Here is a scenario that came up in the nationally syndicated column called "Ask Marilyn" in Parade Magazine. Suppose a certain d

Jason can confirm the accuracy of his solution by substituting the calculated x value back into the original equation to check if it holds true. If the equality fails, it indicates that his calculated x is incorrect.

Upon reviewing the functions based on the tables, it is determined that (f - g)(x) is positive in the range of (–∞, 9).----------------------

For the

• subtractive
• function, we simply subtract the two functions, leading to:

It retains a

• positive
• value when f is greater than g, which means: f(x) > g(x).Being a linear function, one will be greater prior to the equality, while the other will take precedence afterward.
• They intersect at x = 9.
• If x < 9, then f(x) is greater than g(x), thus, (f - g)(x) remains positive, which indicates that the
• required interval is:(–∞, 9)

A related problem can be found at

Response:

The height of the water when it reaches 4 inches is .

Detailed Explanation:

Flow rate of water from the cone = R=

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

r = h/2

Volume of the cone =

h = 4 inches

The height of the water when it is 4 inches deep is .

Begin by creating a system of equations: let 'a' represent the amount Mary earns per student, and 'b' denote her fixed amount. The equations are 90=15a+b (subtracting the lower from the upper equation) and 62=8a+b. From these, we have 90-62=28, leading to 15a-8a=7a, and b cancels itself out. This gives us 7a=28, resulting in a=4. Substituting 'a' into 62=8a+b reveals b=30. Since Lisa earns half of Mary's base, her fixed amount is 15, but she makes twice as much per student, bringing her rate to 8 per student. Thus, we can formulate: m=4c+30 for Mary's earnings, and l=8c+15 for Lisa's. Setting c=20 results in m=110 and l=175, showing that Lisa makes more when teaching a class of 20 students. I trust this information helps.

Answer:

The least quantity of water needed to fill the sphere is

Step-by-step explanation:

We know that

The volume of the sphere (the glass sphere) can be defined as

We have

----> the radius equals half the diameter

Let’s assume

Now substitute