A company makes two kinds of animal food, A and B, which contain two food supplements. It takes 2 pounds of the first supplement and one pound of the second to make a dozen cans of food A, and 4 pounds of the first supplement and 5 pounds of the second to make a dozen cans of food B. On a certain day 80 pounds of the first supplement and 70 pounds of the second are available.   Use the geometrical approach to find the number of cans of each food should be made to maximize profit, if the profit on a dozen cans of food A is $3 and the profit on a dozen cans of food B is $10. Show every necessary steps.

Zion is given four coordinates of a quadrilateral: (-4,-2),(4,2),(6,-2),(-2,-6). Zion wants to determine what kind of quadrilateral is made. Which of the following statements are true and useful to determine which figure is made? Select all that apply. Both diagonals have a length of 10, so it cannot be a parallelogram. The segments have slopes of 1/2,-2,1/2,-2 so it is a parallelogram. The diagonals are perpendicular to each other, so it is a rhombus or a kite. The lengths of the sides are 8.94 and 10 so it is a rectangle. The lengths of the sides are 8.94 and 10 so it is a square. Adjacent sides have slopes of 1/2 and -2, so they are perpendicular.

The three vertices of a parallelogram taken in order are (-1, 0).(3, 1) and (2, 2)respectively.Find the coordinates of the fourth vertex.

If the three points A(3,1), B(2k, 3k) and C(k, 2k) are in line, determine the value of k.

If the points (h, 0), (a, b), and (0, k) lie on a line, show that 1 + k h

a and b are two points in the third dimension. Write an equation that describes the set of points that are equidistant to a and b. Draw a picture of this set in the case where a = i and b = j.

ans. and 7) show that the lines リ-3 メ-2 = -2 2ー3 メー2-4 intersect. X-2 = %3D 2

Given the following points on the graph, A (0,2), B (-5,3), and C (-3,6). If we want to create a figure ABCD into a parallelogram, then what should the coordinate pair be for D? -7 C 6 5 B A (-2,-1) B. (1,4) C. (2,5) D. (3,3) -2 -1 -4 3 → 0

A battery for an electric vehicle will provide a range of 5 miles for each battery, but for each battery the range of all the batteries is decreased by 0.3 miles because of the added weight. a) If it wasn’t for this decrease due to weight, the relationship between range and number of batteries would be linear. Write the formula for this linear relationship. b) now modify the linear case to the non-linear case and write the formula for range in terms of the number of batteries that includes the decrease due to weight. c) Find the maximum range for this vehicle design and the number of batteries that gives the maximum range.