Answer:
y = x - 5
Step-by-step explanation:
Given the point, (10, 5), and the slope, m = 1:
Substitute these values into the <u>slope-intercept form</u> to solve for the y-intercept, <em>b</em>:
y = mx + b
5 = 1(10) + b
5 = 10 + b
Subtract 10 from both sides to isolate b:
5 - 10 = 10 - 10 + b
-5 = b
The y-intercept of the line is: b = -5. This represents the y-coordinate of the y-intercept, (0, -5), which represents the point on the graph where it crosses the y-axis. Along the y-axis, the value of x = 0. Hence, the y-intercept is (0, -5).
Therefore, given the slope, m = 1, and the y-intercept, b = -5:
The equation of the line in slope-intercept form is: y = x - 5.
Answer:
x = -14
Step-by-step explanation:
The expression to write in this problem is:
"the sum of x and 12 equals the sum of half of x and 5"
We have:
- The sum of x and 12 is: 
- The sum of half of x and 5 is: 
So, the equation to write in this problem is

We solve it as follows:
1) First, we subtract
from both sides, and we get

2) Then, we subtract 12 from both sides:

3) Now we multiply both sides by 2:

So, this is the solution.
<h3>Answer:</h3>
x/tan(x) is an even function
sec(x)/x is an odd function
<h3>Explanation:</h3>
<em>x/tan(x)</em>
For f(x) = x/tan(x), consider f(-x).
... f(-x) = -x/tan(-x)
Now, we know that tan(x) is an odd function, so tan(-x) = -tan(x). Using this, we have ...
... f(-x) = -x/(-tan(x)) = x/tan(x) = f(x)
The relation f(-x) = f(x) is characteristic of an even function, one that is symmetrical about the y-axis.
_____
<em>sec(x)/x</em>
For g(x) = sec(x)/x, consider g(-x).
... g(-x) = sec(-x)/(-x)
Now, we know that sec(x) is an even function, so sec(-x) = sec(x). Using this, we have ...
... g(-x) = sec(x)/(-x) = -sec(x)/x = -g(x)
The relation g(-x) = -g(x) is characeristic of an odd function, one that is symmetrical about the origin.
Turn f(x) into y so the equation is y=x+2. Now switch their places so it is x=y+2. Now solve for y. The answer is y=x-2.
If you would like to know the solution to the equation (x - 2) * (x + 5) = 18, you can calculate this using the following steps:
(x - 2) * (x + 5<span>) = 18
</span>x^2 + 5x - 2x - 10 = 18
x^2 + 3x - 28 = 0
(x + 7) * (x - 4) = 0
1. x = - 7
2. x = 4
The correct result would be x = - 7.