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Answer:

noo

Step-by-step explanation:

Answer:

  substitution (or addition)

Step-by-step explanation:

A simple strategy for this system is to use substitution. The first equation is easily solved for x, so you could substitute that into the second equation:

  x = 6y -8

  7(6y -8) -y = -2 . . . . . x variable eliminated

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The second equation is easily solved for y, so you could substitute that into the first equation.

  y = 7x +2

  -x +6(7x +2) = 8 . . . . . y-variable eliminated

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The "addition" method is always a good way to eliminate a variable.

When the coefficient of a variable in one equation is a divisor of the coefficient of that variable in the other equation, a simple multiplication and addition will do.

To make the coefficient of x in the first equation the opposite of the coefficient of x in the second, multiply the first equation by 7. Adding that result to the second equation will eliminate x:

   7(-x +6y) +(7x -y) = 7(8) +(-2)

  42y -y = 56 -2 . . . . . . x-variable eliminated

Likewise, the second equation can be multiplied by 6 and added to the first to eliminate the y-variable:

  (-x +6y) +6(7x -y) = (8) +6(-2)

  -x +42x = -4 . . . . . . . . y-variable eliminated

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It is often the case that using either substitution or "addition" requires about the same amount of work.

Here, the solutions are (x, y) = (-4/41, 54/41).

Final answer:

To eliminate a variable in the given system of equations, you can use the elimination method. By multiplying the equations by suitable numbers and adding them, you can cancel out one of the variables, simplifying the process to solve for the other variable.

Explanation:

You can eliminate a variable in the given system of equations: −x+6y=8 and 7x-y=−2 by using either the substitution method or the elimination method. For this scenario, the elimination method will work best.

Strategy:

1. To eliminate x, you should first multiply the first equation by 7 and the second by 1, resulting in the equations: -7x+42y=56 and 7x-y=-2
2. Adding these two equations together, the x terms (-7x and 7x) cancel out, giving us: 41y=54.
3. Finally, you divide both sides by 41 to solve for y. This process effectively eliminates the variable x from the equation, providing a solution for y.

This variable eliminationstrategy lets you solve one equation for one variable, simplifying the process of finding solutions for a system of equations.

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Final answer:

To mix with 4 quarts of yellow paint, one would need approximately 2.67 quarts of red paint. This was determined through the use of ratio and proportion.

Explanation:

To determine how much red paint needs to be mixed with 4 quarts of yellow paint, we use ratio and proportion. We know the paint is mixed at a ratio of 3:2 yellow to red. Hence, we assume that 3 parts is equivalent to 4 quarts of yellow paint. So, we can use cross-multiplication to find the equivalent volume of red paint:

3 yellow : 2 red = 4 quarts yellow : x quarts red.

So, we solve 2x = 4 * 3/3. Doing the maths, we get, x = 2.67 quarts it’s the required volume of red paint for 4 quarts of yellow paint.

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Answer:

22F

Step-by-step explanation:

Answer: The maximum amount of profit the company can make is $1604.

Step-by-step explanation:

To find the maximum amount of profit the company can make, we need to determine the vertex of the quadratic equation y = -5x^2 + 263x - 1844. The x-coordinate of the vertex represents the selling price that will yield the maximum profit, and the y-coordinate represents the maximum profit itself.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.

In this case, a = -5 and b = 263. Let's substitute these values into the formula:

x = -263 / (2 * -5)

Now, let's simplify the expression:

x = -263 / -10

x = 26.3

To find the maximum profit, we substitute the x-coordinate of the vertex into the equation:

y = -5(26.3)^2 + 263(26.3) - 1844

Now, perform the calculations:

y = -5(691.69) + 6906.9 - 1844

y = -3458.45 + 6906.9 - 1844

y = 1604.45

Therefore, to the nearest dollar, the maximum amount of profit the company can make is $1604.

Final answer:

Profit is a financial gain that occurs when the revenue from a company activity is more than the costs, costs, and taxes required to support the activity. To put it another way, profit is what is left over after all costs have been subtracted from revenue

Explanation:

The corporation can earn a maximum profitof $1,292 to the nearest dollar.

Using the given equation y = -5x² + 263x - 1844 we can utilise the procedures below to get the greatest profit the corporation may make:

1. Using the equation x = -b/2a, where a = -5 and b = 263, determine the x-coordinate of the parabola's vertex.

2. To determine the highest possible value of y, substitute this x value into the equation.

These actions result in:

When we enter this x value into the equation, we obtain:

As a result, the corporation can earn a maximum profit of $3,440 to the nearest dollar.

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