46 inches
(2x10 + 2x13 = 46)
Answer:
1.6$ (1.7$ rounded) for ceramic vases and 3$ for glass vases
Step-by-step explanation:
Assignment: ![\bold{Simplify \ Expression: \ 80g+30h=10\left(g+h\right)}](https://tex.z-dn.net/?f=%5Cbold%7BSimplify%20%5C%20Expression%3A%20%5C%2080g%2B30h%3D10%5Cleft%28g%2Bh%5Cright%29%7D)
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Answer: ![\boxed{\bold{g=-\frac{2h}{7}}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbold%7Bg%3D-%5Cfrac%7B2h%7D%7B7%7D%7D%7D)
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Explanation: ![\downarrow\downarrow\downarrow](https://tex.z-dn.net/?f=%5Cdownarrow%5Cdownarrow%5Cdownarrow)
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[ Step One ] Expand ![\bold{10\left(g+h\right): \ 10g+10h}](https://tex.z-dn.net/?f=%5Cbold%7B10%5Cleft%28g%2Bh%5Cright%29%3A%20%5C%2010g%2B10h%7D)
![\bold{80g+30h=10g+10h}](https://tex.z-dn.net/?f=%5Cbold%7B80g%2B30h%3D10g%2B10h%7D)
[ Step Two ] Subtract 30h From Both Sides
![\bold{80g+30h-30h=10g+10h-30h}](https://tex.z-dn.net/?f=%5Cbold%7B80g%2B30h-30h%3D10g%2B10h-30h%7D)
[ Step Three ] Simplify
![\bold{80g=10g-20h}](https://tex.z-dn.net/?f=%5Cbold%7B80g%3D10g-20h%7D)
[ Step Four ] Subtract 10g From Both Sides
![\bold{80g-10g=10g-20h-10g}](https://tex.z-dn.net/?f=%5Cbold%7B80g-10g%3D10g-20h-10g%7D)
[ Step Five ] Simplify
![\bold{70g=-20h}](https://tex.z-dn.net/?f=%5Cbold%7B70g%3D-20h%7D)
[ Step Six ] Divide Both Sides By 70
![\bold{\frac{70g}{70}=\frac{-20h}{70}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cfrac%7B70g%7D%7B70%7D%3D%5Cfrac%7B-20h%7D%7B70%7D%7D)
[ Step Seven ] Simplify
![\bold{g=-\frac{2h}{7}}](https://tex.z-dn.net/?f=%5Cbold%7Bg%3D-%5Cfrac%7B2h%7D%7B7%7D%7D)
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Answer:
![y = x +7](https://tex.z-dn.net/?f=y%20%3D%20x%20%2B7)
Step-by-step explanation:
Given
![Point\ (x_1,y_1) = (4,11)](https://tex.z-dn.net/?f=Point%5C%20%28x_1%2Cy_1%29%20%3D%20%284%2C11%29)
Perpendicular to ![y = -x + 14](https://tex.z-dn.net/?f=y%20%3D%20-x%20%2B%2014)
Required
Determine the line equation
An equation has the form
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where
![m = slope](https://tex.z-dn.net/?f=m%20%3D%20slope)
By comparison with ![y = -x + 14](https://tex.z-dn.net/?f=y%20%3D%20-x%20%2B%2014)
![m = -1](https://tex.z-dn.net/?f=m%20%3D%20-1)
Because the line is perpendicular to
, the following relationship exists
i.e. the condition for perpendicularity
Where m1 is the slope of the equation that passes through ![Point\ (x_1,y_1) = (4,11)](https://tex.z-dn.net/?f=Point%5C%20%28x_1%2Cy_1%29%20%3D%20%284%2C11%29)
So, we have:
![m_1 = \frac{-1}{-1}](https://tex.z-dn.net/?f=m_1%20%3D%20%5Cfrac%7B-1%7D%7B-1%7D)
![m_1 = 1](https://tex.z-dn.net/?f=m_1%20%3D%201)
The line equation is then calculated using:
![y - y_1 = m_1(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m_1%28x%20-%20x_1%29)
Where
![m_1 = 1](https://tex.z-dn.net/?f=m_1%20%3D%201)
![Point\ (x_1,y_1) = (4,11)](https://tex.z-dn.net/?f=Point%5C%20%28x_1%2Cy_1%29%20%3D%20%284%2C11%29)
So, we have:
![y - 11 = 1(x - 4)](https://tex.z-dn.net/?f=y%20-%2011%20%3D%201%28x%20-%204%29)
![y - 11 = x - 4](https://tex.z-dn.net/?f=y%20-%2011%20%3D%20x%20-%204)
Add 11 to both sides
![y - 11+11 = x - 4+11](https://tex.z-dn.net/?f=y%20-%2011%2B11%20%3D%20x%20-%204%2B11)
![y = x - 4+11](https://tex.z-dn.net/?f=y%20%3D%20x%20-%204%2B11)
![y = x +7](https://tex.z-dn.net/?f=y%20%3D%20x%20%2B7)
<em>The B, C and D parts of your question are not clear.</em>
<em>Apply the same steps used in (a) above and you'll get your answers</em>
dustin is correct because 8*-1 is 8 beacse its diffent and u soppse to sub