Topic
Q:
6. \( 81 r+48 m-6 \)
Q:
Write the system of equations and then use a matrix to solve.
6. Raina, Justin, and Kevin sent a total of 118 text messages during class yesterday. Justin sent 7 fewer
messages than Raina. Kevin sent 3 times as many messages as Raina. How many messages did each
student send?
Q:
Write the system of equations and then use a matrix to solve.
5. The Varsity Bearcat football team scored a total of 50 points in one game. They scored 14 times. The
scoring was made up of touchdowns ( 6 points each), PATs ( 1 point each), and field goals ( 3 points
each). They had 3 more touchdowns than field goals. How many of each type of score did the team
have?
Q:
18 Consider the equation \( x^{2}-2 x+r=0 \), where \( r \) is a real parameter.
\( 1^{\circ} \) Calculate \( r \) so that the roots \( x_{1} \) and \( x_{2} \) exist.
\( 2^{\circ} \) Calculate \( r \) so that :
\( \begin{array}{lll}\text { a) } \frac{1}{x_{1}}+\frac{1}{x_{2}}=-\frac{1}{2} & \text {; b) } x_{1}^{2}+x_{2}^{2}=6 & \text {; ce } \frac{1}{x_{1}^{2}}+\frac{1}{x_{2}^{2}}=1 \\ \text { d) }\left(x_{1}-x_{2}\right)^{2}=4 & \text {; e) } \frac{1}{x_{1}-2}+\frac{1}{x_{2}-2}=3\end{array} \)
Q:
Determine the value of the variable \( y \).
\[ \left\{\begin{array}{c}x+y+z=1 \\ -2 x-y-z=3 \\ x+y+3 z=-1\end{array}\right. \]
Q:
Jesarrolla la función polinomial racional,
Jtilizando fracciones parciales:
\[ \frac{11 x+21}{(x+6)(x+1)} \]
Q:
Write an equation using four numbers that multiply to 0, none of which
are opposites.
Q:
Factoriza el polinomio:
\[ x^{3}-11 x^{2}+30 x= \]
Q:
Solve the given system of 3 -variable equations by hand with elimination.
2. \( \left\{\begin{array}{l}5 x+7 y-3 z=3 \\ 3 x+4 y+2 z=6 \\ x+3 y-5 z=-7\end{array}\right. \)
Q:
18 Consider the equation \( x^{2}-2 x+r=0 \), where \( r \) is a real parameter.
\( 1^{\circ} \) Calculate \( r \) so that the roots \( x_{1} \) and \( x_{2} \) exist.
\( 2^{\circ} \) Calculate \( r \) so that :
\( \begin{array}{lll}\text { a) } \frac{1}{x_{1}}+\frac{1}{x_{2}}=-\frac{1}{2} & ; \text { b) } x_{1}^{2}+x_{2}^{2}=6 & \text {; c) } \frac{1}{x_{1}^{2}}+\frac{1}{x_{2}^{2}}=1 \\ \text { d) }\left(x_{1}-x_{2}\right)^{2}=4 & \text {; e) } \frac{1}{x_{1}-2}+\frac{1}{x_{2}-2}=3\end{array} \)
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