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# Tutor profile: Danielle K.

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Danielle K.
High School Math Teacher for 8 years
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## Questions

### Subject:Geometry

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Question:

Given \$\$11\$\$ and \$\$4\$\$ are the lengths of two sides of a triangle, find the range of possible values for the third side.

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Danielle K.

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\$\$

### Subject:Pre-Algebra

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Question:

Evaluate: \$\$3-4 * (2-1) \$\$.

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Danielle K.

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\$\$

### Subject:Algebra

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Question:

Given the \$\$line L\$\$ with equation \$\$y=3x\$\$ and the \$\$line M\$\$ \$\$y=1/3x\$\$. Which line is steeper?

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Danielle K.

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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