Answer:
The expression that shows how long the two machines will operate simultaneously is:

Step-by-step explanation:
We know that:
x: hours to manufacture a deck of cards for machine A
y: hours to manufacture a deck of cards for machine B
z: hours that machine A operates alone
The number of decks manufactured only by machine A is:

So, the remaining decks are given by:

Then, the combined rate of machines A and B would be:

The work-rate formula is:

Hence, the time that the two machines work simultaneously is:


Answer:

Step-by-step explanation:
Given the following quadratic equation:

The steps to solve it are:
1. Move the terms to one side of the equation:

2. Apply the Quadratic formula
.
In this case we can identify that:

Then, substituting these values into the Quadratic formula we get the following solutions:


9514 1404 393
Answer:

Step-by-step explanation:
In the English expression, you need to understand that "A divided by B" means that A is the numerator and B is the denominator of the fraction representing the division. Here, "B" is "the quantity of ...", which means that the stuff after "of ..." is to be treated as a single item, the denominator in this case. That item is "x plus y." So, the expression in math terms is ...

When this is written in plain text, the "quantity" is put in parentheses, because the fraction bar no longer serves as a grouping symbol:
9/(x+y)
These expressions match the first choice, A.
The slope is 5/4. Hope this helps!
Answer:
C. Capture theory
Step-by-step explanation:
- The capture theory states that the moon originated in some other part of the solar system and later it was captured by the gravitational pull of our planet.
- The co-formation theory states that the moon formed simultaneously with the earth from the same nebula that formed the solar system.
- The impact theory states the moon formed of a chunk of earth separated form it after a large meteorite impact.
- The synchronous theory is not a theory about the formation of the moon.
We can conclude that the correct answer is C. Capture theory.