# Tutor profile: Erica H.

## Questions

### Subject: Geometry

Find the area of a hexagon with sides that are 12 inches long, and an apothem of 10 inches long.

The equation for the area of a hexagon is: $$Area = \frac{1}{2}(perimeter)(apothem)$$ To find the perimeter of a hexagon, we can add up the length of each side ($$12+12+12+12+12+12$$) or multiply the length of one side ($$12$$ inches) by the number of sides in a hexagon ($$6$$). $$12+12+12+12+12+12=72$$ or $$12 * 6 = 72$$ Either way, we come to the same conclusion that the perimeter of the hexagon is $$72$$ inches. An apothem is similar to a radius, but where a radius is a line from the center to the perimeter (usually found in circles), an apothem is a line from the center of a regular polygon to the center of a side. The apothem creates a right angle with a side. The length of the apothem is given to us in the question: $$10$$ inches. Now that we know the values for the $$perimeter$$ and the $$apothem$$, we can plug these values into the equation and solve: $$Area=\frac{1}{2}(perimeter)(apothem)$$ $$Area=\frac{1}{2}(72$$ inches$$)(10$$ inches$$)$$ $$Area=\frac{1}{2}(720$$ inches$$^2)$$. ---> multiplying by $$\frac{1}{2}$$ is the same as dividing by $$2$$. $$Area= 360$$ inches$$^2$$ Final answer: $$Area= 360$$ inches$$^2$$ Please take note of the measurement unit in our final answer. Area is always measured in units squared or $$units^2$$. While finding the area, we multiplied inches in the perimeter by inches in the apothem, giving us $$inches^2$$.

### Subject: Pre-Algebra

Follow the order of operations to find the value of $$n$$: $$8+4*3=n$$

When following the order of operations, we first solve any expressions in parentheses, then any exponents. This equation has neither parentheses nor exponents in this equation, so we can skip these steps. Next, we want to multiply or divide, which ever comes first when reading an equation left to right. In this equation, there is multiplication: $$4*3$$. $$8+4*3=n$$ --> multiply $$4*3$$ $$8+12=n$$ Last, we want to add or subtract, which ever comes first when reading an equation left to right. In this equation, there is addition. $$8+12=n$$ --> add $$8$$ plus the $$12$$ we got while multiplying in the previous step. $$20 = n$$ Final answer: The value of $$n=20$$.

### Subject: Algebra

Use substitution to find the values for x and y for the following related equations: $$\binom{2x+y=6}{y-8x=1}$$

Substitution is when we find the value of one variable and then substitute that variable into the other equation. Step 1- Isolate a variable on one side of the equal sign of any equation. I am going to isolate the y variable in the 2nd equation. $$y-8x=1$$ ---> Solve for $$y$$ by adding $$-8x$$ to both sides. $$-8x$$ cancels out on the left side. $$y= 1 +8x$$ Step 2- Now that we know the value of $$y$$ is $$1+8x$$, we can substitute $$(1+8x)$$ where we see a y in the 1st equation. $$2x+y=6$$ ---> Substitute in $$(1+8x)$$ for $$y$$. $$2x+(1+8x) = 6$$ $$2x+1+8x = 6$$ ---> Combine like terms (add $$2x$$ and $$8x$$). $$10x+1=6$$ ---> Isolate $$10x$$ by subtracting $$1$$ on each side $$10x=5$$. ---> Divide by $$10$$ on each side to isolate $$x$$. $$x = \frac{1}{2}$$ Step 3- Now that we know $$x = \frac{1}{2}$$, we can plug $$\frac{1}{2}$$ into either equation where we see an $$x$$ in order to find $$y$$. $$y-8x=1$$ $$y-8(\frac{1}{2})=1$$ $$y-4=1$$ $$y=5$$ Final Answers: $$x = \frac{1}{2}; y = 5$$ or $$ (\frac{1}{2}, 5)$$

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