Let $\mathrm { a } , \mathrm { b } , \mathrm { x }$ and y be positive numbers such that $$\begin{aligned}
& \frac { x } { a } \cdot \frac { b } { y } = 2 \\
& \frac { a ^ { 2 } } { x ^ { 2 } } + \frac { b ^ { 2 } } { y ^ { 2 } } = 20
\end{aligned}$$ Given this, which of the following is the value of x in terms of a? A) $\frac { a } { 2 }$ B) $\frac { 3 a } { 4 }$ C) $\frac { 3 a } { 5 }$ D) $\frac { 4 a } { 5 }$ E) $\frac { 5 a } { 6 }$
For real numbers $x , y$ and $z$ $$\begin{aligned}
& y > 0 \\
& x - y > z
\end{aligned}$$ Given this, which of the following is always true? A) $x > z$ B) $x > y$ C) $z > y$ D) $x > 0$ E) $z > 0$
$$\begin{aligned}
& f ( x ) = x ^ { 2 } \\
& g ( x ) = 2 x - 1
\end{aligned}$$ For these functions, what is $\mathbf { g } ( \mathbf { f } ( \mathbf { 2 } ) )$? A) 0 B) 3 C) 5 D) 7 E) 9
A bag contains 2 red, 2 white, and 1 yellow marble. When 4 marbles are randomly drawn from the bag, what is the probability that the remaining marble in the bag is red? A) $\frac { 1 } { 2 }$ B) $\frac { 2 } { 3 }$ C) $\frac { 3 } { 4 }$ D) $\frac { 2 } { 5 }$ E) $\frac { 3 } { 5 }$
ABCD is a parallelogram AECD is a trapezoid $| \mathrm { BE } | = 3 \mathrm {~cm}$ $| \mathrm { DC } | = 4 \mathrm {~cm}$ If the area of the parallelogram ABCD in the figure is $20 \mathrm {~cm} ^ { 2 }$, what is the area of triangle $CBE$ in $\mathbf { cm } ^ { \mathbf { 2 } }$? A) 7 B) 7,5 C) 8 D) 8,5 E) 9
ABCD is a rectangle $\wideparen { \mathrm { CE } }$ is a circular arc with center A $| \mathrm { DA } | = 4 \mathrm {~cm}$ $| \mathrm { AC } | = 8 \mathrm {~cm}$ According to the given information, what is the area of the shaded circular sector in $\mathbf { cm } ^ { \mathbf { 2 } }$? A) $\frac { 16 \pi } { 3 }$ B) $\frac { 20 \pi } { 3 }$ C) $\frac { 25 \pi } { 3 }$ D) $\frac { 28 \pi } { 3 }$ E) $\frac { 32 \pi } { 3 }$
O is the center of the circle AT is tangent to the circle at point T $$\begin{aligned}
& | A T | = 3 \mathrm {~cm} \\
& \mathrm {~m} ( \widehat { \mathrm { OAT } } ) = 45 ^ { \circ }
\end{aligned}$$ According to the given information, what is the length of arc BT in cm? A) $\frac { \pi } { 2 }$ B) $\frac { 2 \pi } { 3 }$ C) $\frac { 3 \pi } { 4 }$ D) $\frac { 4 \pi } { 5 }$ E) $\frac { 5 \pi } { 6 }$
The vertices of a parallelogram with diagonals $[ AC ]$ and $[ BD ]$ are $\mathrm { A } ( 3,1 ) , \mathrm { B } ( 5,3 ) , \mathrm { C } ( 2,5 )$ and $\mathrm { D } ( \mathrm { a } , \mathrm { b } )$. What is the length of diagonal $[ BD ]$ in units? A) 1 B) 2 C) 3 D) 4 E) 5