The unit normal for the given plane is <5,2,-1>.
The equation of the plane parallel to the given plane passing through (5,5,4) is therefore
5(x-5)+2(y-5)-1(z-4)=0
simplify =>
5x+2y-z=25+10-4=31
Answer: the plane through (5,5,4) parallel to 5x+2y-z=-6 is 5x+2y-z=31
Answer:
(-4, 0) U (1, ∞)
Step-by-step explanation:
Set each factor EQUAL to zero to find the zeroes (since it is not actually equal to zero, you will use an open circle when graphing and an open bracket when writing in interval notation).
x = 0 x-1 = 0 x + 4 = 0
x = 1 x = -4
Next, choose a value to the far left, between each of the zeroes, and to the far right to evaluate if it makes a true statement when input into the given inequality.
far left (I choose -5): -5(-5 - 1)(-5 + 4) > 0 → (-)(-)(-) > 0 → negative > 0 FALSE
- 4 to 0 (I choose -2): -2(-2 - 1)(-2 + 4) > 0 → (-)(-)(+) > 0 → positive > 0 TRUE
0 to 1 (I choose 0.5): .5(.5 - 1)(.5 + 4) > 0 → (+)(-)(+) > 0 → negative > 0 FALSE
far right (I choose 2): 2(2 - 1)(2 + 4) > 0 → (+)(+)(+) > 0 → positive > 0 TRUE
Answer:
No solution
Step-by-step explanation:
Substitution is done by substituting one equation into another. To begin solve one equation for a variable.
Substitute y=-4x+3 into -4x-y=-2.
-4x -(-4x + 3) = -2
-4x + 4x - 3 = -2
-3=-2
This is a false statement and there is no variable present anymore. This means the equations have no solution.
Answer:
The correct expression is n + 8
The value of the expression = 5.3 + 8
The answer is 13.3
Step-by-step explanation:
The expression for eight increased by a number
Assume that the number is n
Increased eight by n means add n to eight
The correct expression is n + 8
When n = 5.3
Substitute 5.3 for the variable n
The value of the expression = 5.3 + 8
Simplify by adding 5.3 and 8
5.3 + 8 = 13.3
The answer is 13.3
