28x%29%5Cin%5Cmathbb%7BR%7D%5C%20%7C%5C%20f%28x%29%5Cleq3%5C%7D%20)
(this just means "f(x) is a real number less than or equal to 3")
and in interval notation:
![(-\infty,3]](https://tex.z-dn.net/?f=%20%28-%5Cinfty%2C3%5D%20)