A hyperbola is represented using the equation (x-1)^2/4-(y+2)^2/16=1. What are the slopes of the asymptotes?

Tthe options that can be used as a reason in a two-column proof are:

a. a premise

b. a definition

d. a postulate

In a two-column proof, each step or statement in the proof is accompanied by a reason to justify why that step is valid. The reasons are typically based on established mathematical principles, and the choices for reasons often include premises, definitions, postulates, and previously proven theorems. Let's delve into each of these options in more detail:

Premise (a): A premise is a statement or fact that is given to you as true. It serves as a foundational piece of information on which your proof is built. For example, if you're working with a geometry proof, you might be given the premise that two angles are congruent.

Definition (b): Definitions provide the meanings of mathematical terms and concepts. You can use definitions as reasons to clarify the meaning of specific terms or properties used in your proof. For instance, you might use the definition of a right angle to justify a particular statement in a proof.

Conjecture (c): Conjectures are unproven statements or hypotheses. They are not typically used as reasons in a proof because they lack the mathematical rigor and certainty required in a proof. However, conjectures can serve as a starting point for exploring and formulating proofs.

Postulate (d): Postulates (or axioms) are fundamental statements or principles in mathematics that are accepted as true without proof. Postulates are often used as reasons in geometric proofs to justify certain statements or relationships, such as the postulate that states two points determine a unique line.

for such more question on two-column proof

brainly.com/question/1788884

#SPJ2

Well if her simplifies 1 3/7 to 1 1/2 and 5 4/5 to 6 then he would be overestimating because 1 1/2 is greater than 1 3/7 and 6 is greater than 5 4/5

Hope this helps!

Answer:

option B. 5 units.

Step-by-step explanation:

If a Δ XYZ is translated 4 units up and 3 units left to yield X'Y'Z'.

If we consider one vertex  X (x, y) of the triangle XYZ then after translation X will form new vertex as

x' (x-3, y-4)

Then we have to find the distance between x and x' after translation.

In the figure attached we have to find the distance a.

a² = 3² + 4² ( By Pythagoras Theorem)

a² = 9 + 16

a = √25 = 5 units

Therefore, answer will be option B. 5 units.

The answer is B- 5 units

24 percent of 50 is equal to 12.

We have,

To find the number when 24% of it is equal to 12, we can set up the following equation:

0.24 * x = 12

Here, x represents the unknownnumber.

To solve for x, we divide both sides of the equation by 0.24:

x = 12 / 0.24

Simplifying the division gives us:

x = 50

Therefore,

24 percent of 50 is equal to 12.

Learn more about expressions here:

brainly.com/question/3118662

#SPJ6