The common factor is 3.
You would write it out as...
3(5x-4)
B
Step-by-step explanation:
because the figure is based on the graphic law
![VWX\cong KLJ](https://tex.z-dn.net/?f=VWX%5Ccong%20KLJ)
means that the triangles are congruent, that is exactly identical.
The order of letters is very important. Form the given congruence we can write the following ratio:
![\frac{VW}{KL} = \frac{WX}{LJ} = \frac{VX}{KJ} =1](https://tex.z-dn.net/?f=%20%5Cfrac%7BVW%7D%7BKL%7D%20%3D%20%5Cfrac%7BWX%7D%7BLJ%7D%20%3D%20%5Cfrac%7BVX%7D%7BKJ%7D%20%3D1)
(notice that we do not mix the order: the first 2 letters of VWX are compared to the first 2 letters of KLJ and so on)
the ratio is one because the corresponding sides are equal.
![\frac{VW}{KL}=1\\\\ \frac{2z-1}{z+2}=1\\\\2z-1=z+2\\\\2z-z=2+1\\\\z=3](https://tex.z-dn.net/?f=%5Cfrac%7BVW%7D%7BKL%7D%3D1%5C%5C%5C%5C%20%5Cfrac%7B2z-1%7D%7Bz%2B2%7D%3D1%5C%5C%5C%5C2z-1%3Dz%2B2%5C%5C%5C%5C2z-z%3D2%2B1%5C%5C%5C%5Cz%3D3%20)
![|VW|=2z-1=2.3-1=6-1=5](https://tex.z-dn.net/?f=%7CVW%7C%3D2z-1%3D2.3-1%3D6-1%3D5)
Answer: 5 units
Answer:
<em>The probability that the second ball is red is 71%</em>
Step-by-step explanation:
<u>Probabilities</u>
We know there are 5 red balls and 2 green balls. Let's analyze what can happen when two balls are drawn in sequence (no reposition).
The first ball can be red (R) or green (G). The probability that it's red is computed by
![\displaystyle P(R)=\frac{5}{7}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28R%29%3D%5Cfrac%7B5%7D%7B7%7D)
The probability is's green is computed by
![\displaystyle P(G)=\frac{2}{7}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28G%29%3D%5Cfrac%7B2%7D%7B7%7D)
If we have drawn a red ball, there are only 4 of them out of 6 in the urn, so the probability to draw a second red ball is
![\displaystyle P(RR)=\frac{5}{7}\cdot \frac{4}{6}=\frac{10}{21}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28RR%29%3D%5Cfrac%7B5%7D%7B7%7D%5Ccdot%20%5Cfrac%7B4%7D%7B6%7D%3D%5Cfrac%7B10%7D%7B21%7D)
If we have drawn a green ball, there are still 5 red balls out of 6 in the urn, so the probability to draw a red ball now is
![\displaystyle P(GR)=\frac{2}{7}\cdot \frac{5}{6}=\frac{5}{21}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28GR%29%3D%5Cfrac%7B2%7D%7B7%7D%5Ccdot%20%5Cfrac%7B5%7D%7B6%7D%3D%5Cfrac%7B5%7D%7B21%7D)
The total probability of the second ball being red is
![\displaystyle P(XR)=\frac{10}{21}+\frac{5}{21}=\frac{5}{7}=0.71](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28XR%29%3D%5Cfrac%7B10%7D%7B21%7D%2B%5Cfrac%7B5%7D%7B21%7D%3D%5Cfrac%7B5%7D%7B7%7D%3D0.71)
The probability that the second ball is red is 71%
Answer:
232
Step-by-step explanation: