False is the answer i believe tried my best with this one >.< hopes this helps
Half of 20 the line is in the middle of the triangle
Let P=Perm cost
Let H = Haircut cost
Let L = Lunch cost
Perm costs twice as much as haircut so.. P = 2H
L = 5
H + P + L = 68 the total cost is $68
H + 2H + 5 = 68 since P = 2H and L=5
3H + 5 = 68
3H =63
H = 63/3
H = 21
A Haircut is $21
Perm = 2H = 2(21) = $42
<span>. 6 times a number is 6x, so quotient of 6x and 16 is the same as saying 6x16
</span>So your answer is:=<span>96<span>x</span></span>
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
