Using the quadratic formula to solve 2x2 = 4x – 7, what are the values of x? 2 plus-or-minus StartRoot 10 EndRoot i 1 plus-or-mi

Solution:

Let x be the distance in miles from the house to the theater.

Total time taken for the trip

Then average speed

Terrence walks at a speed of 2 miles per hour to the theater and returns home at 40 miles per hour.

Thus, Average Speed mi/hr

Both average speeds must be equivalent. Hence, we can express this as:

Consequently, the distance from home is 13.125 miles.

Answer:

What are the statements?

Step-by-step explanation:

Response:

Correlation.

In-depth explanation:

When the goal is to determine the connection between two or more variables to assess the impact of one variable (the independent one) on another variable (the dependent one), this is referred to as a correlation study or analysis. In this case, the link between employee shifts and sales or productivity is analyzed; it shows how the number of shifts worked by a specific employee correlates positively with the revenue generated. Here, the shift worked by the employee acts as the independent variable while the generated revenue is the dependent one.

A) The speed of pedestrian BC is 5 km/h

    The speed of pedestrian CD is 0 km/h

    The speed of pedestrian DE is 5 km/h

B) He reached E since the stop after 6 hours

C) The formula for section BC is d(t) = 40 - 5t

    The formula for section CD is d(t) = 20

    The formula for section DE is d(t) = 50 - 5t

Step-by-step breakdown:

A)

In the time-distance graph, speed represents the change in distance with respect to time

this means speed = Δd/Δt ⇒ (slope of the line)

For line BC:

1. Δd = 40 - 20 = 20 km

2. Δt = 4 - 0 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed of pedestrian BC stands at 5 km/h

For line CD:

1. Δd = 20 - 20 = 0 km

2. Δt = 6 - 4 = 2 hours

3. The speed = 0 ÷ 2 = 0 km/h

The speed of pedestrian CD is 0 km/h

For line DE:

1. Δd = 20 - 0 = 20 km

2. Δt = 10 - 6 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed for pedestrian DE is 5 km/h

B)

∵ He stopped at t = 4 hours

∵ He reached point E at t = 10 hours

∵ 10 - 4 = 6 hours

He arrived at E since the stop took 6 hours

C)

<pthe line="" equations="" are="" characterized="" by:=""><pthe general="" form="" of="" a="" line="" equation="" is="" f="" mx="" c="" where="" m="" represents=""><pthe slope="" and="" c="" is="" the="" y-intercept="" value="" of="" y="" when="" x="" equals="">

1. f(x) is referenced as d(t)

2. m is the speed

3. x corresponds to t

4. You can calculate c by substituting any coordinates of a point along the line into the formula

<pline bc="">

Line BC has a negative slope because d decreases as t increases

∵ m = -5 and c = 40

Thus, d(t) = 40 - 5t

The equation for section BC is d(t) = 40 - 5t

Line CD

Line CD is a horizontal line (which follows the form of any horizontal line represented as y = c)

Thus, m = 0 and c = 20

Therefore, d(t) = 20

The equation for section CD is d(t) = 20

Line DE

Line DE features a negative slope as d decreases along with an increase in t

∵ m = -5

Thus, d(t) = -5t + c

The value of c can be determined by substituting point D's coordinates into the equation

∵ D's coordinates are (6, 20)

Thus, 20 = -5(6) + c

So, 20 = -30 + c

Adding 30 to both sides yields

∴ c = 50

Thus, d(t) = 50 - 5t

The equation for section DE is d(t) = 50 - 5t

Further Learning:

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</padditional></pline></pthe></pthe></pthe>

Among the options provided, the statement that holds true is the third one: "Nina makes 20x dollars each week at the clothing store." The information given explicitly mentions that x denotes the total hours she has worked within a week. This assertion renders the other statements incorrect.