Answer:
y = 8x + 4
Step-by-step explanation:
combine 1/2 and y:
-4x + y/2 = 2
add 4x to both sides:
+4x -4x + 1/2y = 2 +4x
mutiple both sides by 2 :
2 (y/2) = 2 (2 +4x)
simplify both sides:
y= 8x + 4
Answer:
See below.
Step-by-step explanation:
because we combine like terms. You will essentially ignore the x and just do -2 + 1, which is -1. So, the answer would be -1x which is simply just -x.
To see why we can combine like terms, use the distributive property. So we have:
This is the same thing as saying:
Factor out the x:
Add:
And simplify:
Working with the right side:
cot(<em>x</em>) + 2 tan(<em>x</em>) + tan³(<em>x</em>) = cos(<em>x</em>)/sin(<em>x</em>) + 2 sin(<em>x</em>)/cos(<em>x</em>) + sin³(<em>x</em>)/cos³(<em>x</em>)
… = (cos⁴(<em>x</em>) + 2 sin²(<em>x</em>) cos²(<em>x</em>) + sin⁴(<em>x</em>)) / (sin(<em>x</em>) cos³(<em>x</em>))
Factorize the numerator as a sum of squares:
<em>a</em>⁴ + 2 <em>a</em>² <em>b</em>² + <em>b</em>⁴ = (<em>a</em>² + <em>b</em>²)²
… = (cos²(<em>x</em>) + sin²(<em>x</em>))² / (sin(<em>x</em>) cos³(<em>x</em>))
Recall that
cos²(<em>x</em>) + sin²(<em>x</em>) = 1
… = 1 / (sin(<em>x</em>) cos³(<em>x</em>))
… = 1 / (sin(<em>x</em>) cos³(<em>x</em>)) • cos(<em>x</em>)/cos(<em>x</em>)
… = cos(<em>x</em>) / (sin(<em>x</em>) cos⁴(<em>x</em>))
… = cot(<em>x</em>) sec⁴(<em>x</em>)
Multiply those 2 numbers and divide that answer by 2
Answer:
The solution to the inequality is:
Please also check the graph of the solution to the inequality.
Step-by-step explanation:
Given the inequality
switch sides
Multiply both sides by -1 (reverse the inequality)
Simplify
Multiply both sides by 4
Simplify
Therefore, the solution to the inequality is:
Please also check the graph of the solution to the inequality.
