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mixas84 [53]
3 years ago
11

Oz makes lion food out of giraffe and gazelle meat. Giraffe meat has 16 grams of protein and 32 grams of fat per pound, while ga

zelle meat has 32 grams of protein and 16 grams of fat per pound. A batch of lion food must contain at least 25,600 grams of protein and 38,400 grams of fat. Giraffe meat costs $1 per pound and gazelle meat costs $2 per pound. How many pounds of each should go into each batch of lion food in order to minimize costs

Mathematics
1 answer:
Alex3 years ago
5 0

Answer:

To minimize costs, the pounds of giraffe meat are 1,067 and the pounds of gazelle meat are 267.

Step-by-step explanation:

Let

x -----> pounds of meat of giraffe

y -----> pounds of meat of gazelle

we know that

16x+32y \geq 25,600 -----> inequality A

32x+16y \geq 38,400 -----> inequality B

C=x+2y ----> the function cost

using a graphing tool    

The solution of the system of inequalities is the shaded area (positive values of x and y between the two solid lines)

see the attached figure

Three vertices of the shaded area are (0,2,400), (1,067,267) and (1,600,0)

Substitute in the function cost and then compare the results

For (0,2,400)

C=0+2(2,400)=\$4,800   ---> It doesn't make sense, because lion food should contain giraffe meat and gazelle meat.

For (1,067,267)

C=1,067+2(267)=\$1,601

For (1,600,0)

C=1,600+2(0)=\$1,600 ---> It doesn't make sense, because lion food should contain giraffe meat and gazelle meat.

therefore

To minimize costs, the pounds of giraffe meat are 1,067 and the pounds of gazelle meat are 267.

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Dont really understand how to do this
bija089 [108]

Answers:

t_{10} = -22 \ \text{ and } S_{10} = -85

========================================================

Explanation:

t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4

and so on. This process may take a while to reach t_{10}

There's a shortcut. The nth term of any arithmetic sequence is

t_n = t_1+d(n-1)

We plug in t_1 = 5 \text{ and } d = -3 and simplify

t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8

Then we can plug in various positive whole numbers for n to find the corresponding t_n value. For example, plug in n = 2

t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2

which matches with the second term we found earlier. And,

tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}

---------------------

The notation S_{10} refers to the sum of the first ten terms t_1, t_2, \ldots, t_9, t_{10}

We could use either the long way or the shortcut above to find all t_1 through t_{10}. Then add those values up. Or we can take this shortcut below.

Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}

The sum of the first ten terms is -85

-----------------------

As a check for S_{10}, here are the first ten terms:

  • t1 = 5
  • t2 = 2
  • t3 = -1
  • t4 = -4
  • t5 = -7
  • t6 = -10
  • t7 = -13
  • t8 = -16
  • t9 = -19
  • t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that S_{10} = -85 is correct.

6 0
2 years ago
Identify the property used in the first four steps to solve the equation 4(x-7)=2x-6
myrzilka [38]

Answer:

x = 11

distributive law

additive law

multiplication property

Step-by-step explanation:

Given in the question an equation

4(x-7) = 2x-6

Distributive law

a(b+c) = ab +ac

4x - 4(7) = 2x - 6

4x -28 = 2x - 6

Use the addition property of equality to reduce the 2x on the right.

4x - 2x - 28 = 2x - 2x -6

4x -2x -28 = -6

Use the addition property of equality to reduce -28 to zero on the left.

4x - 2x- 28 + 28 = -6 + 28

2x = 22

Use the multiplication property of equality to reduce 2x to just x

2x2 = 22/22

x = 22/2

x = 11

4 0
3 years ago
A state has a sales tax of 7 percent.
Alona [7]

Answer:

Florida

Step-by-step explanation:

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5 0
3 years ago
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Alona [7]

Answer:

Eva's age is 44 years

Step-by-step explanation:

Let

x ----> Brita's age

y ----> Eva's age

we know that

The sum or their ages 118

so

x+y=118 ----> equation A

The difference in age between Brita and her daughter Eva is 30 years

so

x-y=30 ----> equation B

Solve the system by elimination

Adds equation A and equation B

x+y=118\\x-y=30\\---------\\x+x=118+30\\2x=148\\x=74

<em>Find the value of y</em>

substitute the value of x in any equation

74+y=118\\y=118-74\\y=44

therefore

Eva's age is 44 years

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3 years ago
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Xelga [282]
The slope is 4
slope intercept form : y=4x-2
point slope form: y-2= 4(x-1)

6 0
2 years ago
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