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Just in case you don't get the "binomials equal to 0 part"  this fact that you can use the two factors to solve for x comes from the "zero property of multiplication". If two numbers (known as factors) give a product of zero when multiplied together, then the only way...

You are right, you need a piecewise function, which you can separate based on the the segments of the domain that are given in words... First, there is the the segment from 0-400 kwh, then the segment from 400 - infinity (what an electric bill!)   Here is how to write...

The slopes of two perpendicular lines, when multiplied, have a product of -1.  Therefore, given the eq of the line with a slope of -1/3, we can conclude that the perpendicular line will have a slope of 3. so to start, our equation of interest is y=3x + b, where b is unknown.  Since...

I think you should play angry birds! No really, we do it in math class all the time.  A quadratic equation describes a parabola, which just happens to be the shape of the curve made by the bird as it is sling-shotted through the air.  Well, really it is an inverted parabola, and I will...

If your friend likes art, you can use that to motivate discussions about math.  For instance symmetry is a concept that has a lot of art application, as do triangles, squares, etc.  It all depends on what subject she is studying.  You can find interesting lesson plans and tools on...

You must draw a force diagram on the box.  The weight acts down and is perpendicular to the movement.  It doesn't do any "work" The Floor acts horizontally, opposing motion Normally, I would consider the friction to be proportional to the Normal force and do some...

I think you start with setting each of the equations equal to 29: 5x+2y=29 solve this one for y (in terms of x) 43x+4y+2z=29 67x+3y+4z=29 combine these two so that you eliminate z y= (29-5x)/2 and (86 - 67)x +(8-3)y = 19x+5y = 29. Now you could use these two equations to...

I deleted this answer and tried to post a corrected comment with better formatting...and a sign correction (thanks sung!)

Well, if the grip strip were of no width and could be straightened out to a line (which a piece of rubber cut in a circle couldn't be), then the length of the grip would correspond to the circumference of the manhole cover.   Circumference = 2*PI*radius = PI*diameter  so your answer...

You can determine the possible range of mean values since you know that the missing value is either a 6,7, or 8... minimum mean = {sum(3, 5, 9, 1, 9, 2, 0, 3, 9) + 6}/10 maximum mean = {sum(3, 5, 9, 1, 9, 2, 0, 3, 9) + 8}/10 range for mean is {4.7<= m <= 4.9}   You...