Answer:
Step-by-step explanation:
If we let x = the amount of 5% solution and y = the amount of pure alcohol, we can set up that
.05x+y is the amount of alcohol in our resulting mixture, and x+y is the total amount in our resulting mixture (which we know is 380)
so we also know that:
(.05x+y)/380 = .6
If we simplify this we come up with:
.05x+y=228
and we know x+y=380
If we solve this as a system of equations, we will find that:
x=160 ml
y=220 ml
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
<h2><em>If you put and label the three points in a line, you will see that RS + ST = RT.
</em></h2><h2><em>
</em></h2><h2><em>Then you only need to substitue with the expressions given for RS and ST to find RT.
</em></h2><h2><em>
</em></h2><h2><em>RT = x +1 + 2x - 2 = 3x - 1
</em></h2><h2><em>
</em></h2><h2><em>Also, RT = 5x - 5
</em></h2><h2><em>
</em></h2><h2><em>Then, 3x - 1 = 5x - 5
</em></h2><h2><em>
</em></h2><h2><em>5x - 3x = 5 - 1
</em></h2><h2><em>
</em></h2><h2><em>2x = 4
</em></h2><h2><em>
</em></h2><h2><em>x = 4/2 = 2
</em></h2><h2><em>
</em></h2><h2><u><em>X=2</em></u></h2>
Answer:
6x+8
Step-by-step explanation:
2(x+4)+4x
2x+8+4x
6x+8
Answer:
D: 0.05
Step-by-step explanation:
Since the question says UNLIKELY, it would be the smallest number, which is 0.05 in this case.
