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?

Without additional information correlating the number of hats sold to the number of scarves sold, it is impossible to determine how many hats the knitter sold.

Based on the question, there isn't enough information provided to determine how many hats the knitter sold. The information given tells us only about the number of scarves sold, which is 5. If any relationship between the number of hats and scarves sold was provided, then the solution could be possible. For example if the knitter sells an equal amount of hats and scarves then we could say she sold 5 hats. However, without any such information, it is impossible to ascertain the number of hats sold.

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32 rose arrangements and 8 tulip arrangements

8 times 4 = 32

8 + 32 = 40

Heidi's mom made 8 tulip arrangements and 32 rose arrangements. This was determined by setting up equations based on the given information and solving for the number of each type of arrangement.

With 4 times as many rose arrangements as tulip arrangements. Let's denote the number of tulip arrangements as T and the number of rose arrangements as R. According to the information, R = 4T and R + T = 40.

Substituting R in the second equation gives 4T + T = 40, which simplifies to 5T = 40. Solving for T, we find T = 8. Therefore, the number of tulip arrangements is 8. Substituting T = 8 into the equation R = 4T gives R = 32, meaning that there are 32 rose arrangements. Thus, Heidi's mom made 8 tulip arrangements and 32 rose arrangements for the party.

1997 = 3.40

1998 = 2.70

Here, we are required to find the value of Q in the following system so that the system to the solution is {(x,y) : x-3y=4}

x-3y=4

2x-6y=Q

Therefore, Q = 8.

By comparison between equations: x-3y=4 and 2x - 6y = Q.

We need to multiply equation x - 3y = 4 by 2 so that it somewhat resembles 2x-6y=Q;

Ultimately, we have;

Therefore, the two equations now resemble one another and therefore, Q = 8

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The value of Q that makes the system have the same solution as {(x, y) : x - 3y = 4} is Q = 8.

To find the value of Q in the given system so that the solution is {(x, y) : x - 3y = 4}, you need to make sure that the second equation, 2x - 6y = Q, is equivalent to the first equation, x - 3y = 4.

This means that the two equations have the same solution.

To do this, we can start by simplifying the second equation to be equivalent to the first one:

2x - 6y = Q

We can simplify this equation by dividing both sides by 2:

x - 3y = Q/2

Now, we want this equation to be the same as the first equation, x - 3y = 4.

To make them equal, we need to have Q/2 equal to 4.

Therefore:

Q/2 = 4

To solve for Q, multiply both sides of the equation by 2:

Q = 2 * 4

Q = 8

For similar question on equation.

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V = bh Dividing both sides by "b" we get

(V / b) = h

Solving for h means to isolate h by move everything else to the other side of the equal sign.

V = b * h

[tex]\frac{V}{b} = \frac{b*h}{b}[/tex]     divide both sides by b

[tex]\frac{V}{b} = h[/tex]     h is now isolated

To do a problem like this, multiply the base height by the rate.  So here is how you do it:

64.5 times 1.25

The easiest way is to get a calculator and plug in the equation

Your answer should be 80.625

*If you multiply by hand, remember to move the decimal back to the left three places.*

7x > -35    |divide both sides by 7

x > -5

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

3x ≤ 30    |divide both sides by 3

x ≤ 10

-5 < x ≤ 10

Answer: b.

Step 1. Since the power of 2 is even, the result will be positive

(3j^2k^3)^2(2j^2k)^3

Step 2. Use Multiplication Distributive Property

3^2(j^2)^2(k^3)^2(2j^2k)^3

Step 3. Simplify 3^2 to 9

9(j^2)^2(k^3)^2(2j^2k)^3

Step 4. Use the Power Rule

9j^4(k^3)^2(2j^2k)^3

Step 5. Use the Power Rule

9j^4k^6(2j^2k)^3

Step 6. Use Multiplication Distributive Property

9j^4k^6 * 2^3(j^2)^3 k^3

Step 7. Simplify 2^3 to 8

9j^4k^6 * 8(j^2)^3 k^3

Step 8. Use the Power Rule

9j^4k^6 * 8j^6k^3

Step 9. Take out the constants

(9 * 8)j^4j^6k^6k^3

Step 10. Simplify 9 * 8 to 72

72j^4k^6k^3

Step 11. Use the Product Rule

72j^4+6k^6+3

Step 12. Simplify 4 + 6 to 10

72j^10k^6 + 3

Step 13. Simplify 6 + 3 to 9

72j^10k^9

Answer:

its y

Step-by-step explanation:

In order to check if a comparison such as this is true, you can use this logical equivalence:

[tex] \dfrac{a}{b} > \dfrac{c}{d} \iff ad > bc,\quad \dfrac{a}{b} < \dfrac{c}{d} \iff ad < bc [/tex]

Anyway, it's not always necessary to make this check. We know that every proper fraction represents a number between 0 and 1, and any improper fraction represents a number greater than 1. So, every proper fraction is less than every improper fraction.

So, the first two options are surely wrong, because they ask for a proper fraction to be more than an improper fraction.

The third option compares two proper fractions, so we actually have to check:

[tex] \dfrac{16}{26}>\dfrac{30}{31} \iff 16 \cdot 31 > 26 \cdot 30 \iff 496 > 780[/tex]

which is false.

Last option:

[tex] \dfrac{35}{30}<\dfrac{22}{12} \iff 35 \cdot 12 < 30 \cdot 22 \iff 420 < 660[/tex]

Which is true.

c. Due to c. and the equation above would be equal just in a different arrangement

Answer:

[tex](f-g)(x)=3x^2+4x+2[/tex]

C is correct

Step-by-step explanation:

Given: [tex]f(x)=4x^2-6[/tex]

[tex]g(x)=x^2-4x-8[/tex]

To find : (f-g)(x)

[tex](f-g)(x)=f(x)-g(x)[/tex]

[tex]\Rightarrow (4x^2-6)-(x^2-4x-8)[/tex]

using Distributive property

[tex]\Rightarrow 4x^2-6-x^2+4x+8[/tex]

[tex]\Rightarrow 4x^2-x^2+4x+8-6[/tex]

Combine like term

[tex]\Rightarrow 3x^2+4x+2[/tex]

[tex](f-g)(x)=3x^2+4x+2[/tex]

Hence, The composite function is [tex](f-g)(x)=3x^2+4x+2[/tex]

ANSWER

The correct answer is option D.

EXPLANATION

The given function is

[tex]k(x)=-3x^6-0.7x+x^3[/tex]

This a polynomial function. All degrees are greater than or equal to zero.

The coefficient being decimals does not disqualify it from being a polynomial.

The highest degree of this polynomial is 6.

Therefore the correct answer is D

y = a(1 + r)ˣ

a = 15  "initial" means what you started with on the first day

r = 6   the rate it increased is the slope ([tex](\frac{21 - 15}{2 - 1})[/tex]

y = 15(1 + 6)ˣ

Answer: y = 15(7)ˣ

A.

600 : 2 = 300

300 : 2 = 150

150 : 2 = 75

75 : 5 = 15

15 : 5 = 3

3 : 3 = 1

600 = 2 · 2 · 2 · 5 · 5 · 3 = 2³ · 5² · 3

B.

1050 : 2 = 525

525 : 5 = 105

105 : 5 = 21

21 : 3 = 7

7 : 7 = 1

1050 = 2 · 5 · 5 · 3 · 7 = 2 · 5² · 3 · 7

600 = 2 · 2 · 2 · 5 · 5 · 3

HCF(600, 1050) = 2 · 3 · 5 · 5 = 150

Final answer:

The algebraic equation based on the statement '5 times a number, subtracted from six, is triple the number' is 6 - 5x = 3x. Solving for 'x' gives us x = 3/4.

Explanation:

The student's question involves creating an algebraic equation based on a verbal statement. To translate the statement '5 times a number, subtracted from six, is triple the number' into an equation, let's use 'x' to represent the unknown number. The statement can be written as: 6 - 5x = 3x. To solve for 'x', we need to get all terms involving 'x' on one side and constants on the other. Here's how you can do it:

Add 5x to both sides of the equation to get: 6 = 3x + 5x

Combine like terms: 6 = 8x

Divide both sides by 8 to get the value of x: x = 6/8

Simplify the fraction: x = 3/4

Therefore, the number in question is 3/4.

Let the amount saved by Gayle be = x

Cost of the bicycle = $119.90

Gayle's saving till now = 0.7% of 119.90

[tex]\frac{0.7}{100}\times119.90=x[/tex]

[tex]x=0.83[/tex]

Hence, Gayle has saved $0.83 so far.

Answer:

She has saved $83.93.

Step-by-step explanation:

Gayle is saving to buy a bicycle.

The cost of bicycle = $119.90

She has saved = 0.7 of $119.90

                        = 0.7 × 119.90

                        = $83.93

The amount she needs more = 119.90 - 83.93

                                                 = $35.97

She has saved $83.93.

In 63, 6 is in the tenths place, meaning it represrents the number 60.

In 46, 6 is in the ones place, meaning it represents the number 6.

So, given that, in the first example 6 is x times the value of 6 in the second example:

x = 60 / 6

x = 10

Hope it helped,

BioTeacher101

The value of the digit 6 in the number 63 is 10 times the value of the digit 6 in the number 46.

In the number 63, the 6 is in the tens place, meaning it represents 60 (6 tens). In the number 46, the 6 is in the ones place, meaning it simply represents 6 (6 ones). Therefore, the 6 in 63 is 10 times the value of the 6 in 46.

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Answer:

17.30 dollars

Step-by-step explanation:

Given that Payton and James mow the lawns.

They do this during summer.

The amount they spend are:

Gas  cost  = 3.50

Leaf bags =  1.20

Add these to get total costs

Total cost  = 4.70

Charge they get per lawn = 22.00

Profit = Revenue - cost

Here revenue per lawn = 22 and cost per lawn = 4.70

Hence profit = 22-4.70 = 17.30 dollars.

Answer is they make 17.30 dollars per lawn.

Answer:

The answer is B

Step-by-step explanation:

The answer is A. 85/4=21 with 1 left over. They will need 22 golf carts.

The answer is 65! Just took the test

Answer: Choice A) (5+a)/(a-1)

Step-by-step explanation:

In the numerator, we originally have 3+x. Replace the x with a+2 and we get 3+x = 3+a+2 = 5+a. So the answer will have a numerator of 5+a.

The denominator in the answer will be x-3 = a+2-3 = a-1

Overall that's how the answer is (5+a)/(a-1)

The slope-point formula:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (0, 6) and (1, 3),

Substitute:

[tex]m=\dfrac{3-6}{1-0}=\dfrac{-3}{1}=-3\\\\y-6=-3(x-0)[/tex]

Since she donates 25%, take 25% and multiply it by 1,200

[tex].25 * 1,200 = 300[/tex]

or,

[tex]\frac{1}{4} * 1,200 = 300[/tex]

well if he started his day on Wednesday with 75 end he ended with 74.32 he lost -0.68

of his share hope this helped theres alot of extra information in the question

Answer:

-0.68

Step-by-step explanation:

The slope is 4. The y intercept is 3.

plz give brainliest if possible

yes you did a very good job