Examine how the completing-the-square method is used to solve the quadratic equation \( x^{2}-4 x-9=0 \) below. Step \( 1 x^{2}-4 x-9+13=0+13 \) Step \( 2 \quad x^{2}-4 x+4=13 \) Step \( 3 \quad(x-2)^{2}=13 \) Step \( 4 \quad x-2= \pm \sqrt{13} \) Step \( 5 \quad x-2+2=2 \pm \sqrt{13} \) Step \( 6 \quad x=2 \pm \sqrt{13} \) If the same solution method is used to solve the quadratic equation \( x^{2}+10 x-7=0 \), what value should be added to both sides of the equation in Step 1 ? 25 32 20 11

50 g calcium carbonate is heated to form calcium oxide and \( \mathrm{CO}_{2}(\mathrm{~g}) \) Calculate the percentage yield if 21 g facut Calciam axiae. is formed.

Find the values of the indicated functions assuming \( \theta \) is an acute angle. Given \( \cos \theta=\frac{40}{41} \), find \( \sin \theta \) and \( \cot \theta \). \( \sin \theta=\square \) (Simplify your answer.)

33. Ikkita ishehi birgalikda ishlab 1456 stul yasadi. Agar birinchi ishchi bir kunda 32ta, ikkinchisi esa 24 ta stul yasagan bo'lsa, ularning har biri jami necha stuldan yasagan?

La ecuación de la parábola con vértice en el origen y foco en el punto \( (0,-5) \), es: a. \( x^{2}=-20 y \) \( b . x^{2}=-5 y \) \( c y^{2}=20 x \) \( v^{2}=5 v \)

Find all solutions of the equation in the interval \( [0,2 \pi) \) \[ \cot ^{2} x-3 \csc x=-3 \] Write your answer in radians in terms of \( \pi \). If there is more than one solution, separate them with commas.