Tutor profile: Danielle K.
Given $$11$$ and $$4$$ are the lengths of two sides of a triangle, find the range of possible values for the third side.
The Triangle Inequality tell us that the sum of the lengths of any two sides of a triangle should be greater than the length of the third side. We know the side lengths are 4, 11, and x (some unknown value). So let's start with some inequalities, a) $$4+11> x $$ $$15>x$$ $$x<15$$ b) $$4+x>11 $$ $$x>7$$ c) $$11+x> 4$$ $$x> -7$$ If we graph all three inequalities on a number line we will find the numbers in the solution set of all three inequalities are between 7 and 15 so $$7<x<15$$. So the range of possible values for the third side of the triangle are $$7<x<15$$. A short cut for finding the solution is $$|a-b|<x< a+b$$ where $$a$$ and $$b$$ are the given side lengths. So with the shortcut: $$|4-11|<x<4+11$$ $$|-7|<x<15$$ $$ 7<x<15$$
Evaluate: $$3-4 * (2-1) $$.
Explanation: Remember the order of operations: your teacher may have used the memory tool PEMDAS or GEMS to help you remember this. P-Parenthesis G- Grouping Symbols E- Exponents E-Exponents M-Multiplication or M- Multiply/divide D-Division S- Subtract/Add A-Addition S-Subtraction G: We need to start with the grouping symbol/Parenthesis. Since 2-1 is in parenthesis, we need to do that first. $$2-1=1 $$ so we are left with: $$3-4 * 1$$. E: Now we can deal with any exponents. Since there aren't any we can move on. M: Next is multiplication and/or division. I see $$4*1$$. $$4*1 =4.$$ so we are left with: $$3-4$$. S: Finally, we add and/or subtract. $$3-4=-1$$. Answer= -1 What would my work look like? $$3-4 * (2-1) $$ $$=3-4*1$$ $$=3-4$$ $$=-1$$
Given the $$line L$$ with equation $$y=3x$$ and the $$line M$$ $$y=1/3x$$. Which line is steeper?
The slope or rate of change of a function determines how steep a line is. Let's compare the slopes of the two lines. $$m_L =3$$ . and $$m_ M= 1/3$$. A slope of $$3$$ means that the function rises 3 units and runs 1 unit to the right. Sketch a quick graph. A slope of $$1/3$$ means that the function rises 1 unit and runs 3 units to the right. Sketch another quick graph. Which line looks closer to vertical? That is the steepest line. Answer: $$Line L$$ is steeper.
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