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dimulka [17.4K]
3 years ago
14

Factor if possible x/2+9x+18

Mathematics
1 answer:
Tju [1.3M]3 years ago
8 0

Answer:

3) (x+6)(x+3)=0

4) (x+2)(x-6)=0

Step-by-step explanation:

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A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out st
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Answer:

Objective Minimize 10x1 +15x2 + 12x3+18x4+15x5+ 21x6

The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.

The total minimum cost would $ 17586 +$260+ $300= $ 18146

Step-by-step explanation:

Let

X1 = # of undergraduate students from the East region,

X2 = # of graduate students from the East region,

X3 = # of undergraduate students from the Central region,

X4 = # of graduate students from the Central region,

X5 = # of undergraduate students from the West region, and

X6 = # of graduate students from the West region.

Then  the cost functions are

y1= 10x1 +15x2

y2= 12x3+18x4

y3= 15x5+ 21x6

According to the given conditions

The constraints are

x1 +x2 + x3+x4+ x5+ x6 ≥ 1500------- A

15X2 +18X4+21X6 ≥ 400---------B

21X6 ≥ 100

X6 ≥ 100/21

X6 ≥ 4.76

Taking

X6= 5

10X1 ≤ 500

X1 ≤ 500/10

X1≤ 5

18X4 ≥ 75

X4 ≥ 75/18

X4 ≥ 4.167

Taking

X4= 5

Putting the values

15X5+ 21X6 ≥ 300

15X5+ 21(5) ≥ 300

15X5+ 105 ≥ 300

15X5 ≥ 300-105

15X5 ≥ 195

X5 ≥ 195/15

X5 ≥ 13

Putting value of X6 and X4 in B

15X2 +18X4+21X6 ≥ 400

15X2 +18(5)+21(5) ≥ 400

15X2 +195 ≥ 400

15X2  ≥ 400-195

15X2  ≥ 205

X2  ≥ 205/15

X2  ≥ 13.67

Taking X2= 14

Now putting the values in the cost equations to check whether the conditions are satisfied.

y1= 10x1 +15x2

y1= 10 (5) + 15(14)= 50 + 210= $ 260

y3= 15x5+ 21x6

y3= 15 (13) + 21(5)

y3= 195+105= $ 300

x1 +x2 + x3+x4+ x5+ x6 ≥ 1500

5+14+x3+5+13+5≥ 1500

x3≥ 1500-42

x3≥ 1458

y2= 12x3+18x4

y2= 12 (1458)  + 18 (5)

y2= 17496 +90

y2= $ 17586

The cost can be minimized if the number of students from

                                 Undergraduate         Graduate

East Region              X1≤ 5                            X2  ≥ 13.67

Central                      X3≥ 1458                   X4 ≥ 4.167

West                          X5 ≥ 13                          X6 ≥ 4.76

This will result in the required number of students that is 1500

Constraints:

East Undergraduate must not be greater than 5

East Graduate must not be less than 13

Central Undergraduate must  be greater than 1458

Central Graduate must  be greater than 4

West Undergraduate must  be greater than 13

West Graduate must  be greater than 4

The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.

The east region has a least cost of $260 and west region has a cost of $300.

The total minimum cost would $ 17586 +$260+ $300= $ 18146

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3 years ago
Which system of equations shows a solution of (0.5, –1)? On a coordinate plane, 2 lines intersect at (0.5, negative 1). On a coo
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Answer:

B

Step-by-step explanation:

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2 years ago
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8 grams = milligrams
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Answer:

8,000 miligrams

Step-by-step explanation:

There's 1000 milligrams in a gram so you would have to do multiplication.

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8x1000

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8000 milligrams

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3 years ago
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Two friends are reading the same book. Amy can read 3 pages per minute, and she has already read 9 pages. Sam, who has a reading
Daniel [21]
Amy:  (3 pages/min)(x min) + 9 pages
Sam:  (2 pages/min)(x min)  + 47 pages

Equate these:  3x+9 = 2x + 47

Then x = 38.  The two friends will have covered the same number of pages after 38 minutes.  How many pages would that be?  3(38)+9 = 123 pages.
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The graph shows the distance a bicyclist traveled from a starting point in 10-second increments. Which of these is closest to th
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C. 10 m/s

Step-by-step explanation:

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3 years ago
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