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
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Answer:
x = 4/3
y = 1/3
Step-by-step explanation:
System of equations! This is set up really well to make the second equation equal x then substitute.
x - y = 1
x = 1 + y
and then our substitution:
2 (1+y) + y = 3
and solve:
2 + 2y + y = 3
3y + 2 = 3
3y = 1
y = 1/3
And now we can substitute that value into one of our equations:
x - (1/3) = 1
x = 4/3
Next we should check by substituting these values into both of our equations:
2 (4/3) + (1/3) = 3
9 / 3 does equal 3 !
(4/3) - (1/3) does equal 1 !
Therefore, x = 4/3 , and y = 1/3
Hey there!
D is the answer.
I was thinking it might be B but no one said the lines crossed each other.
Hope this helps, Jesus loves you!
Ts temperature as a function of time is given by T(t)=a(1-e^kt)+b
the values of a and b area = 50 Fb = 350 F
this is very evident to equation the b is the initial temperatre of the oven which is 350 F
and also a is the initial temperature of the potato because it is the term multiplied by the exponent term which will indicate the temperature increasse of the potato
