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:
C: 1.5
Step-by-step explanation:
For point D, the y value goes from 4 -> 6. This means that 4x = 6 , 
.
For point F, both values (x and y) are multiplied by 1.5.
the answer for this would be 10,946,988.
Answer:
20x-12
Step-by-step explanation:
Given:
7(3x−1)−(x+5)
Step 1: Distribute the Negative Sign:
=7(3x−1)+−1(x+5)
=7(3x−1)+−1x+(−1)(5)
=7(3x−1)+−x+−5
Step 2: Distribute:
=(7)(3x)+(7)(−1)+−x+−5
=21x+−7+−x+−5
Step 3: Combine
=21x+−7+−x+−5
=(21x+−x)+(−7+−5)
=20x+−12
Answer : $18.75
Bethany is paid time-and-a-half for each hour she works above her normal 40 hours each week. Last week, Bethany worked 44 hours and her gross pay was $575.
Total hours worked = 44 hours
Normal 40 hours + 4 hours extra
Let x be the amount earned for 1 hour for regular 40 hours
1.5x be the amount earned for extra hours
40 (amount earned for normal hours ) + 4(amount for extra hours ) = gross pay
40x + 4(1.5x) = 575
40x + 6x = 575
46 x = 575
Now divide both sides by 46
x = 12.5
1.5x is the amount earned for extra hours
1.5 * 12.5 = 18.75
Bethany earn for each hour of overtime she worked is $18.75
