7 and 2 are addents
+ addition sign
= equal sign
9 sum
Step-by-step explanation:
For the cubic function to be an increasing function, dy/dx > 0 for all real values of x.
dy/dx
= d/dx [4x³ + 4px² + 16x - 9]
= 12x² + 8px + 16.
We have 12x² + 8px + 16 > 0.
=> 3x² + 2px + 4 > 0,
where a = 3, b = 2p and c = 4.
For the quadratic function to have a range that is always positive, the discriminant must be less than 0.
(in order to have no real roots)
We have b² - 4ac < 0.
=> (2p)² - 4(3)(4) < 0
=> 4p² - 48 < 0
=> p² - 12 < 0
=> p² < 12
=> -√12 < p < √12
=> -2√3 < p < 2√3.
That was a very long process but hopefully you understand all of it!
The left term is 8x⁶ = (2x²)³.
The right term is 27y³ = (3y)³.
The sum of cubes identity is
... a³ +b³ = (a +b)(a² -ab +b²)
Filling in the values for <em>a</em> and <em>b</em>, the factors of your expression are ...
... (2x² +3y)(4x⁴ -6x²y +9y²)
Answer:
The signup fee is $17
Step-by-step explanation:
we know that
The equation in point slope form is equal to
where
m is the slope or unit rate of the linear equation
(x1,y1) is a ordered pair of the line
Let
x -----> the number of months
y -----> the total cost of a gym membership
In this problem we have
The slope of unit rate is equal to
The ordered pair is
substitute
----> equation in point slope form
Convert to slope intercept form
---> equation in slope intercept form
The y-intercept is the signup fee (value of y when the value of x is equal to zero)
therefore
The signup fee is $17
Answer:
There were 36 space rocks in total.