Answer:
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Step-by-step explanation:
![\boxed{slope = \frac{y1 - y2}{x1- x2} }](https://tex.z-dn.net/?f=%5Cboxed%7Bslope%20%3D%20%20%5Cfrac%7By1%20-%20y2%7D%7Bx1-%20x2%7D%20%7D)
☆ (x₁, y₁) is the 1st coordinate and (x₂, y₂) is the 2nd coordinate.
Slope of the line
![= \frac{ - 2 - ( - 10)}{ - 1 - ( - 1)}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B%20-%202%20-%20%28%20-%2010%29%7D%7B%20-%201%20-%20%28%20-%201%29%7D%20)
![= \frac{8}{0}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B8%7D%7B0%7D%20)
(undefined)
Notice that the 2 points have the same x-coordinate of -1, which means that the line is a vertical line. Vertical lines have an undefined slope.
The amount of substance left of a radioactive element of half life,
![t_{\frac{1}{2}}](https://tex.z-dn.net/?f=t_%7B%5Cfrac%7B1%7D%7B2%7D%7D)
after a time, t, is given by:
![N(t)=N_0\left( \frac{1}{2} \right)^ \frac{t}{t_{ \frac{1}{2} }}](https://tex.z-dn.net/?f=N%28t%29%3DN_0%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5E%20%5Cfrac%7Bt%7D%7Bt_%7B%20%20%5Cfrac%7B1%7D%7B2%7D%20%7D%7D)
Given that <span>potassium-40 has a half life of approximately 1.25 billion
years.
The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:
![0.1=100\left( \frac{1}{2} \right)^ \frac{t}{1.25}} \\ \\ \Rightarrow\left( \frac{1}{2} \right)^ \frac{t}{1.25}}=0.001 \\ \\ \Rightarrow\frac{t}{1.25}\ln\left( \frac{1}{2} \right)=\ln(0.001) \\ \\ \Rightarrow \frac{t}{1.25}= \frac{\ln(0.001)}{\ln\left( \frac{1}{2} \right)} =9.966 \\ \\ t=9.966(1.25)=12.5](https://tex.z-dn.net/?f=0.1%3D100%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5E%20%5Cfrac%7Bt%7D%7B1.25%7D%7D%20%5C%5C%20%20%5C%5C%20%5CRightarrow%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5E%20%5Cfrac%7Bt%7D%7B1.25%7D%7D%3D0.001%20%5C%5C%20%20%5C%5C%20%5CRightarrow%5Cfrac%7Bt%7D%7B1.25%7D%5Cln%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%3D%5Cln%280.001%29%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cfrac%7Bt%7D%7B1.25%7D%3D%20%5Cfrac%7B%5Cln%280.001%29%7D%7B%5Cln%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%7D%20%3D9.966%20%5C%5C%20%20%5C%5C%20t%3D9.966%281.25%29%3D12.5)
Therefore, </span><span>the maximum age of a fossil that we could date using 40k is
12.5 billion years.</span>
X+3 and y=5
Let’s start with finding X
5x+3y=30
5x+3(5x-10)=30
20x-30=30(simplified)
20x-30+30=30+30(+30 to each side)
20x=60(divide by 20)
20x/20 60/20
X=3
Now to Y
Y=5x-10
Y=(5)(3)-10
Y=5 (simplified)
The answer is 1 + 4 = 5 + 4= 9 + 4 = 13 + 4 = 17 + 4 = 21 + 4 = 25