P = 2L +2w = 58 ----> L+w = 29 ----> L = 29-w
A = L*w = 204
Now substitute "29-w" for L in Area equation:
(29-w)w = 204
This gives a quadratic
w^2 - 29w + 204 = 0
Use quadratic formula:
![w = \frac{29 \pm \sqrt{29^2 -4(1)(204)}}{2} = \frac{29 \pm 5}{2}](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B29%20%5Cpm%20%5Csqrt%7B29%5E2%20-4%281%29%28204%29%7D%7D%7B2%7D%20%3D%20%5Cfrac%7B29%20%5Cpm%205%7D%7B2%7D)
w = 12, w = 17
Either value will work since L=29-w, the other number becomes length.
Therefore the final dimensions of the rectangle are 12 by 17.
100,000
0 is in the ten thousands place, 2 in the thousands. If the number to the right of the placeholder of the number you're rounding is five or more, you round up. Otherwise, you round down.
Answer:
the slope is -7
Step-by-step explanation:
![\frac{-2-5}{3-2} =\frac{-7}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B-2-5%7D%7B3-2%7D%20%3D%5Cfrac%7B-7%7D%7B1%7D)
Answer:
<h3>The answer is option C</h3>
Step-by-step explanation:
2√24 + 5√54
To combine the radicals first make sure the radicals have the same square root
That's
<h3>
<u>For 2√24</u></h3>
<h3>
![2 \sqrt{24} = 2 \sqrt{4 \times 6} = 2 \times 2 \sqrt{6}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B24%7D%20%20%3D%202%20%5Csqrt%7B4%20%5Ctimes%206%7D%20%20%3D%202%20%5Ctimes%202%20%5Csqrt%7B6%7D%20)
</h3><h3>
![= 4 \sqrt{6}](https://tex.z-dn.net/?f=%20%3D%204%20%5Csqrt%7B6%7D%20)
</h3><h3 /><h3>
<u>For 9√54</u></h3>
<h3>
![5 \sqrt{54} = 5 \sqrt{9 \times 6} = 5 \times \sqrt{9} \times \sqrt{6}](https://tex.z-dn.net/?f=5%20%5Csqrt%7B54%7D%20%20%3D%205%20%5Csqrt%7B9%20%20%5Ctimes%206%7D%20%20%3D%205%20%5Ctimes%20%20%5Csqrt%7B9%7D%20%20%5Ctimes%20%20%5Csqrt%7B6%7D%20)
</h3><h3>
![= 5 \times 3 \times \sqrt{6}](https://tex.z-dn.net/?f=%20%3D%205%20%5Ctimes%203%20%5Ctimes%20%20%5Csqrt%7B6%7D%20)
</h3><h3>
![= 15 \sqrt{6}](https://tex.z-dn.net/?f=%20%3D%2015%20%5Csqrt%7B6%7D%20)
</h3><h3 />
Since they have the same square root we can combine them
That's
<h3>
![4 \sqrt{6} + 15 \sqrt{6} = (4 + 15) \sqrt{6}](https://tex.z-dn.net/?f=4%20%5Csqrt%7B6%7D%20%20%2B%2015%20%5Csqrt%7B6%7D%20%20%3D%20%284%20%2B%2015%29%20%5Csqrt%7B6%7D%20)
</h3>
We have the final answer as
<h2>
![19 \sqrt{6}](https://tex.z-dn.net/?f=19%20%5Csqrt%7B6%7D%20)
</h2>
Hope this helps you
The answer is below
we're given
![y = \frac{7}{5} x + 6](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B7%7D%7B5%7D%20x%20%2B%206)
we need to convert to point slope form with our slope and point given
point slope form is
![y - y1 = m(x - x1)](https://tex.z-dn.net/?f=%20y%20-%20y1%20%3D%20m%28x%20-%20x1%29)
so we fill in slope and our point
![y + 6 = \frac{7}{5} (x - 2)](https://tex.z-dn.net/?f=y%20%20%2B%206%20%3D%20%20%5Cfrac%7B7%7D%7B5%7D%20%28x%20-%202%29)
we simplify the left side and get
![y + 6 = \frac{7}{5} x - \frac{14}{5}](https://tex.z-dn.net/?f=y%20%2B%206%20%3D%20%20%5Cfrac%7B7%7D%7B5%7D%20x%20-%20%20%5Cfrac%7B14%7D%7B5%7D%20)
then we subtract 6 from the left and get
this as our final answer