Answer:
Carlos is incorrect.
Step-by-step explanation:
We have been given that a line through the origin has a slope of 
. Carlos thinks the slope of a perpendicular line at the origin will be 3.
We know that the slope of a perpendicular line to a given line is always negative reciprocal of the slope of the given line.
The slope of the perpendicular line at the origin will be negative reciprocal of .
Let us find negative reciprocal of as:
Since the slope of a perpendicular line at the origin is 
, therefore, Carlos is incorrect.
Answer:
No, According to triangle Inequality theorem.
Step-by-step explanation:
Given:
Length given are 4 in., 5 in., 1 in.
We need to check whether with these lengths we can create triangular components.
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
These must be valid for all three sides.
Hence we will check for all three side,
4 in + 5 in > 1 in. (It is a Valid Condition)
1 in + 5 in > 4 in. (It is a Valid Condition)
4 in + 1 in > 5 in. (It is not a Valid Condition)
Since 2 condition are valid and 1 condition is not we can say;
A triangular component cannot be created with length 4 in, 5 in, and 1 in by using triangle inequality theorem (since all three conditions must be valid).
Answer:
-1
Step-by-step explanation:
The mean is the sum of all values divided by the amount of values.
We take the sum of all the numbers:
-3 + -8 + 12 + -15 + 9
-11 + 12 + -15 + 9
1 + -15 + 9
10 + -15
-5
We then divide the sum by how many number we have (we are given 5 numbers):
-5/5 = -1
Therefore, our mean is equal to -1.
Answer:
23,24,26,27 sorry if you get it wrong
is the same as 
Dividing by 3 is the same as multiplying by the fraction 1/3
