Answer:
The intersection is 
.
The Problem:
What is the intersection point of 
and 
?
Step-by-step explanation:
To find the intersection of and , we will need to find when they have a common point; when their 
and 
are the same.
Let's start with setting the 's equal to find those 's for which the 's are the same.
By power rule:
Since 
implies 
:
Squaring both sides to get rid of the fraction exponent:
This is a quadratic equation.
Subtract 
on both sides:
Comparing this to 
we see the following:
Let's plug them into the quadratic formula:
So we have the solutions to the quadratic equation are:
or 
.
The second solution definitely gives at least one of the logarithm equation problems.
Example: 
has problems when 
and so the second solution is a problem.
So the where the equations intersect is at .
Let's find the -coordinate.
You may use either equation.
I choose .
The intersection is .
Answer:
x=57
Step-by-step explanation:
63+60= 123
A triangle is 180 degrees
180-123= 57
x=57
I'm guessing your problem is this:
y³ - 9y² + y - 9 = 0
right?
In solving this problem, I recommend doing this:
y³ - 9y² + y - 9 = 0
Factor out a y² from the first two numbers in the problem:
y²(y - 9) + (y - 9) = 0
Separate the parentheses which means y - 9 goes on one side. The y² added a one since it came from the + 1 in the middle of expression. When you're separating parentheses like this you just take the outside numbers and combine them together. Since + 1 came from the outside of the (y - 9) and y² also was sitting on the outside of (y - 9) combine them to make y² + 1. Like this:
(y² + 1)(y - 9) = 0
Now separate your two parentheses to two separate problems:
(y² + 1) = 0 and (y - 9) = 0
Now you're y² + 1 will equal:
y² = -1
y = √-1 <-- This number doesn't exist so it will be an imaginary number (i). If you guys didn't learn that in your class I recommend just leaving it as i for that part.
Now solve y - 9 = 0:
y = 9 <-- Since we added nine to both sides to get this.
So you're final answer should be y = i and 9
Answer:
The LCM of 15 and 5 is, 15.
Step-by-step explanation:
Answer:
D
A=-5
Step-by-step explanation:
