Answer: -5/2 or 1/6
Step-by-step explanation:
I6n + 7I = 8
Therefore (6n + 7) = 8 or -8 because modulus means we're only getting it's absolute value, (it's positive value) meaning it could equal 8 or -8 before it's modulus'ed.
Therefore 6n + 7 = 8
or 6n + 7 = -8
Leaving us with:
6n = 1
6n = -15
So n = 1/6
or n = -5/2 (-2.5)
Answer:
Step-by-step explanation:
1) Rewriting for the sake of clarity:
2) To solve it, we need to turn the rational exponent equal to 1 via exponent rule of product. Multiplying 2/3 by its reciprocal 3/2 we get 1, since this is an equality we need to do it on the other side.
![(x-1)^{\frac{2}{3}}=64\\\\((x-1)^{\frac{2}{3}}]^{\frac{3}{2}}=(64)^{\frac{3}{2}}\\(x-1)=\sqrt{64^{3}}\\x-1+1=512+1\\x=513](https://tex.z-dn.net/?f=%28x-1%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D64%5C%5C%5C%5C%28%28x-1%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5D%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%3D%2864%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5C%5C%28x-1%29%3D%5Csqrt%7B64%5E%7B3%7D%7D%5C%5Cx-1%2B1%3D512%2B1%5C%5Cx%3D513)
Short Answer: A
Remark
The second cut is going to have the same slope as the original line. The lines are parallel.
Step One
You need to find the slope. That is the main part of this problem. You can pick any 2 points on the graph to do that.
<em>Point one</em>
(- 11, 10) That point is on the upper left of the line
<em>Point Two</em>
The y intercept is a handy point in this question. It is right on the y axis. Each square counts as 2, so it is at (0,6)
<em>Formula</em>
slope = m = (y2 - y1) / (x2 - x1)
<em>Givens</em>
y2 = 10
y1 = 6
x2 = -12 Each square counts as 2 in the x direction.
x1 = 0
<u>Substitute and solve.</u>
m = (10 - 6) / (-12 - 0)
m = 4/ - 12
m = - 1/3
Step Two
Find the y intercept of the new line using the given point.
So far what we have is
y = (-1/3)x + b
The point used for the second line is (0,-2)
-2 = (-1/3)*0 + b
b = - 2
Answer
The second line is
y = (-1/3)x - 2
Volume is a three-dimensional scalar quantity. The volume of the water that Marry should pour into the vase is 241.28 cubic inches.
<h3>What is volume?</h3>
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the radius of the flower vase is 4 inches, while the height of the vase is 6 inches, therefore, the total volume of the vase is,
Volume = πR²×H = π× 4²×6 = 301.6 in³
Since the volume of the vase is 301.6 in³, but the store has told her to fill the vase 4/5 of its capacity, therefore, the volume of water Marry should pour is,
Volume of water = (4/5) × 301.6 in³ = 241.28 cubic inches
Hence, the volume of the water that Marry should pour into the vase is 241.28 cubic inches.
Learn more about Volume:
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1/3 can be written as 33.33333333333% as well as other forms so the answer is 1/3
