Use the linear programming procedure to solve the problem below. Natasha's cat, Dancer, will eat both dry food and wet (canned) food. Natasha wants Dancer to eat meals that are nutritious, but would also like to save some money on her cat's food bill. Dancer usually eats wet food. However, the wet food is more expensive. In order to save money, Natasha is trying to decide if she can switch her cat to a diet with some wet and some
dry food, or perhaps all dry food. However, she wants to ensure that the new diet satisfies Dancer's nutritional requirements.

Protein and fat are two important components of a cat's diet. Proteins serve as building blocks for bones and muscles, while fat provides energy and helps with the absorption of vitamins. Dancer needs at least 60 grams of protein per day and at least 12 grams of fat per
day. The wet food provides about 12 grams of protein per serving while the dry food
provides about 24 grams of protein per serving. The wet food contains about 6 grams of fat while dry food contain about 4 grams of fat per serving. The wet food costs 80 cents per serving and the dry food costs 66 cents per serving. How many servings of wet and dry food will Dancer need each day to meet her nutritional requirements while keeping Natasha's pet food bill a minimum?

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb