Answer:
24 is the LCM of 4,6,8. I think thats what your looking for.
Hope this helps!
Step-by-step explanation:
The expression for the greatest common factor of 20 and 30 using the distributive property is 10(2 + 3)
Pounds of ice = 20
Number of cups = 30
The relation for the distributive property :
a × (b + c)
Expand ;
a × (b + c) = (a × b) + (a × c) = ab + ac
Finding the greatest common factor of 20 and 30 ;
(2 × 10) + (3 × 10)
According to the distributive property
(2 × 10) + (3 × 10) = 10(2 + 3)
Therefore, the expression for the greatest common factor is 10(2 + 3)
Learn more :brainly.com/question/15263211
The answer is <span>5, 4, 2
</span>
Among all choices we have 5, so
x = 5
x - 5 = 0
Let's divide the expression by (x - 5) using the long division:
x³ - 11x² + 38x - 40
(x - 5) * x² = x³ - 5x² Subtract
____________________________
-6x² + 38x - 40
(x - 5) * (-6x) = -6x² + 30x Subtract
____________________________
8x - 40
(x - 5) * 8 = 8x - 40 Sutract
____________________________
0
Thus: x³ - 11x² + 38x - 40 = (x - 5)(x² - 6x + 8)
Now, let's simplify x² - 6x + 8.
x² - 6x + 8 = x² - 2x - 4x + 8 =
= x² - 2*x - (4*x - 4*2) =
= x(x - 2) - 4(x - 2) =
= (x - 4)(x - 2)
Hence:
x³ - 11x² + 38x - 40 = (x - 5)(x - 4)(x - 2)
To calculate zero:
x³ - 11x² + 38x - 40 = 0
(x - 5)(x - 4)(x - 2) = 0
x - 5 = 0 or x - 4 = 0 or x - 2 = 0
x = 5 or x = 4 or x = 2
Put ur equation in y = mx + b form because the slope will be in the m position.
5x + 3y + 12 = 0
3y = -5x - 12
y = -5/3x - 4
y = mx + b
y = -5/3x + (-4)......as u can see, the number in the m position (the slope) is -5/3 <===
we have a maximum at t = 0, where the maximum is y = 30.
We have a minimum at t = -1 and t = 1, where the minimum is y = 20.
<h3>
How to find the maximums and minimums?</h3>
These are given by the zeros of the first derivation.
In this case, the function is:
w(t) = 10t^4 - 20t^2 + 30.
The first derivation is:
w'(t) = 4*10t^3 - 2*20t
w'(t) = 40t^3 - 40t
The zeros are:
0 = 40t^3 - 40t
We can rewrite this as:
0 = t*(40t^2 - 40)
So one zero is at t = 0, the other two are given by:
0 = 40t^2 - 40
40/40 = t^2
±√1 = ±1 = t
So we have 3 roots:
t = -1, 0, 1
We can just evaluate the function in these 3 values to see which ones are maximums and minimums.
w(-1) = 10*(-1)^4 - 20*(-1)^2 + 30 = 10 - 20 + 30 = 20
w(0) = 10*0^4 - 20*0^2 + 30 = 30
w(1) = 10*(1)^4 - 20*(1)^2 + 30 = 20
So we have a maximum at x = 0, where the maximum is y = 30.
We have a minimum at x = -1 and x = 1, where the minimum is y = 20.
If you want to learn more about maximization, you can read:
brainly.com/question/19819849
