Problem: (3x-5)+(-4x+1)
Get rid of the parentheses. You distribute 1 to the sets of parentheses.
This turns to: 3x-5-4x+1
Solve and combine like terms.
3x-5-4x+1
-x-5+1
-x-4
Let (15+x) and (22+x) be the future ages of the brothers
15+x+22+x= 408
Collect like terms
37+2x=408
Move 37 to the other side as a negative number
2x=371
Divide both sides by 2
371/2 is 185.5
So, after 185.5 years, their ages will add up to be 408
Answer:
Dimensions of the poster
Width 29.10 cm
Height 38.80 cm
A(min) = 1129.08 cm²
Step-by-step explanation:
Printed area = 390 cm² = Ap
Lets call x and y dimensions of printed area
x width
y height
Then Ap = x*y and
y = Ap/x ⇒ y = 390/x
Then total area of the poster is:
A(t) = ( x + 12 ) * ( y + 16 ) and y = 390/x
A as a function of x
A(x) = ( x + 12 ) * ( 390/x + 16 ) ⇒ A(x) = 390 + 16x + 4680/x + 192
A(x) = 582 + 16x + 4680/x (1)
Taking derivatives
A´(x) = 16 - (4680/x²) ⇒ A´(x) = 0
[ 16x² -4680] /x² = 0 16x²- 4680 = 0 ⇒ x² = 4680/16
x = 17.10 cm and y = 390/x y = 390/17.10 y = 22.80 cm
A(t) = ( 17.10 + 12 ) * ( 22.80 + 16 )
A(t) = 29.10 * 38.80
A(t) = 1129.08 cm²
If we substitute in equation (1) the value of x ( 17.10) we see A(x) > 0
Then there is a minimun at the point x = 17.10
Answer:
Its gonna be in the same spot but just on the left
Step-by-step explanation:
