The answer is 1, the first option
Answer:
88
Step-by-step explanation:
44 / 0.5 = 44*2 = 88
1.) a>10
2.) a<3.5
How I got it: 1.) Subtract 3 from both sides, leaving -2a<10.
2.) Divide by -2 from both sides, remember to flip the inequality sign when dealing with negatives. This leaves you with a>10.
For number 2.) I divided both sides by 5, leaving a<3.5, though this answer may be wrong.
Answer:
It will take about 35.439 years to triple.
Step-by-step explanation:
Recall the formula for continuously compounded interest:
![A=P\,e^{r*t}](https://tex.z-dn.net/?f=A%3DP%5C%2Ce%5E%7Br%2At%7D)
where "A" is the total (accrued or future) accumulated value, "r" is the rate (in our case 0.031 which is the decimal form of 3.1%), "P" is the principal, and "t" is the time in years (our unknown).
Notice also that even that the final amount we want to get is three times $48,000. So our formula becomes:
![3\,*\,48,000=\,48,000\,\,e^{0.031\,*t}\\\frac{3\,*\,48,000}{48,000} =e^{0.031*t}\\3=e^{0.031*t}](https://tex.z-dn.net/?f=3%5C%2C%2A%5C%2C48%2C000%3D%5C%2C48%2C000%5C%2C%5C%2Ce%5E%7B0.031%5C%2C%2At%7D%5C%5C%5Cfrac%7B3%5C%2C%2A%5C%2C48%2C000%7D%7B48%2C000%7D%20%3De%5E%7B0.031%2At%7D%5C%5C3%3De%5E%7B0.031%2At%7D)
Now,in order to solve for "t" (which is in the exponent, we use logarithms:
![ln(3)=0.031\,*\,t\\t=\frac{ln(3)}{0.031} \\t=35.439 \,\,years](https://tex.z-dn.net/?f=ln%283%29%3D0.031%5C%2C%2A%5C%2Ct%5C%5Ct%3D%5Cfrac%7Bln%283%29%7D%7B0.031%7D%20%5C%5Ct%3D35.439%20%5C%2C%5C%2Cyears)
Answer:
They are congruent by SAS
Step-by-step explanation:
MQ=PN
The angles with markings also go together
The line right in the middle is the second side because of the reflexive property