Answer:
x = 20
Step-by-step explanation:
The two angles are verticals angles and vertical angles are equal
7x -99 = 2x+1
Subtract 2x from each side
7x-99-2x =2x+1-2x
5x-99 =1
Add 99 to each side
5x-99+99 = 1+99
5x =100
Divide each side by 5
5x/5 =100/5
x = 20
Answer:
on product side there will also 6 carbon atom
Find a common denominator for 5 and 3 and go on from there
Answer:
4492 years (to the nearest year)
Step-by-step explanation:
The quantity of radium left after a time t can be modeled using the equation below:
![Q(t)=Q_0(\frac{1}{2})^{\frac{t}{t_{1/2}} }\\Q_0 =$Initial Amount$\\t_{1/2}=$Half-Life of the Substance$\\t=$Time elapsed$](https://tex.z-dn.net/?f=Q%28t%29%3DQ_0%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7Bt_%7B1%2F2%7D%7D%20%7D%5C%5CQ_0%20%3D%24Initial%20Amount%24%5C%5Ct_%7B1%2F2%7D%3D%24Half-Life%20of%20the%20Substance%24%5C%5Ct%3D%24Time%20elapsed%24)
Given that:
![Q_0 =70mg\\t_{1/2}=1600 years](https://tex.z-dn.net/?f=Q_0%20%3D70mg%5C%5Ct_%7B1%2F2%7D%3D1600%20years)
The amount of radium left after a t years is:
![Q(t)=70(\frac{1}{2})^{\frac{t}{1600} }](https://tex.z-dn.net/?f=Q%28t%29%3D70%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B1600%7D%20%7D)
If the quantity left is 10 mg, then:
![10=70(\frac{1}{2})^{\frac{t}{1600} }\\\frac{10}{70} =(\frac{1}{2})^{\frac{t}{1600} }\\](https://tex.z-dn.net/?f=10%3D70%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B1600%7D%20%7D%5C%5C%5Cfrac%7B10%7D%7B70%7D%20%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B1600%7D%20%7D%5C%5C)
Changing to logarithm form
![Log_{0.5}\frac{10}{70}=\frac{t}{1600} \\\frac{Log(10/70)}{Log 0.5} =\frac{t}{1600}\\t=\frac{Log(10/70)}{Log 0.5} X 1600\\=4491.8 \approx 4492 \:years\text{ (to the nearest year)}](https://tex.z-dn.net/?f=Log_%7B0.5%7D%5Cfrac%7B10%7D%7B70%7D%3D%5Cfrac%7Bt%7D%7B1600%7D%20%20%5C%5C%5Cfrac%7BLog%2810%2F70%29%7D%7BLog%200.5%7D%20%3D%5Cfrac%7Bt%7D%7B1600%7D%5C%5Ct%3D%5Cfrac%7BLog%2810%2F70%29%7D%7BLog%200.5%7D%20X%201600%5C%5C%3D4491.8%20%5Capprox%204492%20%5C%3Ayears%5Ctext%7B%20%28to%20the%20nearest%20year%29%7D)
In 4492 years, 10 mg of Radium will be left.
Answer:
Step-by-step explanation:
The following points (coordinates) lie on a straight line with slope 3:
(1, 0), (2, 3), (3, 6), (4, 9) ... and so on
So the linear function is y = 3x + b, where b is the y-intercept.