What type of triangle do you have if one angle measures 40 degrees and another angle measures 45 degrees?
The first thing we need to remember is that a triangle has 3 angles, which is why it's called a TRIangle. If we know two of the angles, we need to figure out the third angle in order to determine what ind of triangle we have. The sum of all three angles in a triangle should equal 180 degrees. The sum of the two known angles is 85 degrees (40 + 45). When we subtract 85 from 180, we can determine that the third angle is 95 degrees. So now we have a triangle with angles that measure 40, 45, and 95 degrees. We don't have an equilateral triangle because all three angles would be the same. We don't have an isosceles triangle because two angles would be the same. We don't have a right triangle because one of the angles would be 90 degrees. We don't have an acute triangle because one of the angles is greater than 90 degrees. But since one of the angles IS greater than 90 degrees, that means we have an obtuse triangle! An obtuse triangle has one obtuse angle greater than 90 degrees (95 degrees) and two acute angles less than 90 degrees (40 and 45 degrees). Additionally, because we have three different angles, we also have a scalene triangle. So the correct name for this type of triangle is an obtuse scalene triangle.
How can you tell the difference between a physical change and a chemical change?
Physical and chemical changes can be confusing but looking at the end product of the change will help you figure out what kind of change took place. Ask yourself: did the substance change? Did I end up with a new substance? If you have a new substance, that is a chemical change. If you have the same substance, that is a physical change. When water is frozen into ice, is that a physical or chemical change? While it seems we have a new substance, when we think about it a bit deeper, we are still dealing with water in both instances. One is liquid water and one is solid water, so because we have the same substance, this would be a physical change. If you let the ice melt, you would have water again. When you change from one state (solid, liquid, gas) to another, you will always have a physical change. What about when a piece of paper is burned and you're left with ashes? This would be a chemical change because you have a completely new substance.
How do you solve for "x" in an equation like: 3x + 12 = 24 ?
When you need to solve for a variable like "x" in an equation, just remember the goal is to get x by itself on one side of the equation and everything else on the other side. In order to do this, you will have to do the opposite of the math operation shown. In 3x + 12 = 24, we will first want to move the 12 to the other side to get closer to our goal of having x by itself. Since we are adding 12 on the left, we will need to subtract 12 (the opposite of addition) from both sides (whatever you do to one side, you also have to do to the other!). 3x + 12 = 24 - 12 -12 3x = 12 On the left, 12-12=0 and on the right, 24-12 = 12, so we end up with 3x = 12. To get x by itself here, we need to get rid of the 3. X is being multiplied by 3 on the right so we need to divide (the opposite of multiplying) both sides by 3. 3x = 12 3x/3 = x and 12/3 = 4, which leaves us with x = 4. If we want to make sure we did the problem correctly, we just need to substitute 4 in for x in the original equation. 3x + 12 = 24 3(4) + 12 = 24 12 + 12 = 24 24 = 24 It works!