Use the model to complete the number sentence 1/2
1 answer:
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Answer:
- 3.75 bags of ChowChow
- 0.75 bags of Kibble
Step-by-step explanation:
The constraints on protein, minerals, and vitamins give rise to the inequalities ...
40c +30k ≥ 150 . . . . . . required protein
20c +20k ≥ 90 . . . . . . required minerals
10c +30k ≥ 60 . . . . . . . required vitamins
And we want to minimize 10c +12k.
The graph shows the vertices of the feasible region in (c, k) coordinates. The one that minimizes cost is (c, k) = (3.75, 0.75).
To minimize cost, the daily feed should be ...
- 3.75 bags of ChowChow
- 0.75 bags of Kibble
Daily cost will be $46.50.
Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
. That is, 
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
and replace 
and 
using expressions that contain an expression in terms of x from the first two equations we came up with.
That gives us:
which we solve for x as follows:
Now that we know x we can substitute 36 for x into the equation
and solve for z as follows:
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
That gives us:
Now that we know x we can substitute 36 for x into the equation
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.