Answer:
52
Step-by-step explanation:
Alex earned 156 reward points for selling wrapping paper rolls.
Using the given equation
3r = 156
r = 156/3
r = 52
Alex sold 52 wrapping paper rolls
Answer:
It will take 25.6 years for the mass of the sample to reach 400 grams.
Step-by-step explanation:
Element X is a radioactive isotope such that every 25 years, its mass decreases by half.
This means that the amount of the substance after t years can be modeled by a function in the following format:
![A(t) = A(0)(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
In which A(0) is the initial amount.
Initial mass of a sample of Element X is 910 grams.
This means that ![A(0) = 910](https://tex.z-dn.net/?f=A%280%29%20%3D%20910)
So
![A(t) = A(0)(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![A(t) = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
How long would it be until the mass of the sample reached 400 grams?
This is t for which ![A(t) = 400](https://tex.z-dn.net/?f=A%28t%29%20%3D%20400)
So
![A(t) = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![400 = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=400%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![(0.5)^{\frac{t}{25}} = \frac{400}{910}](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%20%3D%20%5Cfrac%7B400%7D%7B910%7D)
![(0.5)^{\frac{t}{25}} = 0.43956](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%20%3D%200.43956)
![\log{(0.5)^{\frac{t}{25}}} = \log{0.43956}](https://tex.z-dn.net/?f=%5Clog%7B%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%7D%20%3D%20%5Clog%7B0.43956%7D)
![\frac{t}{25}\log{0.5} = \log{0.43956}](https://tex.z-dn.net/?f=%5Cfrac%7Bt%7D%7B25%7D%5Clog%7B0.5%7D%20%3D%20%5Clog%7B0.43956%7D)
![t = \frac{25\log{0.43956}}{\log{0.5}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B25%5Clog%7B0.43956%7D%7D%7B%5Clog%7B0.5%7D%7D)
![t = 25.6](https://tex.z-dn.net/?f=t%20%3D%2025.6)
It will take 25.6 years for the mass of the sample to reach 400 grams.
Answer:
The correct answer is;
ΔANT ≅ ΔFLE by the SIde-Side-Side (SSS) rule of congruency
Step-by-step explanation:
The given information are;
Segment TN is congruent ts segment EL
Segment TA is congruent ts segment EF
Segment AN is congruent ts segment FL
Therefore, triangle ΔANT is congruent to ΔFLE by the Side-Side-Side (SSS) rule of congruency
One of the rule used to serve as proof that two or more triangles are congruent, is the Side-Side-Side (SSS) rule of congruency. The Side-Side-Side rule of congruency states that if the dimensions of the three sides of one triangle are equal to the dimensions of the three sides of another triangle, the two triangles are congruent.
Therefore, the correct option is ΔANT ≅ ΔFLE by the Side-Side-Side (SSS) rule of congruency
Answer:
One solution
Step-by-step explanation:
Cosine is the ratio adjacent over hypotenuse.
The hypotenuse is the diagonal of 6 ft.
The adjacent side of the 60 degree angle is AC.
Therefore: