Answer:
Below.
Step-by-step explanation:
The GCF of 9 , 27 and 45 = 9.
GCF of the d terms is d^2.
So the GCF of the whole expression is 9d^2.
Factors are 9d^2( 1 - 3d^3 + 5d)
Complete question :
Members of the swim team want to wash their hair. The bathroom has less than 5600 liters of water and at most 2.5 liters of shampoo. 70L+ 60S < 5600 represents the number of long-haired members L and short-haired members S who can wash their hair with less than 5600 liters of water. 0.02L + 0.01S < or equal to 2.5 represents the number of long-haired members and short-haired members who can wash their hair with at most 2.5 liters of shampoo. Does the bathroom have enough water and shampoo for 8 long-haired members and 7 short -haired members?
Answer:
Yes , there is enough water and shampoo
Step-by-step explanation:
Given that:
Number of long and short hair member who can wash their hair with less than 5600 litres of water.
70L+ 60S < 5600
Number of long and short hair member who can wash their hair with at most 2.5 litres of shampoo
0.02L + 0.01S ≤ 2.5
To check if bathroom has enough water and shampoo for 8 long haired and 7 short haired members.
Water check:
70L+ 60S < 5600
L = 8 ; S = 7
70(8) + 60(7) < 5600
560 + 420 < 5600
980 < 5600
Inequality constraint is satisfied ; There is enough water.
Shampoo check:
0.02L + 0.01S ≤ 2.5
L = 8 ; S = 7
0.02(8) + 0.01(7) ≤ 2.5
0.16 + 0.07 ≤ 2.5
0.23 ≤ 2.5
Inequality constraint is satisfied ; There is enough shampoo
Answer: The length is 13 inches and the width is 11 inches.
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the area of a rectangle is expressed as
Area = LW
The area of the rectangle is 143 square inches. This means that
LW = 143 - - - - - - - - - - - - --1
The rectangle's length is 2 in more than its width. This means that
L = W + 2
Substituting L = W + 2 into equation 1, it becomes
W(W + 2) = 143
W² + 2W - 143 = 0
W² + 13W - 11W - 143 = 0
W(W + 13) - 11(W + 13) = 0
W + 13 = 0 or W - 11 = 0
W = - 13 or W = 11
Since the width cannot be negative, it means that W = 11
L = W + 2 = 11 + 2
L = 13
If 1 inch equals 20miles then 8 inches equals 20 x 8 = 160 miles.
