Tutor profile: Jeanette Z.
How did you become fluent in Spanish?
Fortunately, I grew up in a bilingual household. We spoke mainly Spanish at home and English elsewhere. Now that I'm older and don't live with my family, I find the best way to improve my Spanish is by practicing. Even saying the words out-loud to yourself helps with pronunciation and becoming comfortable with speaking. We can do a couple of practice conversations relevant to your school assignments to start.
Were humans really once monkeys or how does evolution work?
Shockingly, humans all around us were never monkeys at first. However, there are studies that show that we share somewhere between 80-95% of our DNA with chimps. The best way to describe evolution is by thinking about Darwin's term "survival of the fittest." Let's use a made-up example like a group of ants. Let's say that a group of green ants had the ability to swim but their neighbors, the purple ants couldn't. Then one day both ant villages were hit by a storm that flooded their homes. Unfortunately, because the purple ants couldn't swim, they didn't survive. Therefore, the purple ant population ceased to exist, or became extinct. However, because the green ants had the ability to how to swim, they were able to swim to safety and survive! Their green ant population was able to set up shop and make a new village. They thrived, had baby green ants, and their population kept growing. The lived happily ever after! So basically using this made up story, certain animals and species historically have special traits to be able to survive obstacles that could've led to their extinction. For the green ants it was the ability to swim. So the theory of evolution essentially comes down to whoever is the fittest, is able to survive the longest. This is why some of our shared characteristics with monkeys could have allowed both humans and chimps to survive in similar settings.
Systems of equations using 2 variables Given: 2x-2y=-8 4x+4y=12 solve for x only
Because we don't know what either x or y is, we have to use the information given. When we have two equations with only 2 variables, a good place to start is by isolating y in only one equation. Let's take the first equation. In order to isolate y, we have to put all the other numbers or terms on the other side of the = sign. We do this by thinking about opposites. For instance, the opposite of adding (+) is substracting (-) and the opposite of multiplication (*) is division (/). We also have to make sure that whatever we do on one side of the = sign, we do on the other. So if we add a term on the left of the = sign, we have to add that same term on the right of the = sign. Going back to the first equation 2x-2y=-8, lets look at the first term we can put on the other side which is 2x. Whenever there is a term at the start of an equation without a + or - sign, it is safe to assume no sign means it is a + sign. So in order to get this +2x on the other side, we have to do the opposite of + which is -. Therefore we subtract 2x from the left of the equal sign and since we have to do the same mathematical operation on both sides of the = sign, we also subtract 2x on the right. It'll look like this: 2x-2y = -8 -2x -2x On the left, 2x - 2x = 0 leaving only -2y and to the right of the =, it becomes -8-2x. We are left with -2y = -8 -2x. To continue to isolate the y we have to do the opposite to it. So since y is being multiplied by -2, we have to divide it by -2 and do the same on the other side. So on the left since -2/-2 = 1, we are only left with 1*y, which is also just y. On the right we divide each term by -2. so first -8/-2=4 and for -2x/-2, the negative signs cancel out and 2/2=1 so we are just left with 1*x, or x. Putting our terms together will leave us with y=4+x. Now that y is by itself and we now know y=4+x, we can go back to our second equation and plug it in for y. If we keep it in parentheses for simplicity, plugging it in will look like this: 4x+4(4+x)=12 So now we only have one variable we have to solve for which is x. Using our order of operations PEMDAS, lets simplify. We want to multiply first, therefore, we're going to distribute the 4 outside of the parentheses to each term that is inside of the parentheses. 4*4=16 and 4*x=4x. Putting these together will make 4x+16+4x=12. Next we want to combine like terms by adding. We can add 4x+4x which = 8x. This will leave us 16+8x=12. Now we want to isolate x. We start by subtracting 16 on both sides leaving us with 8x=12-16. When we further simplify, 12-16=-4, so the whole equation becomes 8x=-4. Now we want to divide 8 on both sides to solve for x, leaving us with x=-4/8. After simplifying, we get x=-1/2. Since the question only asks us to solve for x, our answer is x=-1/2