A music teacher asked 23 students in the band how many hours they practiced playing their

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).

An airplane flying at a speed of 950 kilometers per hour would take 0.0010526 hours to travel 1.00 kilometer.

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.

Answer:

3/10 liter

Step-by-step explanation:

Assuming your statement indicates that in 4/3 liters of punch, there is 2/5 liters of water, then the proportion of water in the punch is calculated as:

(2/5)/(4/3) = (2/5)(3/4) = 3/10

So, 3/10 of a liter of water is included in each liter of punch.

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