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zhenek [66]
3 years ago
10

The denarius was a unit of currency in ancient rome. Suppose it costs the roman government 101010 denarii per day to support 444

legionaries and 444 archers. It only costs 555 denarii per day to support 222 legionaries and 222 archers. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier? Choose 1 answer:
Mathematics
1 answer:
givi [52]3 years ago
5 0

<u>the correct question is</u>

The denarius was a unit of currency in ancient rome. Suppose it costs the roman government 10 denarii per day to support 4 legionaries and 4 archers. It only costs 5 denarii per day to support 2 legionaries and 2 archers. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?

Let

x-------> the cost to support a legionary per day

y-------> the cost to support an archer per day

we know that

4x+4y=10 ---------> equation 1

2x+2y=5 ---------> equation 2

If you multiply equation 1 by 2

2*(2x+2y)=2*5-----------> 4x+4y=10

so

equation 1 and equation 2 are the same

The system has infinite solutions-------> Is a consistent dependent system

therefore

<u>the answer is</u>

We cannot solve for a unique cost for each soldier, because there are infinite solutions.

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Nancy’s nut store sells peanuts for $2 per pound and cashews for $10 per pound. The store sells a peanut - cashew mixture for $7
Gelneren [198K]

9514 1404 393

Answer:

  • 25 pounds cashews
  • 15 pounds peanuts

Step-by-step explanation:

Let c represent the number of pounds of cashews in the mix. Then 40-c is the number of pounds of peanuts. The total cost of the mix is ...

  10c +2(40 -c) = 7(40)

  8c +80 = 280 . . . . simplify

  c +10 = 35 . . . . . . . divide by 8

  c = 25 . . . . . . . . . . subtract 10

  40-c = 40-25 = 15 . . . . pounds of peanuts

25 pounds of cashews and 15 pounds of peanuts should be used in the mix.

5 0
2 years ago
24 x1/3
hodyreva [135]

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Answer:

  8

Step-by-step explanation:

  24\times\dfrac{1}{3}=\dfrac{24}{3}= \dfrac{3\cdot8}{3}=\dfrac{3}{3}\cdot8 = 1\cdot8 = \boxed{8}

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Multiplying by 1/3 is the same as dividing by 3.

5 0
3 years ago
Please help me, i only have 30 mins.
Aleks04 [339]

Answer:

Width is 24, length is 40

Step-by-step explanation:

64 can be split into 8 groups of 8, and the 8 groups can be split into 3 and 5. Then, take 3 x 8 for the width and 5 x 8 for the length, and you have the answer! I wish to you best of luck!

4 0
2 years ago
In a line of students, Jenna is number 8.The teacher says that a rule for a number pattern is add 4. The first student inline sa
Virty [35]

Answer:

Formula for nth term in Arithmetic sequences is:

a_n =a+(n-1)d

where a is the first term, d is the common difference and n is the number of terms.

As per the statement:

The rule for the pattern is add 4.

As the first term in line says the first term i,e 7

a= 7

common difference(d)= 7

As the Jenna number is 8th in line.

Series we get;

7, 11, .........a_8

We have to find the 8th term.

n = 8, a = 7 and d = 4

Using above formula:

a_8 = 7+(8-1)4 = 7+7 \cdot 4 = 7 +28 = 35

Therefore, 35 number should Jenna say.

3 0
3 years ago
Read 2 more answers
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Are a and b two points on a line
If they are you can use the distance formula
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