Tutor profile: Elizabeth M.
5 (x+8) = 100 Solve for x
In order to solve for x, we have to isolate it- we want to make sure it's by itself on one side, with no other numbers in the way. First, let's use the distributive property. 5 ( x + 8) = (5*x) + (5*8) = 5x + 40 So, 5x + 40 = 100 Next, we subtract 40 from both sides. We're working in reverse order of operations, so we add/subtract before we multiply/divide. Also, remember- we can't just subtract 40 from one side, because then we're changing the equation. If we do something to one side, we have to do it to the other. 5x + 40 = 100 -40 -40 5x = 60 We only have one step left- time to divide by 5 (on both sides!) (5x)/5 = (60)/5 x = 12 That's the final answer! Let's double check by plugging in. 5 (12 + 8) = 100 5 (20) = 100 100 = 100 Yup, it works out!
Subject: Art History
In 1787, Jacques-Louis David's painted "The Death of Socrates", which now hangs in the Metropolitan Museum of Art. How does this work fit within the scheme of French history? What meaning, if any, can you interpret from this work?
This is a big and open-ended question, so let's start with something concrete- what do we see in this painting? In the foreground, we have a group of men wearing robes of various colors. They all seem to be surrounding a central figure, a man in a white robe who is seated, pointing upward with his left hand and reaching for a cup with his right. The figures around him show various expressions- the one handing him the cup is covering his face and appears to be distraught, another one in a green and blue robe appears to be weeping, and several men have turned away from the central figure completely, showing intense emotion as they hold onto the wall. They are all inside some indoor space, which by itself is quite drab and unornamented. You can, of course, look for more details, but that's not exactly what the question is asking. We do have one more big hint- the title: "The Death of Socrates". In case you're not familiar, Socrates was a Greek philosopher who lived from around 469 to 399 BCE. He didn't leave any recordings, but many of his thoughts, deeds, and theory can be found in the work of his student, Plato. Plato recounts that Socrates was accused by the government of Athens of corrupting the youth. Because of this, Socrates was sentenced to death. He famously refused the opportunity to flee the city, and he instead embraced death and drank poison hemlock. Now that we have the title, this all starts to come together. The man in white must be Socrates, and he is reaching for a cup of poison. The men weeping are his students, friends, or other acquaintances. They know he is about to die and are overcome with grief, but Socrates remains calm in the face of death. Ok, now that we've figured this out, let's look back to the question. We have to think about how this painting fits within the scheme of French history. This painting was made in 1787 by David, who was popular in his lifetime for his paintings and for his active support of the French Revolution. Maybe the Revolution is the key to understanding this painting on a deeper level. Socrates is portrayed positively in this work- he is calm in the face of death, he is physically fit and looks like an ancient Greek idealized statue, and he overall is shown as a hero- note the way the light falls on him, and how his white robes make him stand out and illuminate the people around him. This painting is honoring a man who stood up to political authority and tyranny, who faced death and stood by his political and philosophical ideals. There is a clear connection that can be drawn between Socrates and the French Revolutionaries- and it's clear whose side David stands on. By looking at the composition of this painting, thinking about its title, and making connections between the content of the work and the context of the artist's own life, we were able to understand this painting on a more interesting and complex level.
You are given two points: (4, 10) and (8, 18). How many unique lines would connect these points, and what would their equation(s) be?
Whenever you're stumped on an algebra question, it can be helpful to think about two things: what are the givens, and what am I being asked? In this question we're given two points, and their coordinates. What are we being asked? Well, there are two parts to this question, and the first part is a lot easier than the second. How many unique lines would connect these two points? When you're dealing with two points on a 2D coordinate plane, the answer to this question is always: one. There is only one unique line that connects two planes- you can't have two lines with two different equations connecting the same points! Now let's move on to the second part. What is the equation of this line? Well, first let's make sure we know what a line equation looks like. The standard format is y = mx + b, where 'm' represents the line's slope and 'b' represents the y-intercept. Slope just means the "rise" over "run", or the change in y divided by the change in x. A line's slope never changes, which means that we can use these two points to find the slope for the whole line. All we have to do is calculate the differences between their y and x values. The y value for point #1 is 10, and the y value for point #2 is 18. That means it increases by 8. The x value for point #1 is 4, and the y value for point #2 is 8. That means it increases by 4. Be careful to make sure you look at the signs- here, both values increase, which means we have +8 and +4. Now, in order to get the slope, all we do is divide! 8/4 is 2, so the line's slope, or 'm', is 2. How do we find the y-intercept? The y-intercept is the value for y when x = 0. Basically, where does the line hit when it crosses the y-axis. Well, we have a slope and we have two points, so let's plug in and solve for 'b'. If we use point #1, we get 10 = (2)(4) + b. 2 and 4 multiply to get 8, so 10 = 8 + b, which means b is 2- easy! We can double check with point #2: 18 = (2)(8) + b, so 18 = 16 + b, b=2. It works for both points, which means we got the right answer. We know the slope, and we know the y-intercept, so we have the line's equation! y = 2x + 2
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