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
Answer:
No solution
Step-by-step explanation:
There is one variable. so it can't be two solutions. To the rest, we need to solve the equation.
5-2x=3+x-4-3x
5=3-4
5=-1
Impossible!!!
so no solution.
Hope this helps plz mark brainliest :D
<h2>Answer:</h2><h2>2 hours & 10 minutes
</h2><h2>Step-by-step explanation:</h2><h2>1/6 of an hour is 10 minutes. She vacuumed for 10 minutes. It took 4 times as long to wash the car so 10 * 4 = 40. She washed the car for 40 minutes. It took her twice as long to wax the car as it did for her to wash it so 40 * 2 = 80. She waxed the car for 80 minutes. 10 + 40 + 80 = 130 minutes or 2 hours and 10 minutes.
</h2>
Answer:
A = 73°
Step-by-step explanation:
A + B = 180 because of alternating interior angles
Substitute each angle
6x - 35 + 3x + 53 = 180
9x + 18 = 180
9x = 162
x = 18
Substitute A
A = 6x - 35
A = 108 - 35
A = 73
Hope this helps
Have a great day!
Answer:
1.33333333
Step-by-step explanation:
