Answer:
The minimum value of f(x) is 2
Step-by-step explanation:
- To find the minimum value of the function f(x), you should find the value of x which has the minimum value of y, so we will use the differentiation to find it
- Differentiate f(x) with respect to x and equate it by 0 to find x, then substitute the value of x in f(x) to find the minimum value of f(x)
∵ f(x) = 2x² - 4x + 4
→ Find f'(x)
∵ f'(x) = 2(2)
- 4(1)
+ 0
∴ f'(x) = 4x - 4
→ Equate f'(x) by 0
∵ f'(x) = 0
∴ 4x - 4 = 0
→ Add 4 to both sides
∵ 4x - 4 + 4 = 0 + 4
∴ 4x = 4
→ Divide both sides by 4
∴ x = 1
→ The minimum value is f(1)
∵ f(1) = 2(1)² - 4(1) + 4
∴ f(1) = 2 - 4 + 4
∴ f(1) = 2
∴ The minimum value of f(x) is 2
Answer:
150 pennies were lost altogether
Step-by-step explanation:
Let the initial number of pennies owned by Dante be x pennies
Let the initial number of pennies owned by Mia be y pennies
Mathematically ;
x + y = 350 •••••••(i)
So after losing half, dante will have x/2 pennies left.
Mia lost 1/3 so she will have 2/3y left
So after all the losses, they both had equal amount of pennies
This means that;
x/2 = 2y/3
Cross multiply;
3x = 4y •••••••(ii)
Let’s solve both equations simultaneously;
From i , x = 350-y
Substitute this into equation ii
3(350-y) = 4y
1050-3y = 4y
7y = 1050
y = 1050/7
y = 150
since x = 350-y
x = 350-150 = 200
Now Dante loss x/2 = 200/2 = 100
Mia lost 1/3y = 1/3 * 150 = 50
Total pennies lost = 100 + 50 = 150
The value of the question mark I 8.
Step by step solution:
Values:
Brown frosted donut: 3
Orange frosted donut: 1/3
White frosted donut: 1
Hope this helps!! :)
Answer:
Substitution method can be used
Step-by-step explanation:
Given the system of equations
y = 2x-1 ....1
-12x + 3y = 9 ....2
The best method to use id the substitution method
Substitute equation 1 into 2;
From 2;
-12x + 3y = 9
-4x + y = 3
-4x + 2x-1 = 3
-2x -1 = 3
-2x = 3+1
-2X = 4
x = -4/2
x = -2
Substitute x = -2 into 1
y = 2x - 1
y = 2(-2)-1
y = -4-1
y = -5
Hence the solution to the system of equation is (-2, -5)
Step-by-step explanation:
if three(3) is not less than x, this means it's more than x so it'll be 3+x
