Answer:
in short, Yes they are always rational.
here's why...
E.g. suppose 
and 
are fractions, that means that a,b,c,d are all integers, and b and d are not zero. finding the sum the numerator, and denominator would also have to be integers. the denominator of the sum can't be zero since the denominators of the fractions were not zero, and would give 
and since they are bound by addition (sum means addition) they must also be rational since eit would equal a bigger integer than initially had
Step-by-step explanation:
<h3>
Short Answer: Yes, the horizontal shift is represented by the vertical asymptote</h3>
A bit of further explanation:
The parent function is y = 1/x which is a hyperbola that has a vertical asymptote overlapping the y axis perfectly. Its vertical asymptote is x = 0 as we cannot divide by zero. If x = 0 then 1/0 is undefined.
Shifting the function h units to the right (h is some positive number), then we end up with 1/(x-h) and we see that x = h leads to the denominator being zero. So the vertical asymptote is x = h
For example, if we shifted the parent function 2 units to the right then we have 1/x turn into 1/(x-2). The vertical asymptote goes from x = 0 to x = 2. This shows how the vertical asymptote is very closely related to the horizontal shifting.
Answer:
-10
Step-by-step explanation:
24+8-(7x6)
The graph that shows the solution to the system of inequalities is: C (see the image attached below).
<h3>How to Determine the Graph of the Solution to a
System of Inequalities?</h3>
Given the following systems of inequalities:
y < -1/3x + 1
y ≤ 2x - 3
Below are the features of the graph that represents a solution to the system of inequalities:
- The boundary line of y < -1/3x + 1 would be a dashed line and the shaded area would be below it, because of the inequality sign, "<".
- The boundary lines of y ≤ 2x - 3 would be a solid line and the shaded area would be below it, because of the inequality sign, "≤".
- The slope of the shaded line that represents y < -1/3x + 1, would be -1/3, and the line would be a decreasing line which intersects the y-axis at 1.
- The slope of the line that represents y ≤ 2x - 3, would be 2, and the line would also be an increasing line that intersects the y-axis at -3.
Therefore, the graph that shows the solution to the system of inequalities is: C (see the image attached below).
Learn more about the graph of the system of inequalities on:
brainly.com/question/10694672
#SPJ1
Answer:
52 and 38
Step-by-step explanation:
If x = 13 then 4x = 4 * 13 so 52.
Same for the next one. 2x = 2 * 13 so 26. 26+12 is 38.
Done...
