Given pair of lines are x² + 4xy + y² = 0
⇒ (y/x) ² + 4 y/x + 1 = 0
⇒ y/x = -4±2√3/2 = -2±√3,
∴ The lines y = (-2 + √3) x and y = (-2 - √3) x and x - y = 4 forms an equilateral triangle
Clearly the pair of lines x² + 4xy +y² = 0 intersect at origin,
The perpendicular distance form origin to x - y = 4 is the height of the
h = 2 √ 2
∵ Area of triangle = h²/√3 = 8/√3
Answer:
E, B, A,
Step-by-step explanation:
C is wrong because it isn't decreasing
D is wrong because if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning y goes lower than 5
F is wrong because if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning the y intercept is 2 not 5
Answer:
Step-by-step explanation:
From the first sentence x (the number) is 2 more than another number (y). So, x+2=y. The sum of the squares of the two numbers is 42, meaning that 
+
=42. First, we square root the ENTIRE equation to get rid of the square. If you do one thing to one side, you have to do it to the other. After this, we have x+2+y=
. Now, we subtract 2 from the other side to isolate the variable. You can isolate either one but normally I go for x. Now we have x+y=+2. Now, we want to get y to the other side so we subtract it from the left side and the right side which gives us x=-y++2. now we know what X is equal to. Now we plug in x for +=42, which gives us 
+=42. Now we only have one variable which is what we want. Next, we square root the entire thing to get rid of the squares, which gives us -y++4+y=. I got lost in my work. I must have done something wrong I cant find out. If anyone wants to pick up where I left off go ahead but there's a timer and I have one minute left. I cant finish the problem in a minute. I'm sorry and hopefully I lead you somewhere.
Answer:
5/2
Step-by-step explanation:
When you are finding the slope of a parallel line, the other line always has the same slope as the first line but different y intercept.
Given two points; (x₁,y₁) and (x₂,y₂) the slope is:
m=(y₁-y₂) / (x₁-x₂) or m=(y₂-y₁) / (x₂-x₁)
In this case:
(4,3)
(5,2)
m=(5-4)/(2-3)=1/-1=-1
Answer: the slope is -1
