ALEKS Exam with verified solutions 2024 latest update

what is absolute value? distance from zero on a number line if you get a negative absolute value, why is it said to not have a solution? because distance can't be negative what are integers? all whole negative and positive numbers when should u switch the sign on an inequality? when you're dividing or multiplying by a negative number why is it that you can have a both negative and positive solution for absolute value? because if your main solution is positive, if u plug that back into the absolute value bars, you'll still get a positive number. absolute value always has to be positive, so if you get a negative number its not the absolute value. remember this numbers that u get are the result, not the ones u plug in what to do when vertical shifting a graph? take what's in the parentheses and put it equal to 0, then translate left or right that exact amount when you get 0=0 as the solution to an expression, what does this mean? all real numbers are solutions, because a real number equals a real number when you get 0=-3 as the solution, what does this mean? there's no solution a pair of coordinates represent a function if what? they don't have the same x-coordinates if you have a negative exponent as a denominator and one as the numerator, what rule can you follow to make the numerator positive? move the negative exponent to the numerator and make it positive when using elimination, what is the first step you have to do? isolate one of the variables,you can do this by multiplying both equations by different variables because they're not equal to each other, so you can do that and once its all in order just add down what is the formula for volume of a cylinder? V=pi r squared h what units is volume always in? cubed how do u find the perfect square term? take half of the coefficient term, then square it what's something to keep in mind when you're determining the LCD for one fraction on one side of the equation and one on the other? you have to multiply both sides of the LCD even if one side already has it, because they're equal to each other what should u remember when solving an absolute value equation that is different from an absolute value inequality? if the solution to the equation is bigger than 0, then you split them up and consider both solutions, if the solution is already less than 0, it has no solutions because its already negative the difference between finding a union of a set and the intersection of a set? set of all elements that are in set a or set b for union, set of all elements that are in set a and set b for intersection what is a rational number? a ratio of two integers, also fractions and squares that equal integers what is formula for area of a semicircle a=1/2r^2 what is formula for area of a triangle 1/2bh what do u do to find the roots? get the expression into quadratic form, get solutions and set equal to 0 what happens if you dont get the two identical binomials by grouping? either try grouping them differently or it cant be factored by grouping whats one thing u should add in when doing grouping? if you have to factor by 1 to get the identical binomial, then you have to add a +1 what is the formula for circumference of a circle? C= pi x d what is an LCM? its exactly like the least common denominator but without the fraction what's the first step to solving a quadratic equation needing simplification? foil and get everything on one side, then make it equal 0 what is the distance formula? square root of (x2-x1)^2 + (y2-y1)^2 with absolute value inequalities, do you still have to split them up if the value is greater than 0? yes when you split up an absolute value inequality, what's something you need to do that you wouldn't do for an absolute value equation? change not only the sign of the solution, but also the sign of the inequality to correspond when graphing a parabola, what should the coordinates of the vertex equal to? 0,0 how do u find the other 2 points on each side of the parabola? choose 2 values on each side of x=0 what is the distance formula word problem formula? distance= time x rate how do you convert from a radical form to an exponent form? from radical to exponent you go counterclockwise, from exponent to radical, numerator goes on the inside. also, this rule only works if the number on the outside of the radical is odd, or if the outside is even but the inside is greater than 0 the slope of parallel lines will be what? the same slope as the other line the slope of a perpendicular line will be what? if the product if their slopes is equal to -1 what is the equation for a parabola with (h,k)? y=a(x-h)^2+k what is the vertex with a parabola that has a + something? (h,k) what is the formula for surface area of a cylinder? pir^2 x pir^2 x 2