If you cut a double-napped cone horizontally using a plane figure, what type of conic section will be formed?

Consider an ellipse with its major axis aligned along the x-axis. Which of the following statements is correct regarding the properties of this ellipse?

What number completes the equation of the circle $$x^2+y^2=_{ }$$ ______, if $$r=3\sqrt[]{2}$$ ?

What are the center and radius of the circle $$\left(x-5\right)^2+\left(y+3\right)^2=4$$ ?

Arrange the following steps involved in solving for the value of the unknown variable in the exponential equation $$2^{5x}=64$$  in the correct order:
i. Equate the exponents on both sides of the equation.

                 ii. Solve for the unknown variable.

                 iii. Express 64 as $$2^6$$ .

Consider the exponential equation $$2^x=16$$ . Which of the following logarithmic expressions accurately represents the given equation?

The price of the iPhone 15 Pro Max is ₱108,990.00. According to Northladder, older models of the iPhone lose an average of 30% of their value during the weeks of a new launch. Assuming that Apple releases new models every year, which equation best describes the value of the iPhone 15 Pro Max in t years?

In a wildlife reserve, there were initially 75 wolves. Over the course of nine months, the wolf population increased to 225. Assuming exponential growth, what is the projected number of wolves at the end of three years?

How do you know if a function, $$f\left(x\right)$$ , has an inverse?

The magnitude 9.5 earthquake that occurred in Valdivia, Chile, on May 22, 1960, holds the record as the largest earthquake in world history. This devastating event resulted in the loss of 1655 lives, injuries to 3000 individuals, and the displacement of two million people. Additionally, it triggered a tsunami that caused fatalities and extensive damage as far away as Hawaii, Japan, and the Philippines. How does the intensity of this earthquake compare to the 7.9 magnitude earthquake in Moro Gulf, Mindanao, which is considered the most severe earthquake in the Philippines?

Which expression is equivalent to 1?

If you were asked to verify the identity $$\frac{\sin^2\theta+\cos^2\theta}{\cos\theta}=\sec\theta$$ , what would be the most appropriate initial step to undertake?