Hi, Mario! Is the system supposed to be the following? x2 + 2y2 = 2 x - y = 2 If so, graphing the system shows an ellipse with a line outside of it; they do not intersect, therefore no solution. To solve it algebraically,...
Hi, Mario! Is the system supposed to be the following? x2 + 2y2 = 2 x - y = 2 If so, graphing the system shows an ellipse with a line outside of it; they do not intersect, therefore no solution. To solve it algebraically,...
Hi, Mario. As another tutor pointed out, if you graphed these equations, the figures would not intersect. You can also determine this algebraically. x2 + 3y2 = 6 x2 - 3y2 = 10 Adding the 2 equations causes the y terms to cancel, leaving: 2x2 ...
Hi, Mario! Solve the system of equations using substitution. Since both equations are already in the "y=" form, we can set x2+3 equal to -x2+5: x2 + 3 = -x2 + 5 Rearrange the terms: 2x2...
Hi, Ieasha! This sentence seems a little confusing at first, so let's look at the pieces of it. "The difference of" tells us there will be 2 expressions to subtract. The first expression is "the product of number, y, and 3," that...
Hi, Misty! Given the information here, all of these problems can be set up as linear functions with 2 points, then solved. (If there are scatterplots associated with these questions, then you would likely enter the data points into a calculator to determine the line of best fit...
Hi, Conny! The volume for a cylinder is founding using area of the base x the height (V = Bh). The base is the circle with radius 6 cm, the "height" of the cylinder is the length of the shipping container. Area of the base is pi x radius squared (A = πr2). V...
Hi, Sue. Since you have two points, the first thing to do is find the slope of the line. (Slope is often written as m) The slope formula is: y2-y1 x2-x1 ...
Hi, Daisy. Your first two answers are reversed. A simile uses "like" or "as;" a metaphor is an implied comparison. Question 4 and 5 are correct. I am not sure about number 3; it could also be a metaphor.
Hi, Mondrea. to simplify a radical, we break it up into perfect squares. For variables, even exponents are perfect squares. 448 = 64 * 7 x8 is a square y19 = y18 * y So, we have √64 * √7 * √x8 * √y18 * √y =...
Hi, Maddi. The capacity IS the volume, but since the radius is measured in cm, we need to covert 250 mL to cubic centimeters (cc, or cm3). 1 mL = 1 cm3 so, 250 mL = 250 cm3 The volume of the cone is 250 cm3. The formula for volume of a cone is...
Hi, Maira. The discriminant is the part of the quadratic formula that is under the radical sign, that is, b2-4ac. You can use it to determine how many real solutions the equation has. First, bring all the terms to one side of the equation: 6x2 - 2x + 1 = 0 a = 6 b = -2 c...
Hi, Maira. The vertex form of a parabola is written y = a(x-h)2 + k where h and k are the coordinates of the vertex of the parabola. The x-coordinate of the vertex, or h, also represents the axis of symmetry. So in your problem y=-2(x+w)^2+6, the axis of symmetry...
Hi, Maira. The general equation h = 96x - 16x2 tells us the height at x seconds. We need to have a specific number of seconds to find the exact height. For 1 second, plug 1 in for x: h = 96(1) - 16(1)2 so h = 80 ft For 2 seconds, h = 96(2)...
Hi, Elizabeth. I think you may be missing the division sign in your problem. The monthly payment formula is usually written: M = P(1+r)t r / [(1+r)t-1] Plugging in the numbers provided we get: M = 17,000(1.05)30 (.05) / [(1.05)30 - 1] Remember your order of operations...
Hi, Rebecca. You can find this on a graph by starting at (-3, 3) and counting up 3, right 1 until you get to the y-axis. (The gradient or slope is the "rise over run.") You can also find it by using the slope-intercept equation: y = mx + b Use (-3, 3) for x...
Hi, Charles. To write this in math terms, we use a variable to represent the unknown number. We most often use n or x as the variable, but you can choose almost any letter. There are a lot of ways to write multiplication too. The most common way of writing 7 times n is simply...
Hi, Chewbacca. Actually neither! The variable stands for a number. When you have a variable by itself, it is 1 "number." The coefficient of the variable is 1. In your problem, the x - 5x can be rewritten as 1x - 5x, which simplifies to -4x. Hope this helps!
Hi, The. The domain of a function is the set of all possible values for x. The range is all possible values for y. You should be able to see these pretty easily from the graph. If I understand your function correctly: f(x) = square root(x+2) - 3 then x cannot be less than...
Hi, Bianca. Since this is a monomial (only one term), let's look at what it is made of. 3x^2 means 3 times x times x. Since these are multiplied together, they are the factors. So you would factor it as (3)(x)(x). Hope this helps! Kathye
Hi, Laura. Since the ratio of cash held to cash paid is the same, then the ratio of Tom's money held to Dick's money held to Harry's money held is the same as the ratios they paid. The ratio of cash held is 100:60:40 which simplifies to 10:6:4 or 5:3:2. The ratio of cash paid is the same,...