The product of three integers is −5. Determine all of the possible values for the three factors.

Response:

PQ's slope is 0

MN's slope equals infinity

The lines PQ and MN are perpendicular to one another

Detailed explanation:

For two points in the coordinate plane, denoted as (x1, y1) and (x2, y2), the slope is determined as follows:

If a line has a slope of zero, it runs parallel to the X-axis and stands perpendicular to the Y-axis

If a line's slope is infinite, it is parallel to the Y-axis and perpendicular to the X-axis

Moreover, it is established that X and Y are perpendicular to each other.

As PQ's slope is zero, it runs parallel to the X-axis and perpendicular to the Y-axis

With MN having an infinite slope, it runs parallel to the Y-axis and perpendicular to the X-axis.

Therefore, lines PQ and MN are indeed perpendicular.

Answer:

Detailed solution:

Given:

The problem to solve is:

Convert the equation into the standard quadratic form , where represent constants.

So, by adding to both sides, we get:

Note that .

The roots of this quadratic are found by applying the quadratic formula given as:

Substitute into the formula and calculate for .

Hence, the roots are:

A. Mean and standard deviation.

The sampling distribution’s mean closely matches the population mean. Since the population mean is 174.5, the sampling distribution’s mean equals this value.

The standard deviation of the sampling distribution is:

            σₓ̄ = σ / √n

Plugging in values:

            σₓ̄ = 6.9 / √25 = 1.38

b. Calculate z-scores for both values:
         
      z = (value - mean) / standard deviation

For 172.5:
     z = (172.5 - 174.5) / 1.38 = -1.49
Corresponding probability ≈ 0.068

For 175.8:
   z = (175.8 - 174.5) / 1.38 = 0.94
Corresponding probability ≈ 0.83

The difference between these probabilities is 0.762.

Approximately 0.762 × 200 = 152 sample means lie between 172.5 and 175.8.

c. Z-score for 172 cm:

    z = (172 - 174.5) / 1.38 = -1.81
Probability ≈ 0.03

Hence, samples with means below 172 cm equal 0.03 × 200 = 6.

Y = 3bx - 7x
y = x(3b - 7)

Assuming 3b - 7 ≠ 0, divide both sides by 3b - 7.


Solution:

Answer:

The top surface area of the washer equals 160.14 square millimeters.

Step-by-step Explanation:

The washer's top surface forms an annulus, characterized by an outer radius of 10 mm and an inner radius of 7 mm (obtained since the hole's diameter is 14 mm and the radius is half the diameter).

Recall the formula for the area of an annulus:

where R is the outer radius and r the inner radius.

Substituting the given values:

Thus, the calculation yields: