Let C(x) be the cost to produce x batches of widgets, and let R(xp be the revenue in thousands of dollars. Complete parts (a) through (d) below.
R(X) 12x, C(x) x+ 10
(b) Find the minimum break-even quantity.
Using the expressions -x2 12x and/or x+ 10, identify an equation to be solved in order to find the minimum break-even quantity.
The minimum break-even quantity is:
(Simplify your answer.)
(c) Find the maximum revenue.
How can the maximum revenue be found? choose correct answer below.
A. Find the y coordinate of the vertex of R(x).
B. Find the maximum y-coordinate of a point where R(x) = C(x).
C. Find the x-coordinate of the vertex of R(x).
D. Find the y-intercept of R(x).

Construct the graph that models the given situation

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)

The mean of 10 values is 19. if further 5 values areincluded the mean becomes 20. what is the meanthese five additional values? a) 10b) 15c) 11d) 22