Categories

## Identify the sentence using the indicated pronoun correctly. a reciprocal pronoun We were laughing at one another. We were laughing at ourselves.

Answer: The sentence that uses a reciprocal pronoun correctly is “We were laughing at one another”.

Explanation: A reciprocal pronoun is a type of pronoun that is used when two or more people are acting in the same way towards the other. In other words, when using a reciprocal pronoun, the actions of the people involved correspond to one another. In English, there are two reciprocal pronouns “each other” and “one another”. In that way, the first sentence (“We were laughing at one another”) is the correct one because it includes the reciprocal pronoun “one another” and it makes reference to two or more people carrying out the same action, which is laughing, simultaneously. In contrast, the second sentence includes a reflexive pronoun (ourselves).

Categories

## Eric states that the slopes of perpendicular lines are opposite reciprocals (i.e. that the slope of one is equal to the negative of the reciprocal of the other), and Aviva states that the product of the slopes of perpendicular lines is −1. Who is correct? Why? Explain your reasoning with an example. If one of the lines is vertical and the other one is horizontal, how would your answer change?

Eric’s statement is correct that the slopes of the perpendicular lines are opposites reciprocal with each other compared to Aviva’s. Aviva’s statement is correct but is not usually the case. An example is that when you are given these functions such as y = -2x + 3 and y = 1/2x + 4. The coefficients of the x variable are 2 and negative 1/2. The slopes must be in opposite signs so that the two functions will intersect at a common point and will form a ninety degree angle. This is the very basis of a perpendicular line because if both lines have the same slopes, then both lines are just parallel with each other, they cannot intersect.

Categories

## What is the reciprocal of 0.25

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

Categories

## If you vertically stretch the reciprocal parent function, F(x) = 1/x , by multiplying by 8, what is the equation of the new function?

If you vertically stretch the reciprocal parent function, F(x) = 1/x , by multiplying by 8, what is the equation of the new function?

Categories

## How do you find the reciprocal of 3.6?? …?

How do you find the reciprocal of 3.6?? …?