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Flashcards: HiSET: Math

Consider regular Hexagon ABCDEF $\displaystyle ABCDEF$.

On this hexagon, perform the translation $F\rightarrow B$ $\displaystyle F\rightarrow B$. Then perform a $120^{\circ }$ $\displaystyle 120^{\circ }$ clockwise rotation on the image with center at $\displaystyle B$.

Let $\displaystyle A'$ be the image of $\displaystyle A$ under these transformations, $\displaystyle B'$ be the image of $\displaystyle B$, and so forth. Under these images, which point on the original hexagon does $\displaystyle D'$ fall?

$\displaystyle A$

$\displaystyle F$

$\displaystyle C$

$\displaystyle B$

$\displaystyle E$

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Flashcards: HiSET: Math

Consider regular Hexagon ABCDEF $\displaystyle ABCDEF$.

$\displaystyle A$

$\displaystyle F$

$\displaystyle C$

$\displaystyle B$

$\displaystyle E$

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Flashcards: HiSET: Math

Consider regular Hexagon ABCDEF $\displaystyle ABCDEF$.

Your answer:

$\displaystyle A$

Your answer:

$\displaystyle C$

Your answer:

$\displaystyle B$

Your answer:

$\displaystyle E$

Correct answer:

$\displaystyle F$

Explanation:

The translation $F\rightarrow B$ $\displaystyle F\rightarrow B$ on a figure is the translation that shifts a figure so that the image of $\displaystyle F$ coincides with $\displaystyle B$. All other points shift the same distance in the same direction. Below shows the image of the given hexagon under this translation, with the image of $\displaystyle D$ marked as D'' $\displaystyle D''$:

If this new hexagon is rotated clockwise $120 ^{\circ }$ $\displaystyle 120 ^{\circ }$ - one third of a turn - about $\displaystyle B$ - the image is the original hexagon, but the vertices can be relabeled. Letting $\displaystyle D'$ be the image of D'' $\displaystyle D''$ under this rotation, and so forth:

$\displaystyle D'$ coincides with $\displaystyle F$ in the original hexagon, making $\displaystyle F$ the correct response.

Flashcards: HiSET: Math

Solve.

$\frac{x}{4}+11=15$ $\displaystyle \frac{x}{4}+11=15$

$\displaystyle 4$

$\displaystyle 8$

$\displaystyle 12$

$\displaystyle 16$

$\displaystyle 18$

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Flashcards: HiSET: Math

Solve.

$\frac{x}{4}+11=15$ $\displaystyle \frac{x}{4}+11=15$

Your answer:

$\displaystyle 4$

Your answer:

$\displaystyle 8$

Your answer:

$\displaystyle 12$

Your answer:

$\displaystyle 18$

Correct answer:

$\displaystyle 16$

Explanation:

In order to solve for the variable, $\displaystyle x$, we need to isolate it on the left side of the equation. We will do this by reversing the operations done to the variable by performing the opposite of each operation on both sides of the equation.

Let's begin by rewriting the given equation.

$\frac{x}{4}+11=15$ $\displaystyle \frac{x}{4}+11=15$

Subtract $\displaystyle 11$ from both sides of the equation.

$\frac{x}{4}+11-11=15-11$ $\displaystyle \frac{x}{4}+11-11=15-11$

Simplify.

$\frac{x}{4}=4$ $\displaystyle \frac{x}{4}=4$

Multiply both sides of the equation by $\displaystyle 4$.

$\frac{x}{4}\times 4=4\times 4$ $\displaystyle \frac{x}{4}\times 4=4\times 4$

Solve.

x=16 $\displaystyle x=16$

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