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Tutor profile: Beverly M.

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Beverly M.
Industrial Engineer by Day, Mathematics Tutor by Night
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Questions

Subject: Pre-Algebra

TutorMe
Question:

What is the slope of the line that contains the points $$(4, 6)$$ and $$(13, -9)$$ ?

Inactive
Beverly M.
Answer:

To find the slope of a line given two point. We must know the formula for finding the slope when given two points. Formula: when given points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ $$m = \frac{y_{1} - y_{2}}{x_{1}- x_{2}}$$ = slope Next let's plug our points into the equation: $$(4, 6)$$ and $$(13, -9)$$ $$m = \frac{6 - (-9)}{4 -13}$$ $$m =- \frac{15}{9}$$ The slope of the line is -$$\frac{15}{9}$$

Subject: Basic Math

TutorMe
Question:

Sally walked $$½$$ of a mile yesterday and $$¾$$ of a mile today. How many miles has Sally walked?

Inactive
Beverly M.
Answer:

Set up the expression. We want to know how many total miles Sally walked which requires the use of Addition. Notes for adding fractions. Look at the denominator: If same denominator we can simply add the numerators and simplify. If different denominator we need to find the Least Common Denominator (LCD) Step 1. Setting up our expression $$\frac{1}{2}+\frac{3}{4}=x$$ Step 2: Identify denominator Different denominators Step 3: Find the LCD. Since 2 is a multiple of 4 we know that the LCD is 4. Step 4: Multiply the fraction $$\frac{1}{2}$$ by $$\frac{2}{2} = 1$$ $$\frac{2}{4}+\frac{3}{4}=x$$ *Note: By multiplying by 1 does not change the original equation Step 5: Combine like terms $$\frac{5}{4} = x$$ Solution: Sally walked $$\frac{5}{4}$$ miles.

Subject: Algebra

TutorMe
Question:

Solve for x: $$2x^2+4(x^2 + 3) -2 =22$$

Inactive
Beverly M.
Answer:

First let us take note of the order of operations: Please (Parentheses) Excuse (Exponents) My (Multiplication) Dear (Division) Aunt (Addition) Sally (Subtraction) *Note that the M and D and A and S are to be solved in the order they are received. Let’s solve: $$2x^2+4(x^2+3)-2=22$$ Step 1: My (Multiplication) Multiply 4 by the expressions inside the parentheses. $$2x^2+4x^2+12-2=22$$ Step 2: Aunt (Addition) Add $$2x^2+4x^2$$ $$6x^2+12-2=22$$ Step 3: Sally (Subtraction) Subtract $$12-2$$ $$6x^2+10=22$$ Step 4: Set the equation equal to zero Subtract $$22$$ from both sides $$6x^2+10-22=0$$ Step 5: Sally (Subtraction) Subtract $$10-22$$ $$6x^2-12=0$$ Step 6: Solve for $$x$$ Add $$12$$ to both sides $$6x^2=12$$ Step 7: Solve for $$x$$ ctd. Divide by $$6$$ on both sides $$x^2=2$$ Step 8: Solve for $$x$$ ctd. Take the Square Root of both sides x=$$\sqrt{2}$$ and $$-\sqrt{2}$$ Step 9: Check your answer by plugging in $$x$$ $$2x^2+4(x^2+3)-2=22$$ $$2[(\sqrt{2})^2+4((\sqrt{2})^2+3)-2=22$$ $$2(2)+4(2+3)-2=22$$ $$4+4(5)-2=22$$ $$4+20-2=22$$ $$24-2=22$$ $$22=22$$ *Note: A negative number squared is a positive number thus same answer for $$-\sqrt{2}$$

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