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: x = 8, y = 2, coordinates (8,2)
Step-by-step explanation:
2x = 4y + 8 (divide by 2 to get value of x)
x = 2y + 4
(now substitute x into the second equation to find value of y)
2y + 4 - 2y = 4
2y - 2y = 4 - 4 (divide by 2 to get value of y)
y - y = 2 - 2
y = 2
Now plug in value of "y" to get value of "x".
x - 2(2) = 4
x - 4 = 4
x = 8
Coordinates (8,2)
Answer:
184
Step-by-step explanation:
I took the amount of children, 461, and subtracted the amount of adults surveyed.
461 - 277 = 184