The first thing to do is to write an algebrai equation for the problem:

8x – 9 = 5 – 10

8x – 9 = –5

8x = 4  

x = 1/2

Thus, 4 * x = 2

Add the two equations:

4x - 5y = 12 plus

6y - 3x = -6:

4x - 5y + (6y - 3x) = 12 + (-6)

4x - 3x + 6y - 5y = 12 - 6

x + y = 6

Find out how much a volunteer can produce in 3 hours.

6 tables/hour * 3 hours = 18 tables/hour

180 table need to be setup.  If one volunteer can setup 18 in 3 hours, then 10 volunteers will take care of the 180 tables.

2 auction galleries/hour * 3 hours = 6 galleries/hour

2 volunteers will be able to complete 12 auction galleries

10 + 2 = 12 volunteers

Solve for x, then plug into the formula to find the value.  x = 28 – 12 = 16

(3 * 16 + 2) * (–16 +10) = –300

Setting x and the number of quarters he has and y as the numbver of nickels. x + y = 14 (total coins), 0.25x + 0.05y = 1.50 (total amount). Substituting x = 14 – y from the first equation into the second, we get y = 10. Therefore Joey has 10 nickels.

Setting t as the time elapsed we need to find when 8t = 12 + 4t (this is the distance traveled by the ball compared to the distance traveled by the player+difference from origin). Solving for t we get a travel time of 3 seconds. If the player runs for 3 seconds at 4m/s, the player travels 12m before receiving the ball.

First, we need to find the points of intersection between f(x) and g(x) by setting them equal to one another and solving.

f(x) = g(x)

2x² - 3x + 1 = 13 – x 

Add x to both sides.

2x² – 2x + 1 = 13

Subtract 13 from both sides.

2x² – 2x – 12 = 0.

Divide by two to make the coefficients easier to work with.

x² – x – 6 = 0

Factor.

(x – 3)(x + 2) = 0

Set each of the factors equal to zero and then solve.

x – 3 = 0

x = 3

x + 2 = 0

x = –2

The two functions intersect where x = –2 and where x = 3. 

The question asks us to find the distance between the points of intersection. Therefore, we will need to find the y-coordinates of the points of intersection when x = –2 and when x = 3.

When x = –2, f(–2) = g(–2) = 13 – (–2) = 15.

When x = 3, f(3) = g(3) = 13 – 3 = 10.

Thus, the points of intersection are (–2, 15) and (3, 10).

We can now use the distance formula given below.

The answer is 5√2

We can solve this system of equations by using substitution. Rewriting the first equation, we get x = –5 + 3y. This equation gets substituted into the second equation, then solve for y.  Once we know what y is, we can substitute the value into the first equation to find x. In this case, x = 1 and y = 2.

Define the variables as

x = # of dimes

x + 2 = # of quarters

x + x + 2 = # of nickels

In general, the formula for money problems in V₁N₁ + V₂N₂ + V₃N₃ = $total

0.10x + 0.25(x + 2) + 0.05(2x + 2) = 1.05

Solving the equation we see that there is one dime, three quarters and four nickels.

This problem involves a system of two equations. The first equation is x² – y² = 20, and the second equation is x + y = 10. Let us solve the second equation in terms of y, and then we can substitute this value into the first equation.

x + y = 10

Subtract y from both sides.

x = 10 – y

Substitute 10 - y for x in the first equation.

x² – y² = 20

(10 - y)² – y² = 20

We can use the FOIL method to find (10 – y)². 

(10 – y)² = (10 – y)(10 – y) = 10(10) – 10y – 10y + y² = 100 –20y + y².

Now we can go back to our original equation and replace (10 – y)² with 100 – 20y + y^2.

(100 – 20y + y²) – y² = 20

100 – 20y = 20

Subtract 100 from both sides.

–20y = –80

Divide both sides by –20.

y = 4.

Now that we know that y = 4, we can use either of our original two equations to solve for x. Using the equation x + y = 10 is probably simpler.

x + y = 10

x + 4 = 10

x = 6.

The original question asks for the product of x and y, which would be 4(6), which equals 24.

The answer is 24.