The area of a couple's rectangular living room is 40 sq meters. The length of the room is 3 meters more than the width. What is

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Detailed solution:

Question 1)

We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.

The lines given are:

Line 1 equation:

This line passes through points (0, 2.5) and (2.2, -1.4).

Line 2 equation:

The second line goes through (0, -3) and (2.2, -1.4).

According to the graph and data, the solution to the system is the coordinate where both lines intersect.

The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.

Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.

Therefore, the solution for question 1 is (2.2, -1.4).

Question 2)

The equations given are:

y = 1.5x - 1               Equation 1

y = 1                           Equation 2

The method of substitution can be used to find the solution.

Replacing y from Equation 2 into Equation 1 gives:

1 = 1.5x - 1

Add 1 to both sides:

2 = 1.5x

Dividing both sides by 1.5 yields:

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the system is (1.33, 1).

21 minutes. Step-by-step explanation: Considering the following: Using CITY STREET: The duration to drive to the nearest bowling alley is 45 minutes, which is 0.75 hours. The travel speed is 30 miles per hour. Switching to FREEWAY: the travel speed here is 65 miles per hour. Assuming both routes cover the same distance, the time required on the FREEWAY will be as follows: The distance calculated using the city route results in 30 mph = distance / 0.75 hour, giving a distance of 22.5 miles. As the distance remains consistent: Time taken on the FREEWAY = distance / speed, which results in 22.5 / 65 = 0.3461538 hours. Converting to minutes = 0.3461538 × 60, which rounds to approximately 21 minutes.

2x + 4

To represent 2x + 4, the following is required:

2 positive x-tiles corresponding to 2x.

4 positive unit tiles for the value of 4.

3x + (-1)

To illustrate 3x + (-1), you will need:

3 positive x-tiles to depict 3x.

1 negative unit tile to signify (-1).

In this scenario, the first step is to assign variables.

We define:

x: time measured in minutes

y: distance covered.

The equations formulated are as follows:

For Kathleen:

For Arnob:

At the moment Arnob meets Kathleen, we have:

Next, we isolate x.

We now have:

Answer:

Arnob takes a total of 75 minutes to catch up to Kathleen:

d. 75

To achieve the desired output, first use the machine with the function y = x^2 - 6, followed by the machine that computes y = sqrt(x-5). This way, when you input 6, the output from the first machine is calculated as x = 6, yielding y = 6^2 - 6, resulting in 30 as the input for the second machine. The second machine then processes this to provide the final output of sqrt(30 - 5), which equals sqrt(25) = 5. Alternatively, to obtain a negative final output, you should first utilize the machine with the function y = sqrt(x-5). Assuming you start with the value x = 9, the first machine computes this to sqrt(9-5), which is sqrt(4) = 2. Then, the second machine converts y to 2^2 - 6, leading to a result of 4 - 6 = -2.