Solve for \( x \) by completing the square: \[ x^{2}=-3 x+10 \] Determine the value of \( p \) if \( f(x)=x^{2}+p x^{2}-x+3 \) gives a remainder of 15 when divided by \( x-2 \).

Solve the inequality. Express the solution set in set-builder notation and interval notation. Graph the solution set on a real number line. \[ 5(x-6)>4(x-6)+x \]

в) \( x+15 \frac{3}{17}=20 \frac{14}{17} \) \( x= \) \( x= \) \( x= \)

Graph the parabola. \[ y=(x-1)^{2}+5 \] Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.

3. (*) Dado los vectores \( \vec{a}=\left(1,2 x_{1}, 3\right) \), \( \vec{b}=\left(-1,3 x_{2},-2 x_{1}\right), \vec{c}=\left(2,2,-3 x_{2}\right) \) los valores de \( x_{1} \quad y x_{2} \) para los cuales se cumple que \( 2 \vec{a}-3 \vec{b}+\vec{c}=(7,15,21) \) es respectivamente: a. \( (2,-1) \) b. \( (-1,2) \) c. \( (2,-3) \) d. \( (-3,1) \)

Elsa løper ei løype som er \( 1,75 \mathrm{~km} \) kortere enn den William loper, Tariq løper \( 15,95 \mathrm{~km} \), og det er 2,43 lenger enn William. Hvor langt løper Elsa og William?