Answer:
364
Step-by-step explanation:
2x2x7x13
The prime factorization is just the factors of a number.
To find the number, multiply the numbers together
2*2 = 4
4*7 = 28
28*13 = 364
Answer:
70
Step-by-step explanation:
The angle not marked in the top triangle is 40 degrees since it is an isosceles triangle. That makes the angle opposite it in the other triangle 40 degrees since they are vertical angles and vertical angles are equal.
The bottom triangle has 3 angles that sum to 180 degrees, The other angle not marked is also y since it is an isosceles triangle.
40 + y +y = 180
Subtract 40 from each side and combine like terms
40-40 +2y = 180-40
2y = 140
Divide by 2
2y/2 = 140/2
y = 70
Answer:
Step-by-step explanation:
(9-3)*912 = 6 * 912
= 5472
= 9* 608
Answer:
50 feet
Step-by-step explanation:
We have to find the perimeter of the fence surrounding the garden.
2l+2w
2(15) + 2(10)
30 + 20
= 50
50 feet will be needed.
Answer:
![t=-20ln\left(\dfrac{1}{3}\right)](https://tex.z-dn.net/?f=t%3D-20ln%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29)
Step-by-step explanation:
The relationship between A, the area of the glacier in square kilometers, and t, the number of years the glacier has been melting, is modeled by the equation.:
![A=45e^{-0.05t}](https://tex.z-dn.net/?f=A%3D45e%5E%7B-0.05t%7D)
We want to determine the value of t for which the area, A(t)=15 square kilometers.
![15=45e^{-0.05t}\\$Divide both sides by 45\\\dfrac{15}{45} =\dfrac{45e^{-0.05t}}{45}\\\dfrac{1}{3}=e^{-0.05t}\\$Take the natural logarithm of both sides\\ln\left(\dfrac{1}{3}\right)=ln\left(e^{-0.05t}\right)\\ln\left(\dfrac{1}{3}\right)=-0.05t\\$Divide both sides by -0.05$\\t=-\dfrac{ln\left(\dfrac{1}{3}\right)}{0.05} \\=-\dfrac{ln\left(\dfrac{1}{3}\right)}{0.05}\\t=-20ln\left(\dfrac{1}{3}\right)](https://tex.z-dn.net/?f=15%3D45e%5E%7B-0.05t%7D%5C%5C%24Divide%20both%20sides%20by%2045%5C%5C%5Cdfrac%7B15%7D%7B45%7D%20%3D%5Cdfrac%7B45e%5E%7B-0.05t%7D%7D%7B45%7D%5C%5C%5Cdfrac%7B1%7D%7B3%7D%3De%5E%7B-0.05t%7D%5C%5C%24Take%20the%20natural%20logarithm%20of%20both%20sides%5C%5Cln%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%3Dln%5Cleft%28e%5E%7B-0.05t%7D%5Cright%29%5C%5Cln%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%3D-0.05t%5C%5C%24Divide%20both%20sides%20by%20-0.05%24%5C%5Ct%3D-%5Cdfrac%7Bln%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%7D%7B0.05%7D%20%5C%5C%3D-%5Cdfrac%7Bln%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%7D%7B0.05%7D%5C%5Ct%3D-20ln%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29)
Therefore, the time for which the area will be 15 sqyare kilometers is:
-20 ln(1/3) years.