Answer:
1) A because of vertical angle theorem (VAT), which means that b=37 degrees
2) C because a right angle is= to 90 degrees. Take away 23, you get 67 degrees
3) B because the image shows a full angle, which is equal to 360 degrees. Take away 207 and 58, you get 95 degrees
4) D because a right angle is= to 90 degrees. Take away 44, you get 46 degrees
5) A because a right angle is=to 90 degrees. Take away 58, you get 32 degrees
Answer: 2s + 1
Explanation:
1) Given expression: 6s² - 7s- 5 = (3s - 5) ( )
2) The missing factor ( ) is such that when it is multiplied by (3s - 5) the product is 6s² - 7s- 5.
3) Since the first term of the first factor starts with 3s, the first term of the second factor shall be 2s (since they have to yield 6s²). Then, you can write:
6s² - 7s- 5 = (3s - 5) (2s + )
4) The second term of the missing factor is positive because the product (+)(-) = (-) which is the sign of the third term of the polynomial.
5) The second term is such that when multiplied by - 5 is equal to the last term of the polynomial (also - 5), so this second terms is +1.
And you get: 6s² - 7s- 5 = (3s - 5) (2s + 1)
6) You can expand, using distributive property to confirm the result:
(3s - 5) (2s + 1 ) = (3s)(2s) + (3s)(1) - (5)(2s) -(5)(1) = 6s² - 7s- 5, which confirms the result.
Answer:
![=13ab](https://tex.z-dn.net/?f=%3D13ab)
Step-by-step explanation:
![5ab+9ab-ab\\\mathrm{Add\:similar\:elements:}\:5ab+9ab-ab=13ab\\=13ab](https://tex.z-dn.net/?f=5ab%2B9ab-ab%5C%5C%5Cmathrm%7BAdd%5C%3Asimilar%5C%3Aelements%3A%7D%5C%3A5ab%2B9ab-ab%3D13ab%5C%5C%3D13ab)
Answer:
The population will be 39400 in approximately 17 years
Step-by-step explanation:
The increase in population after t years is given by the formula
![P_t = P_0(1+r)^t](https://tex.z-dn.net/?f=P_t%20%3D%20P_0%281%2Br%29%5Et)
Here
P_0 is the initial population
r is the growth rate and t is time in years
So far we know,
P_0 = 20000
r = 4%
P_t = 39400
Putting the values in the formula
![39400 = 20000(1+0.04)^t\\39400 =20000(1.04)^t\\\frac{39400}{20000} = (1.04)^t\\1.97 = (1.04)^t](https://tex.z-dn.net/?f=39400%20%3D%2020000%281%2B0.04%29%5Et%5C%5C39400%20%3D20000%281.04%29%5Et%5C%5C%5Cfrac%7B39400%7D%7B20000%7D%20%3D%20%281.04%29%5Et%5C%5C1.97%20%3D%20%281.04%29%5Et)
Taking natural log on both sides
![ln |(1.04)^t| = ln |1.97|\\t\ ln\ |1.04| = ln\ |1.97|\\t = \frac{ln\ 1.97}{ln\ 1.04}\\t = 17.287\\t \approx 17](https://tex.z-dn.net/?f=ln%20%7C%281.04%29%5Et%7C%20%3D%20ln%20%7C1.97%7C%5C%5Ct%5C%20ln%5C%20%7C1.04%7C%20%3D%20ln%5C%20%7C1.97%7C%5C%5Ct%20%3D%20%5Cfrac%7Bln%5C%201.97%7D%7Bln%5C%201.04%7D%5C%5Ct%20%3D%2017.287%5C%5Ct%20%5Capprox%2017)
Hence,
The population will be 39400 in approximately 17 years