Ok thanks. I have two questions that I am stuck on.

c and d are defined as

c={w|w<2}

d={w|w is greater than or equal sign to 7}

and

The Lewis family and the Cook family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was per hour. The water output rate for the Cook family's sprinkler was per hour. The families used their sprinklers for a combined total of hours, resulting in a total water output of . How long was each sprinkler used?

2. The Lewis family and the Cook family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 35 L per hour. The water output rate for the Cook family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 1000 L. How long was each sprinkler used? By the Cook family? By the Lewis family?

C and D are defined as C={w|w<2} D={w|w the greater than or equal to symbol 7 Write in interval notation.

C={w|w<2}

Answer: In interval notation: (-∞, 2)

D={w|w the greater than or equal to symbol 7

Answer: In interval notation: [7, ∞)

2. The Lewis family and the Cook family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 35 L per hour. The water output rate for the Cook family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 1000 L. How long was each sprinkler used? By the Cook family? By the Lewis family?

Solution: Let Cook family used sprinkler for x hours and Lewis family used for y hours. The families used their sprinklers for a combined total of 35 hours. x+y = 35

The water output rate for the Cook family's sprinkler was 20 L per hour. The water output rate for the Lewis family's sprinkler was 35 L per hour. Total water output of 1000 L. 20x + 35y = 1000

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1.Graph the solution below and write its solution.

2x+y=4

y=1/3x-3

2.Solve the compound inequality, and graph on the number line.

2x+4 less than or equal to sign -4 or 2x+3 greater than or equal to 5

3. Solve the compound inequality, write the solution in interval notation

4w+5>25 or 3w+1 greater than or equal sign 4

4. Two mechanics worked on a car. The first mechanic worked for 5 hours and the second mechanic worked for 15 hours. Together they charged a total of $1825. What was the rate charged per hour by each mechanic if the sum of the two rates was $185 per hour?

Also I wanted to know if an equation is always true does it have a unique solution or an infinite solution?

1.Graph the solution below and write its solution. 2x+y=4 y=1/3x-3

Take Equation 2x+y=4 ----------------------

Put x = 0 2x+y=4 0+y= 4 y = 4

Put x = 2 2x+y=4 2(2)+y= 4 4 + y = 4 y =0

Points will be (0, 4) and (2,0)

Take Equation y=1/3x-3

---------------------- Put x = 0 y=1/3x-3 y=1/3(0)-3 y = -3

Put x = 9 y=1/3x-3 y=1/3(9)-3 y = 3-3 y =0

Points will be (0, -3) and (9,0)

Use these points to plot each line

From the graph, we can note that solution is (3, -2). Answer: x = 3, y = -2 In ordered pair: (3, -2)

2. Solve the compound inequality, and graph on the number line. 2x+4 ≤ -4 or 2x+3 ≥ 5

2x+4 ≤ -4 Add -4 to each side 2x + 4 + (-4) ≤ -4 + (-4) 2x ≤ -8 Divide by 2 x ≤ -4

2x+3 ≥ 5 Add -3 to each side 2x+3 + (-3)≥ 5+ (-3) 2x ≥ 2 Divide by 2 x ≥ 1

Since there is or between two inequalities so solution will be union of solutions of both inequalities. In interval notation: (-∞, -4] U [1, ∞) Graph is shown below:

3. Solve the compound inequality, write the solution in interval notation 4w+5>25 or 3w+1 ≥ 4

4w+5>25 4w+5+(-5)>25+(-5) 4w > 20 Divide by 4 w > 5

3w+1 ≥ 4 Add -1 to each side 3w+1 + (-1)≥ 4+ (-1) 3w ≥ 3 Divide by 3 w ≥ 1

Since there is or between two inequalities so solution will be union of solutions of both inequalities. Solution will be w ≥ 1. In interval notation: [1, ∞).

4. Two mechanics worked on a car. The first mechanic worked for 5 hours and the second mechanic worked for 15 hours. Together they charged a total of $1825. What was the rate charged per hour by each mechanic if the sum of the two rates was $185 per hour?

Solution:

Let x be the rate of first mechanic and y be the rate of second mechanic

Sum of the two rates was $185 per hour

x + y = 185

The first mechanic worked for 5 hours and the second mechanic worked for 15 hours. Together they charged a total of $1825

5x + 15y = 1825

System of equations will be

x + y = 185-------------(i)

5x + 15y = 1825-------(ii)

From first equation, we will get

x = 185-y

substitute it in (ii)

5(185-y) + 15y = 1825

925 - 5y + 15y = 1825

10y = 1825-925

10y = 900

y = 90

x = 185-y = 185-90 = 95

Answer:

Rate charged by first mechanic: $95

Rate charged by second mechanic: $90

Also I wanted to know if an equation is always true does it have a unique solution or an infinite solution?

If an equation is always true, it will have infinite number of solutions.

Example:

2(x-1) = (2x-1) - 1

Sandhya_sharma and other Math Homework Specialists are ready to help you

Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2 (www.sailing.com). For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function

a)

Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet.

b)

Solve this formula for d.

c)

The accompanying graph shows C in terms of d for the Tartan 4100 (b = 13.5). For what displacement is the Tartan 4100 safe for ocean sailing?

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Sailboat speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a displacement of d pounds and a sail area of A square feet S is determined by the function

a)

Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds.

Ok great thank you so much. Also I wanted help understanding this problem that I have to turn in today its a^1/2 over a^2. My answer is a^1 or a. I just want to make sure I have it right before i turn it in.