Answer:
Find five rational numbers between 2/3 and 4/5 -
61/90 62/90 63/90 64/90 65/90 66/90 67/90
choose any five :)
Answer:
A) Values in the solution set satisfy both inequalities.
B) It is the intersection of two solution sets.
Step-by-step explanation:
We denote intersection as AND.
![A \cap B \implies \text{A and B}](https://tex.z-dn.net/?f=A%20%5Ccap%20B%20%5Cimplies%20%5Ctext%7BA%20and%20B%7D)
Take those sets. The intersection is what A and B share.
Answer: $5100
Step-by-step explanation:
I am attaching a sketch for reference, the quadrilateral that is formed is the red area ABDC. First of all, we have that the quadrilateral has all of its sides equal. We also know that the crosswalks are parallel in pairs, because they are both normal to the same two parallel lines (that define a road in our sketch). AB is parallel to CD this way and AC is parallel to BD (in Euclidean Geometry, two lines normal to the same line are parallel). Thus, ABDC is a parallelogram with equal sides. It is either a square or a rhombus. It cannot be a square since one of its angles is 30 degrees, thus it is a rhombus (also called an equilateral quadrilateral).
Law of Sines can help with this problem. Law of Sines can help find a missing angle or side if given two sides with respective opposite angles or two angles with respective sides. The formula for Law of Sines is sin(A)/a = sin(B)/b. A and B are the angles and a and b are the sides opposite the angles. Hopefully, the picture above helps you visualize everything.
Anyways, we know two sides and one angle, so Law of Sines is possible to use. The side opposite the right angle is 11. So, we have sin(90)/11. The other angle, we're looking for but we do know the side. The side opposite of angle M is 5. So, we have sin(M)/5. The Law of Sines formula tells us that Sin(A)/a = Sin(B)/b = Sin(C)/c but we don't need all the angles but just angle M. So we're going to just use Sin(A)/a = Sin(B)/b. We have already set up the equations so plug them in.
Sin(90)/11 = Sin(M)/5. Cross multiplication will get 5 × Sin(90) = Sin(M) × 11.
Sin(90) = 1. So, we get 1 × 5 and get after simplifying, 5 = Sin(M) × 11. We divide both sides by 11 to get Sin(M) by itself.
5/11 = Sin(M). Now we run into a problem. How do we get the angle M? We do the inverse sin or sin^-1 key if you're using a calculator. So, (5/11)sin^-1 = M. Our final answer is angle M = 27.03569... Hope this helped!
Side Notes: Make sure if you're using a calculator that you're in degrees and NOT radians unless the question calls for radians. Also, if you wanted to find all the angles of the triangle then once you find M, you could add that to the 90 degree angle and then subtract that from 180. You will find the other angle since you know two of them and there are only three of them that have to add to 180 degrees. I just like triangles, ;-) Good luck!