Practice Quiz Mode
Take all 4 MCQs in interactive quiz mode with timer and progress tracking
The measure of angle $R$ is $\frac{2\pi}{3}$ radians. The measure of angle $T$ is $\frac{5\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?
Difficulty: Medium
A:
75
B:
120
C:
195
D:
390
Triangle $ABC$ is similar to triangle $DEF$, where $A$ corresponds to $D$ and $C$ corresponds to $F$. Angles $C$ and $F$ are right angles. If $\tan(A)=\sqrt{3}$ and $DF=125$, what is the length of $\overline{DE}$?
Difficulty: Hard
A:
$125\frac{\sqrt{3}}{3}$
B:
$125\frac{\sqrt{3}}{2}$
C:
\(125\sqrt{3}\)
D:
$250$
The equation $x^{2}+\left(y-1\right)^{2}=49$ represents circle A. Circle B is obtained by shifting circle A down $2$ units in the $xy$-plane. Which of the following equations represents circle B?
Difficulty: Hard
A:
$(x-2)^{2}+(y-1)^{2}=49$
B:
$x^{2}+(y-3)^{2}=49$
C:
$(x+2)^{2}+(y-1)^{2}=49$
D:
$x^{2}+(y+1)^{2}=49$
A circle has center $O$, and points $A$ and $B$ lie on the circle. The measure of arc $AB$ is $45^{\circ}$ and the length of arc $AB$ is $3$ inches. What is the circumference, in inches, of the circle?
Difficulty: Hard
A:
3
B:
6
C:
9
D:
24
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