Answer:
<h2>x = 7</h2>
Step-by-step explanation:
To find the value of the value of x when
y = 14 we must first find the relationship between them
The statement
The value of y varies directly with x is written as
where k is the constant of proportionality
when x = 218
y = 436
So we have
436 = 218k
Divide both sides by 218
k = 2
So the formula for the variation is
<h2>y = 2x</h2>
when y = 14
We have
14 = 2x
Divide both sides by 2
<h3>x = 7</h3>
Hope this helps you.
4x - 12 = -7x - 111
11x = -99
x = -9
Answer:
$13.50
Step-by-step explanation:
First, we got to multiply $18 by 25% or .25
$18 x .25 = $4.50
Lastly, we just subtract $4.50 from $18.
$18 - $4.50 = $13.50
a. The first variable is x and the second variable is y.
b. The equations are 
and 
Step-by-step explanation:
Step 1:
The first step is to define the variables. The variables can be any two symbols, letters, characters, etc.
Here let the first variable be x and the let the second variable be y.
So the variables are defined as x and y.
Step 2:
The sum of the given variables is 12.
The first variable + the second variable = 12,
The difference between the two variables is 4.
The first variable - the second variable = 4.
Step 3:
If we add both the equations we get, 
and 
x = 8 and y = 4.
<h3>
Answer: Choice C) </h3><h3>
The system can only be independent and consistent</h3>
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Explanation:
Let's go through the answer choices
- A) This isn't possible. Either a system is consistent or inconsistent. It cannot be both at the same time. The term "inconsistent" literally means "not consistent". It's like saying a cup is empty and full at the same time. We can rule out choice A.
- B) This is similar to choice A and we cannot have a system be both independent and dependent. Either a system is independent or dependent, but not both. Independence means that the two equations are not tied together, while dependent equations are some multiple of each other. We can rule out choice B.
- C) We'll get back to this later
- D) The independence/dependence status is unknown without the actual equations present. However, we know 100% that this system is not inconsistent. This is because the system has at least one solution. Inconsistent systems do not have any solutions at all (eg: parallel lines that never cross). We can rule out choice D because of this.
Going back to choice C, again we don't have enough info to determine if the system is independent or dependent, but we at least know it's consistent. Consistent systems have one or more solutions. So part of choice C can be confirmed. It being the only thing left means that it has to be the final answer.
If it were me as the teacher, I'd cross out the "independent" part of choice C and simply say the system is consistent.
