Answer:
The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Step-by-step explanation:
Given
Rectangle Pyramid
Base Length = 3x + 1
Base Width = x
Height = 12
Volume = 96
Required
Dimension of the base of the pyramid
Given that the volume of the pyramid is ⅓ of the base area * the height.
This is represented mathematical as
Volume = ⅓ * base area * height.
Where
Base area = width * length
Base area = (3x + 1) * x
Base area = 3x² + x.
So,
Volume becomes
Volume = ⅓ * (3x² + x) * 12.
Volume = (3x² + x) * 4
Substitute 96 for volume
96 = (3x² + x) * 4
Divide both sides by 4
96/4 = (3x² + x) * 4/4
24 = 3x² + x
Subtract 24 fr both sides
24 - 24 = 3x² + x - 24
0 = 3x² + x - 24
3x² + x - 24 = 0
Expand
3x² + 9x - 8x - 24 = 0
Factorize
3x(x + 3) - 8(x + 3) = 0
(3x - 8)(x + 3) = 0
3x - 8 = 0 or x + 3 = 0
3x = 8 or x = -3
x = 8/3 or x = -3
Recall that
Length = 3x + 1
Width = x
For any of the above expression, x can't be less than 0; so, x = -3 can't be considered.
Substitute x = 8/3
Length = 3x + 1
Length = 3(8/3) + 1
Length = 8 + 1
Length = 9
Width = x
Width = 8/3
Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
There are 52 weeks in a year and if she gets paid every two weeks then divide 52 by 2 to get 26 so she would get paid 26 times a year so divide her annual salary by 26 to get $1,346.15 every other week. So her biweekly salary is $1,346.15.
Answer:
4(x) + 4(2)
Step-by-step explanation:
4(x+2) = 4(x) + 4(2)
Distribution property
Answer:
SU=5 the first option.
Step-by-step explanation:
I did the assignment.
The weight of a 170 cm steel bar will be 5 Kg
Step-by-step explanation:
Derek uses a 136 cm flat steel bar that weighs 4 kg to make rack in the garage.
1 kg = 1000 gm
So the weight of 1 cm steel bar will be 
kg
Weight of 1 cm bar = 
gm
Let the weight of a 170 cm steel bar will be 
× 
gm
⇒
× 
gm
⇒ 5000 gm
⇒5 kg
Hence, the weight of a 170 cm steel bar will be 5 Kg
