What is the position of C on the number line below?
Write your answer as a fraction or mixed number.

Complete question :

The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarius per day to support 3 legionaries and 3archers. It only costs 3 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?

Answer:

No unique solution

Step-by-step explanation:

Given that:

Cost of supporting 3 legion aries and 3 archers = 10 denarius daily

Cost of supporting one legionary and one archer = 3 denarius

Let:

Legionaries = l ; archers = a

Equation for the first sentence :

3l + 3a = 10 - - - (1)

Second sentence :

l + a = 3 - - - - - (2)

From (2)

l = 3 - a

Substituting l = 3 - a into (1)

3(3 - a) + 3a = 10

9 - 3a + 3a = 10

9 - 0 = 10

The variable cancels out, Hence, ( there is no unique solution to find the cost of each soldier)

Answer:

No; the system has no solution.

Step-by-step explanation:

We'll use L to represent the cost per day of a legionary, and we'll use A to represent the cost per day of an archer. So we have the following system of equations:

3L+3A=10

L+A=3

If we multiply both sides of the second equation by 3, we get the equation 3L+3A=9

But this indicates that the cost to support 3 legionaries and 3 archers is 9 denarius. The first equation indicates that it costs 10 denarius to support 3 legionaries and 3 archers.

The cost cannot be 9 denarius and 10 denarius at the same time.

Henceforth the answer is:

No; the system has no solution.

Answer:

43 degrees. b and the other angle being compared too are vertical angles- vertical angles are AND have to be identical to each other.

Answer:

x = 7

Step-by-step explanation:

Answer:

21.46 cm squared

Step-by-step explanation:

3.8x5.8=21.46

Answer:

Step-by-step explanation:

Answer:

j=6

Step-by-step explanation:

2=5j-28

+28  +28

30=5j

/5    /5

j=6  

Answer:

The correct options are;

D. Triangles ABC and A'B'C' are congruent

E. Angle ABC is congruent to angle A'B'C'

F. Segment BC is congruent to segment B'C'

H. Segment AQ is congruent to segment A'Q'

Step-by-step explanation:

The given information are;

The angle of rotation of triangle ABC = 60°

Therefore, given that a rotation of a geometric figure about a point on the coordinate plane is a form of rigid transformation, we have;

1) The length of the sides of the figure of the preimage and the image are congruent

Therefore;

BC ≅ B'C'

2) The angles formed by the sides of the preimage are congruent to the angles formed by the corresponding sides of the image

Therefore;

∠ABC ≅ ∠A'B'C'

3) The distances of the points on the figure of the preimage from the coordinates of the point of rotation are equal to the distances of the points on the figure of the image from the coordinates of the point of rotation

Therefore;

Segment AQ ≅ A'Q'.

Answer:

i think its B or A

Step-by-step explanation:

Answer:

2 5/8

Step-by-step explanation:

1 3/4 + 7/8

add the fractions together

look for the lcm bwt 4 and 8

1 6 + 7

____

8

= 13/8 = 1 5/8

1 + 1 5/8

= 2 5/8

[tex]f(2) = \frac{1}{2} \times 2 = 1\\f^{-1}(1) = 2 \times 1 = 2\\f^{-1}(f(2)) = f^{-1}(1) = 2[/tex]

Note: [tex]f^{-1}(f(x)) = x[/tex] because f -1 and f cancel each other out.

Answer:

f(2) =  

⇒ 1

f−1(1) =  

⇒ 2

f−1(f(2)) =  

⇒ 2

f−1(−2) =  

⇒ -4

f(−4) =  

⇒ -2

f(f−1(−2)) =  

⇒ -2

Step-by-step explanation:

Answer:

Graph 1: Parallel

Graph 2: Perpendicular

Graph 3: Neither

Graph 4: Neither

Answer:

Graph 1: parallel

Graph 2: Perpendicular

Graph 3: Neither

Graph 4: Neither

Step-by-step explanation:

The ones that are neither would technically be labeled intersecting just for future reference but it is not required in this problem. Hope this helps!

Answer:

23

Step-by-step explanation:

232323

3

3

3

3

23

23

3

this isnt correct btw

Answer:

x = -3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

To find the value of x, you need to get rid of parentheses! So, 4*x=4x. 6*4=24. Now we have, -2x+6=4x+24. Then we want to get all the x on one side, and the other numbers on the other side. We can add -2x to make it 0, but to make it equal, you need to add it to the other side. So, 4x+2x=6x. You can subtract 24 too! After we do all that, we get: -18=6x. To get x, we need to divide by 6. 6x/6=x. -18/6=-3.

Answer:

u457sups

Step-by-step explanation:

= 89 - 89b 67 =  80

Answer:

A

Step-by-step explanation:

Answer:

The answer is 8x - 3

Answer:Letter D.

Step-by-step explanation:

Answer:

40 units to the right and 7 units down

Answer:

π radians

Step-by-step explanation:

The arc cos(- 1) in degrees is 180° and 180° = π radians

Answer:

c/9 >= 15

Step-by-step explanation:

c divided by 9 is greater than or equal to 15

Answer:

5o mile trip=2 gallon

50÷2=25

1 mile trip=25

so 125÷25=5

5 gallon of gas use

Answer:

A. The equation representing the bicyclist with equal speed, v, meeting after x hours is 75 - v·x = 45 + v·x

B. The bicyclist meet after 1.5 hours

C. They were 60 miles from the parking lot when they meet

Step-by-step explanation:

A. The starting location of the one of the bicyclist = 75-mile marker

The starting location of the other bicyclist = 45-mile marker

The direction of motion of the bicyclist = Towards each other

The time after which the bicyclist meet = x hours

The expression for the distance from the parking lot are

75 - 10x and 45 + 10x

Whereby the bicyclist are have the same speed, v, we have;

The location where they meet is 75 - v×x = 45 + v×x

B. Solving for x, we have;

75 - v×x = 45 + v×x

75 - 45 = v×x + v×x = 2×v×x

30 = 2×v×x

x = 30/(2×v)

Taking the speed of the bicyclist as 10 mph from the equation of their distance from the parking lot, by dimensional analysis, we have;

x = 30/(2×v) = 30/(2×10) = 1.5

x = 1.5 hours

The bicyclist meet after 1.5 hours

C. Their distance from the packing lot is given by substituting the time, x, it took them to meet into the expression for the distance from the parking lot as follows;

75 - 10 × 1.5 = 60 miles

45 + 10 × 1.5 = 60 miles

Therefore, they were 60 miles from the parking lot when they meet.

Answer:

A. The equation representing the bicyclist with equal speed, v, meeting after x hours is 75 - v·x = 45 + v·x

B. The bicyclist meet after 1.5 hours

C. They were 60 miles from the parking lot when they meet

Step-by-step explanation:

A. The starting location of the one of the bicyclist = 75-mile marker

The starting location of the other bicyclist = 45-mile marker

The direction of motion of the bicyclist = Towards each other

The time after which the bicyclist meet = x hours

The expression for the distance from the parking lot are

75 - 10x and 45 + 10x

Whereby the bicyclist are have the same speed, v, we have;

The location where they meet is 75 - v×x = 45 + v×x

B. Solving for x, we have;

75 - v×x = 45 + v×x

75 - 45 = v×x + v×x = 2×v×x

30 = 2×v×x

x = 30/(2×v)

Taking the speed of the bicyclist as 10 mph from the equation of their distance from the parking lot, by dimensional analysis, we have;

x = 30/(2×v) = 30/(2×10) = 1.5

x = 1.5 hours

The bicyclist meet after 1.5 hours

C. Their distance from the packing lot is given by substituting the time, x, it took them to meet into the expression for the distance from the parking lot as follows;

75 - 10 × 1.5 = 60 miles

45 + 10 × 1.5 = 60 miles

Therefore, they were 60 miles from the parking lot when they meet.

Answer:

Price of each bracelet = $4.75

Step-by-step explanation:

Given:

y =4.75x

In equation;

y = kx

where k is constant

So , we say that 4.75 is constant of proportionality

So price of each bracelet = $4.75

Answer:

its c

Step-by-step explanation:

trust me

Answer:

c

Step-by-step explanation:

Answer:

noshe

Step-by-step explanation:

Answer:

8.1240384 i

Step-by-step explanation:

Answer:

It doesn't have a square root

Step-by-step explanation:

All negative numbers don't have a square root. Because you would have to use a negative and a positive number, and that is not possible when squaring a number. For example, 8² = 64, but what is the square root of -64 there isn't one because if you did -8² = 64. So No Square Root.

Answer:

X= 20

Step-by-step explanation:

x/5 + 13 = 17

x/5 + 13 =17

- 13. -13

x/5×5 4×5=20

So X=20

Answer:

45

Step-by-step explanation:

if Sara has 30 more than Gordon and the ratio is 5:3. then sara has 2× X more than Gordon. 30 ÷ 2 = 15.

15 = X

15 × 3 = 45

Sara has 75

(sorry if it's confusing)

Answer:

x = 5

The two consecutive odd integers are: 5, 7

And...checking

sum = 12

Step-by-step explanation: