Determine if the following equations form a perpendicular line or not
1 answer:
- Slope-Intercept Form: y = mx + b, with m = slope and b = y-intercept.
If two lines are perpendicular, then they will have slopes that are <u>negative reciprocals</u> to each other. An example of negative reciprocals are 2 and -1/2
<h2>6.</h2>Now with line 2, I have to convert it to slope intercept form. Firstly, subtract 2x on both sides of the equation:
Next, divide both sides by -5 and your slope-intercept form is
Now since 2/5 is <em>not</em> the negative reciprocal of -2/5, <u>these lines are not perpendicular.</u>
<h2>7.</h2>It's pretty much the same process; convert to slope-intercept and determine if negative reciprocal. This time I'll brush through them:
Now since 2 <em>is</em> the negative reciprocal of -1/2, <u>these lines are perpendicular.</u>
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Answer:
Step-by-step explanation:
Given
See attachment
Required
Find BC
The sum of is 360.
So:
Collect like terms
Solve for n
From the circle:
Substitute 14 for n
Answer:
2. Eunju is right
3. is a factor of
.
Step-by-step explanation:
<u>Polynomial Remainder Theorem</u>
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).
As a consequence, if a polynomial is divisible by x-a, f(a)=0.
Part 1:
Let's make:
To find out if x+b is a factor of f(x), we find f(-b):
Operating:
The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).
Part 2:
We must find out if is a factor of
without using long division or synthetic division.
We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:
Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.
Let's make:
Find f(-2):
Find f(-3):
Since both f(-2) and f(-3) are zero, is a factor of
.