9514 1404 393
Answer:
when (0, 0) is on the boundary line
Step-by-step explanation:
Any test point you use to determine shading must not lie on the boundary line. You need a test point that will make the inequality true or false. That is, it must give a result a > b or a ≥ b, where a ≠ b. A point on the boundary line will give a = b, so is not helpful.
If the test point gives "true", then it lies in the shaded area. If it gives "false," then the other side of the line is shaded.
(0, 0) cannot be used as a test point when it lies on the boundary line.
Answer:
In general, quadratic equations have two x-intercepts. But sometimes it happens that a quadratic eqution has one x-intercept or no interepts. That's why we should fully analyze this equation:
Given the following equation: y=3x^2 + 7 + m
If y=0, then:
3x^2 + 7 + m = 0 ⇒ x^2 = (-m-7)/3
Then 
± 
Given that we can take the square root of a negative number, the only way this equation has two x-intercepts is if m<-7.
Summarizing:
The equation: y=3x^2 + 7 + m has two x-intercepts only if m is less than -7. If m equals -7, the equation has only one x-intercept, and finally, if m is greater than -7, the equation has NO x-intercepts.
Answer: 3y - x - 42 = 0
Step-by-step explanation:
The equation y + 1 = -3(x - 5)
Now expand the expression by opening the brackets
y + 1 = -3x + 15
Recall,
Equation of line , y = mx + c , where m = slope
rearranging the equation above in order to determine the ( m)
y = -3x -1 + 15
y = -3x + 14
Recall again condition for perpendicularity
m₁m₂ = -1
From the equation given, m₁ = -3, therefore , to get m₂
-3 x m₂ = -1
-3m₂ = -1
Therefore m₂ = -1/-3
m₂ = 1/3
Now , to find the equation of the second line parallel to the first one,
Just replaced the -3 in the equation above by m₂ = 1/3 in
y = -3x + 14
y = x/3 + 14
Now , multiply both the RHS and LHS of the equation by 3, to make it a linear.
3y = x + 3 x 14
3y = x + 42
3y - x - 42 =0
How high is a tree that casts a 33 ft shadow at the same time a 5 ft pole casts a shadow which is 12 ft long?
let x=height of the tree
x/33=5/12
x=5*33/12
x=13.75
