Question 1

Solve the problem by using a system of equations.
-South Wind Vineyards uses 830 acres to plant Chardonnay and Riesling grapes. The vintner knows the profits will be greatest by planting 180 more acres of Chardonnay than Riesling. How many acres of each grape should be planted?

Accepted Answer

Let R be the acres of Riesling and C be the acres of Chardonnay. The system of equations is: R + C = 830 (total acres) and C = R + 180 (180 more acres of Chardonnay than Riesling). Solving these equations gives R = 325 acres and C = 505 acres.

Question 2

Solve the problem by using a system of equations.
-A chemist has a 64% solution of alcohol to mix with a 86% solution to get 110 L of a final mixture that is 80% alcohol. How much of each of the original solutions should he use?

Accepted Answer

The answer of Solve the problem by using a system...

Question 3

Solve the problem by using a system of equations.
-Two cars leave from a city at the same time and travel in the same direction. One car travels one-third and one-third times as fast as the other. After 5 hr, they are 300 mi apart. What are the speeds of the cars?

Accepted Answer

The answer of Solve the problem by using a system...

Question 4

Graph the solution set of the system of inequalities.
-X + y $\ge$ 4
5x - 2y $\le$ -10

Accepted Answer

The answer of Graph the solution set of the system...

Question 5

Graph the solution set of the system of inequalities.
-5x + 2y > -4
X - 3 $\le$ 3y

Accepted Answer

The answer of Graph the solution set of the system...

Question 6

Provide an appropriate response.
 
-Without actually graphing, determine which one of the following systems of inequalities has no solution.

Accepted Answer

The system x + y < 2 and x + y > 3 has no solution because there is no value of x and y that can simultaneously satisfy both inequalities.

Quiz 5: Exponents and Polynomials

Solve the problem by using a system of equations. -South Wind Vineyards uses 830 acres to plant Chardonnay and Riesling grapes. The vintner knows the profits will be greatest by planting 180 more acres of Chardonnay than Riesling. How many acres of each grape should be planted?

Solve the problem by using a system of equations. -A chemist has a 64% solution of alcohol to mix with a 86% solution to get 110 L of a final mixture that is 80% alcohol. How much of each of the original solutions should he use?

Solve the problem by using a system of equations. -Two cars leave from a city at the same time and travel in the same direction. One car travels one-third and one-third times as fast as the other. After 5 hr, they are 300 mi apart. What are the speeds of the cars?

Graph the solution set of the system of inequalities. -X + y $\ge$ 4 5x - 2y $\le$ -10 $Graph the solution set of the system of inequalities. -X + y \ge 4 5x - 2y \le -10 A) B) C) D)$

Graph the solution set of the system of inequalities. -5x + 2y > -4 X - 3 $\le$ 3y $Graph the solution set of the system of inequalities. -5x + 2y > -4 X - 3 \le 3y A) B) C) D)$

Provide an appropriate response. -Without actually graphing, determine which one of the following systems of inequalities has no solution.