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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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In 4th grade :) help plss
Soloha48 [4]

Answer:

1. 570

2. 5,700

3. 57,000

Step-by-step explanation:

Hope it helped

4 0
2 years ago
Read 2 more answers
9) True or False: Great Britain officially recognized the Confederate States of America
SpyIntel [72]

It legally recognised the belligerent status of the Confederate States of America (CSA) but never recognised it as a nation and neither signed a treaty with it nor ever exchanged ambassadors.

And i could tell that its not math... :)

Its False

6 0
3 years ago
a painter bought 8 gallons of paint just enough to cover 2 rooms. One room is twice the size of the other and requires only 2 co
e-lub [12.9K]
So, he's got 8 gallons of paint, to paint the two rooms, of the two rooms, one is twice as big as the other

now, "x" is how many gallons to paint the larger room with only one coat, however, the larger room uses 2 coats, so, the larger room uses 2x of paint
now, the client declined to paint the smaller one

so hmmm as I read... well, we dunno how many coats will go to the smaller room for one, we know the larger will use 2 coats, or 2x.. if we assume the smaller room was going to use say 1 coat or 1/2x

then one can say the painter bought enough for both rooms, 1coat for the small one and 2coats for the larger one

so, the paint the larger room, you'll 2x of paint, for 2coatsand to paint the smaller room, you'll need 1/2 x, because x gallons is how much is needed for the larger room, but the larger room is twice as big, thus the smaller room uses 1/2 of that in gallons

thus, with those assumptions, that the small room will use only 1 coat
\bf \cfrac{1}{2}x+2x=8\implies \cfrac{5x}{2}=8\implies x=\cfrac{16}{5}
that's who many gallons are needed for 1 coat in the larger roomrecall "x" is 1coat for the larger room

now, the client decides to skip the smaller roomso, the painter will only need 2x gallons then

\bf 2x\implies 2\cdot \cfrac{16}{5}\implies \cfrac{32}{5}\implies 6.4\ gallons

he bought 8 gallons, 8 - 6.4, he's got left 1.6 gallons
3 0
3 years ago
Read 2 more answers
Big Ben, the famous clock tower in London, has a minute hand that is 14 feet long. How far does the tip of the minute hand of Bi
ycow [4]

Answer:

36.65 ft (2 dp)

Step-by-step explanation:

  • Angles around a point sum to 360°
  • 1 hour = 60 minutes

Therefore, the minute hand of a clock travels 360° in 60 minutes

Number of degrees the minute hand will travel in 25 minutes:

\sf =\dfrac{360}{60} \times 25=150^{\circ}

To find how far the tip of the minute hand travels in 25 minutes, use the Arc Length formula:

\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)

\textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}

Given:

  • r = length of minute hand = 14 ft
  • \theta = 150°

\begin{aligned}\implies \textsf{Arc length} &=2 \pi (14)\left(\dfrac{150^{\circ}}{360^{\circ}}\right)\\ & = 28\pi \left(\dfrac{5}{12}\right)\\ & = \dfrac{35}{3} \pi \\ & = 36.65\: \sf ft\:(2\:dp)\end{aligned}

4 0
2 years ago
Solve the following word problem: Kay made 5 less phone calls today than Stephanie. If together they made 21 calls, how many cal
professor190 [17]
Answer:
Kay made 8 phone calls
Stephanie made 13 phone calls

Explanation:
Assume the number of phone calls that Stephanie made is x.
We are given that:
Kay made 5 phone calls less than Stephanie.
This means that:
Kay made x-5 phone calls

We know that the total number of phones is 21.
This means that:
21 = x + x - 5

Now we solve for x as follows:
21 = x + x - 5
21 = 2x - 5
2x = 26
x = 26/2
x = 13

This means that:
Stephanie made x = 13 phone calls
Kay made x - 5 = 13 - 5 = 8 phone calls

Hope this helps :)
5 0
3 years ago
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