Answers by visitors named: Willie

I think these are trick questions and you have the right idea. 3x = 9 is the equation of a vertical line. There is no y in the equation, so there is no "y = mx + b" form for a vertical line. The simplest way to express this line is x = 3. Its x-intercept is 3 (because (3, 0) is where the line crosses the x-axis). It does not have a y-intercept, because the line never crosses the y-axis. Technically, it has an undefined slope. Similarly, the other equation is a horizontal line. 2y + 16 = 0 is the same as 2y = -16, or y = -8. This is a horizontal line through (0, -8). It has no x-intercept. The y-intercept is -8. The slope is zero. I think you are right to say that the x-intercept is "none."

If you use a calculator with an inverse sine function, you can enter sin^-1 (0.1) = and find out what the acute angle value is. Then you can use that and plug it into the cos, tan, cot, csc, and sec functions of your calculator. If you don't have a calculator, use this fact: (cos a)^2 + (sin a)^2 = 1. Solve to find (cos a)^2 = 1 - (sin a)^2 so cos a = sqrt (1 - [sin a]^2) = sqrt (1 - (0.1)^2) = sqrt (1 - 0.01) = sqrt 0.99. Then you can find tan a = sin a / cos a. The other ratios are reciprocals. You can find formulas for them in your text and use the above results in your calculations.

Use the inverse cosine feature of your calculator. It might look like cos with a little raised -1 next to it. invcos (9/20) = ??? Your answer will be in degrees or radians depending on your calculator setting. Try invcos (1/2). If it gives you 60 then your calculator is giving you degree answers. I am guessing that invcos (9/20) will be a little smaller than invcos (10/20), so it will be a little smaller than 60 degrees. Think of a right triangle with one leg 9 units and longest side 20 units. The unknown you are looking for is the size of the angle formed by the 9 and 20 unit sides.

An arithmetic sequence is one in which the differences between neighboring numbers is the same. The only arithmetic sequences you can get from that set of 5 numbers are: (1, 2, 3), (2, 3, 4), (3, 4, 5), or (1, 3, 5). So only 4 choices. How many ways can you arrange 3 numbers from the set so that they are in increasing order? 123, 124, 125, 134, 135, 145, 234, 235, 245, 345. You should be able to find the probability. Can you argue why you don't have to worry about choices like 524 and so forth?

y varies inversely with x means that y = 1/x times some constant k. So, y = k/x is the general form of an equation of variation where y varies inversely as x. But now you also know that for a specific value x = 6, y = 1. Plug those values in to your equation to get something that only has k in it. 1 = k/6. Solve that for k. Now you can write your equation y = k/x using the number you found for k. The number k is probably what is being called the "variation constant" and the expression y = k/x is the equation of inverse variation. It's funny that something can be called a "variation constant" because those two words seem to mean opposites!

How many parking spaces have a number between 27 and 73? (Include the number 27 in that.) How many parking spaces are there altogether, numbers 1 to 73? The ratio of those numbers will give you the probability, assuming that "randomly parks" means the chance of Jillian parking in any of the spaces is equal.

However, if the equation was this instead ... 2y + 16x = 0 ... then you do have a diagonal line that has both an x-intercept and a y-intercept and a slope that is not zero but not undefined. I think it is a negative slope. Can you figure out the x-intercept of the line? the y-intercept of the line? and the slope of the line? Hint: When y = 0, what is x? That gives you one intercept. When x = 0, what is y? That gives you another intercept. Draw the line and see if you can find the slope.

Let n = number of nickels. Let d = number of dimes. Let q = number of quaraters. n + d + q = ____ 5n + 10d + 25q = 450 (Why?) d = n + 7 (Why?) Rewrite the first to equations but use (n + 7) everywhere you see d. n + (n + 7) + q = ??? 5n + 10(n + 7) + 25q = 450 You have 2 equations with 2 variables and you should now be able to solve using methods you have learned for solving a "system" of equations. Or you could try graphing the lines that the equations represent and see where the lines cross. Another way is to think about all the ways that you could have 40 coins and yet have 7 more dimes than nickels: n d q 0 7 33 1 8 31 2 9 29 3 10 27 4 11 25 5 12 23 etc You could calculate the value of each set of coins until you find the one that has a value of $4.50. That would be the 'brute force' method! I'm guessing you don't really have that many quarters, so it might be better to start looking later in the list. Another thing to think about: the list shows that number of quarters must be odd. So total value from quarters will end in 5 cents (.25, .75, 1.25, etc.). No matter how many dimes you have, their value will end in zero (.10, .20, .30), so to get a value of $4.50, you will need to have an odd number of nickels to 'cancel out' the 5 cents in the value of the quarters. So I'm guessing the answer will have an odd number of nickels, an odd number of quarters, and an even number of dimes. That also helps you cut down the list.

Do you know how to find the asymptotes of a hyperbola with this equation? [x^2]/4 - [y^2]/9 = 1 Hint: To express this in the format x^2/a^2 - y^2/b^2 = 1, what are the values of a and b? How can a and b be used to find the equations of the asymptotes? Then, you'd have to translate (slide) the hyperbola to get the one you described. I think left 3 units and up 1 unit. So you'd have to rewrite the equations of the asymptotes you found after they gets hifted over and up.

If you start at (0, 0) and move right 3 and up 6, you arrive at (3, 6). Then, starting at (3, 6) if you move right 5 and up -5 (i.e. down 5), you end up at (8, 1). The resultant is the vector from your original starting point to your final landing spot. So the vector from (0, 0) to (8, 1), which is simply <8, 1>.

In chemistry class you might write an equation in that fashion to suggest that 1 molecule of water is composed of the "sum" of 1 oxygen atoms and 2 hydrogen atoms. In your math work, since you are doing the topic of "direct variation" you are expected to think about how the quantities vary. That means an equation of the form y = kx, where k is a constant and x and y are the variables. In this case, what is asked for is the ratio of hydrogen to oxygen, which is constant no matter how many molecules you are talking about. For example, you could have (oxygen, hydrogen) values of (1, 2), (2, 4), (3, 6), (4, 8), etc. This can be expressed as H = 2O, in other words, number of hydrogen atoms is two times whatever the number of oxygen atoms. y = k * x H = 2 * O In this case, the equation is expressing how hydrogen "varies directly" with oxygen. The constant of variation is 2. You could also write this: y = k * x O = (1/2) * H That would express how oxygen varies directly with hydrogen. The constant of variation is 1/2. Graph of y = kx is a line through (0, 0) always. The slope of the line is k. So instead of an "addition" equation, direct variation is always a "multiplication" equation. Note: If you have a situation that does not pass through (0, 0), it is not considered "direct variation." So, y = 3x + 5 is not direct variation.

The first rule sends (x, y) to (x - 9, y - 2). That is, it slides every point to the left nine units and down two units. The second rule slides every point to the right 1 unit and down 2 units. The composition is combining the two transformations. In this case, they are both translations (slides), so it doesn't really matter which order you do them in. The first translation could be written in vector form as <-9, -2> and the second is <+1, -2>. To figure out the combined effect, just add the components. <-9 + (+1), -2 + (-2)> <-8, -4> So a single slide left 8 and down 4 does the same thing as the two rules combined. (x, y) --> (x - 8, y - 4) would be a translation rule to use. Note: Sometimes the order you do transformations matters. For example, translate then reflect might be different from reflect, then translate. But in the case of two translations, it doesn't really matter which order you do the slides. You could have done rule 2 first, then rule 1 second. That's because (x - 9 - 2, y - 2 + 1) is the same as (x - 2 - 9, y + 1 - 2).

Thank you so much!

I got the answer nvm =]

Thank you so much

I think I got it the answer is always true, but why

se the equation y = 3.5 x to answer the questions. (a) What is the slope of y = 3.5 x and what does this mean? (Use at least one complete sentence to explain your answer.) (b) What is the y - intercept? (Use at least one complete sentence to explain your answer.) (c) Make up a story that can be represented by y = 3.5 x . (Use at l east two complete sentences to explain your answer)

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