P varies inversely with x. If P = 14 when x= 16, find the value of P when x = 21.

For this inquiry, we are presented with a graph, and we're tasked with determining the x-coordinate of where the two lines intersect.

An examination of the graph indicates that the input value is around 3.3.

In the graph,

To derive g(x), we need the slope and y-intercept.

The slope represents the ratio of vertical change to horizontal change.

In this case, the rise is 3 units and the run is 2 units. The line intersects the y-axis at -2.

Thus, the equation for g(x) becomes

Next, we will perform

Substituting the values of both functions will yield

By adding 2 to both sides, we have

We will apply cross multiplication

Thus, the approximate input value is 3.3.

Answer:

The lines are parallel

Step-by-step explanation:

it's established that

To find the slope between two points, we use the formula

Keep in mind

If lines are parallel, their slopes must be identical

When lines are perpendicular, their slopes are negative reciprocals (the product equals -1)

step 1

Determine the slope of JK

we have

insert the values

step 2

Compute the slope of LM

we have

insert the values

step 3

Analyze the slopes

thus

hence

The lines are parallel

Response:

a. 55 cars

b. 25 cars

Detailed explanation:

Let’s denote the quantity of cars with stereo systems as N(ss), those with air conditioning as N(ac), and those with sunroofs as N(sr).

We find that:

N(ss) = 30

N(ac) = 30

N(sr) = 40

N(ss and ac and sr) = 15

N(at least two) = 30

a.

To calculate how many cars possess at least one feature (N(at least one) or N(ss or ac or sr)), we apply:

N(ss or ac or sr) = N(ss) + N(ac) + N(sr) - N(ss and ac) - N(ss and sr) - N(ac and sr) + N(ss and ac and sr)

N(ss or ac or sr) = 30 + 30 + 40 - (N(at least two) + 2*N(ss and ac and sr)) + 15

Substituting, we find N(ss or ac or sr) = 30 + 30 + 40 - (30 + 2*15) + 15 = 55

b.

For those cars that have exactly one feature, we have:

N(only one) = N(at least one) - N(at least two)

N(only one) = 55 - 30 = 25

The variations occur due to the distinct rows of pennies

The increase in production is found by calculating 180 - 150 = 30 tons. The percentage rise is computed by taking 30 divided by 150, which equals 0.2 or a 20% rise.