Evaluate 0.1(3.7) using distributive proper

We have to check which of the statements can be modeled as y = mx + b. This equation represents a straight line or is a linear equation. Hence, in the given options we will check which statement represents a linear equation.

Statement A: The number of bacterial cells (y) in a Petri dish doubles every hour (x).  

This can be expressed as y (x) = y (x-1) * 2, which is not a linear function. Refer attached image

Statement B: The time (y) it takes to fill an 80-gallon bathtub depends on the number of gallons filled per minute (x).

Here, we can not determine the expression and we just know that the time (y) is a function of number of gallons filled per minute (x).

Statement C: The total cost (y) of publishing a textbook at a printing cost of $9.50 per book depends on the number of books (x) published.  

This can be expressed as y = 9.5 * x. This is a linear function, which will grow by a factor of 9.5 with each unit change in x. Refer attached image.

Statement D: The volume (y) of a conical flask with a height of 6 inches depends on the radius (x) of the flask.

Here, we can not determine the expression, but we know that the volume of a cone with 6 inch height is a function of the cone's radius.

Hence, statement C can be modeled by the equation y = mx + b.

Answer:

minimum value of the function will be 0.5 when x is 0.

Step-by-step explanation:

a) x + 5 = 7

x + 5 - 5 = 7 - 5 (Subtract 5 from both sides)

x = 2

b) 2x - 8 = 20

2x - 8 + 8 = 20 + 8 (Add 8 to each side)

2x = 28

2x/2 = 28/2 (Divide each side by 2)

x = 14

c) 4x - 6x = 200

-2x = 200

-2x/-2 = 200/-2 (Divide each side by -2)

x = -100 (Note that a negative number divided by a negative number is positive, whereas a positive number divided by a negative number is negative)

d) x + 1 = 5

x + 1 - 1 = 5 - 1 (Subtract 1 from each side)

x = 4

Hope it helps and is useful :)