Question 1

In this figure, triangle $GHJ$ is similar to triangle $PQR$.

Based on this information, which ratio represents $	ext{tan}H$?

Accepted Answer

$\frac{8}{15}$

Answer

$\frac{8}{17}$

Answer

$\frac{17}{8}$

Answer

$\frac{15}{8}$

Question 2

A spring is attached at one end to support $B$ and at the other end to collar $A$, as represented in the figure. Collar $A$ slides along the vertical bar between points $C$ and $D$. In the figure, the angle $\Theta$is the angle created as the collar moves between points $C$ and $D$.

When $\Theta=28^\circ$, what is the distance from point $A$ to point $B$ to the nearest tenth of a foot?

Enter your answer in the box.

Accepted Answer

3.4

Question 3

A spring is attached at one end to support $B$ and at the other end to collar $A$, as represented in the figure. Collar $A$ slides along the vertical bar between points $C$ and $D$. In the figure, the angle $\Theta$ is the angle created as the collar moves between points $C$ and $D$.

When the spring is stretched and the distance from point $A$ to point $B$ is $5.2$ feet, what is the value of $\Theta$ to the nearest tenth of a degree?

Accepted Answer

$54.8^\circ$

Answer

$35.2^\circ$

Answer

$45.1^\circ$

Answer

$60.0^\circ$

Question 4

The figure shows line $AC$ and line $PQ$ intersecting at point $B$. Lines $A'C'$ and $P'Q'$ will be the images of lines $AC$ and $PQ$, respectively, under a dilation with center $P$ and scale factor $2$.

Which statement about the image of lines $AC$ and $PQ$ would be true under the dilation?

Accepted Answer

Line $A'C'$ will be parallel to line $AC$, and line $P'Q'$ will be the same line as
line $PQ$.

Answer

Line $A'C'$ will be perpendicular to line $AC$, and line $P'Q'$ will be  parallel to line $PQ$.

Answer

Line $A'C'$ will be parallel to line $AC$, and line $P'Q'$ will be parallel to
line $PQ$.

Answer

Line $A'C'$ will be perpendicular to line $AC$, and line $P'Q'$ will be  the same
line as line $PQ$.

Question 5

In the $xy	ext{-coordinate}$ plane, $\vartriangle ABC$ had vertices $A(-4,6), B(2,6),$ and $C(2,2)$.
$\vartriangle DEF$ is shown in the plane.

What is the scale factor and the center of dilation that maps $\vartriangle ABC$ to $\vartriangle DEF$?

Accepted Answer

The scale factor is $\frac{1}{2}$,and the center of dilation is the origin.

Answer

The scale factor is $2$, and the center of dilation is the origin.

Answer

The scale factor is $2$, and the center of dilation is point $B$.

Answer

The scale factor is $\frac{1}{2}$,and the center of dilation is point , $B$.

Question 6

In right triangle $ABC, m\angle B  
eq m\angle C$. Let $\sin B=r$ and $\cos B$. What is $\sin C - \cos C$?

Accepted Answer

$s-r$

Answer

$\frac{r}{s}$

Answer

$r-s$

Answer

$r+s$

Question 7

The figure shows two semicircles with centers $P$ and $M$. The semicircles are tangent to each other at point $B$, and $\overrightarrow{DE}$ is tangent to both semicircles at $F$ and $E$.

If $PB = BC = 6,$ what is $ED$?

Accepted Answer

$\sqrt{72}$

Answer

$8$

Answer

$\sqrt{48}$

Answer

$6$

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