Unit
Linear Equations and Inequalities
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
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University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
The definition of a function can be extended to define the definition of an inverse, or an invertible function. It's important to understand proving inverse functions, and the method of proving inverse functions helps students to better understand how to find inverse functions. Students should review how to find an inverse algebraically and the basics of proofs.
Solving a applied linear equation, so in this case we're dealing with a Geometry application where we are given the angles of a triangle and we're asked to find each angle. So each angle in this case is in terms a variable x+59, x+3, and 2x+6.
What we have to remember is our rules from Geometry the angles of a triangle add up to 180. So using that we can add these three angles up and study for the 180 and we've turned our word problem into an equation which we can then solve. So x+59 is one angle +x+3 second 2x+6=180. We've turned our sentences into an equation. Okay from here we need to combine like terms like we would in the other linear equation.
Now x, x, 2x does make 4x, 59+3 is 62+6 is 68 and the other side hasn't changed at all. Okay we then want to isolate our variable get our x by itself, so I need to subtract 68. 180-68 is 112 if you want a short cut you could subtract 70 which is 110, 68 is 2 less than that which will bunk you back up to 112 and to solve for x divide by 4. 4 cancels over here, if you want to figure this one out you can always plug in your calculator but you know 100 divide by 4 is 25, 12 is more than 100, 12 divie by 4 is 3. So you actually have to add those 2 up 25+3 would give you 28. So we end up getting x=28.
In doing this problem that we have to be careful with what the problem is actually asking for. It's asking us to find each angle. We found x which is just a variable. So in order just to actually answer this question we need to go back and plug in x for each of these variables. The plug in 28 in over here 28+59 this gives us 87, 28 into here 28+3 is 31 and then plug in 28 over here 28 times 2 is 56+6 is 62. You can always plug these into a calculator to make sure we did it right, and we're good to go. Underneath these are [IB] to 180 so we know we did our math right so the answers for the three angles are 87, 31, and 62.