X + y = 120000
0.15x - 0.10y = 5500
Multiply both sides of bottom by 100 to remove decimals
x + y = 120000
15x - 10y = 550000
Multiply both sides of top by 10
10x + 10y = 1200000
15x - 10y = 550000
Add the two
25x = 1750000
x = 70000
He paid $70,000 for the property that made a profit, and paid $50,000 for the property that lost value.
Answer:
![\tan{\theta} = \frac{\sqrt{11}}{11}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B11%7D)
Step-by-step explanation:
Cosecant:
The cosecant is one divided by the sine. Thus:
![\csc{\theta} = \frac{1}{\sin{\theta}}](https://tex.z-dn.net/?f=%5Ccsc%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csin%7B%5Ctheta%7D%7D)
Tangent is sine divided by cosine, so we first find the sine, then the cosine, to find the tangent.
Sine and cosine:
![\sin{\theta} = \frac{1}{\csc{\theta}} = \frac{1}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{6}](https://tex.z-dn.net/?f=%5Csin%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Ccsc%7B%5Ctheta%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B2%5Csqrt%7B3%7D%7D%20%5Ctimes%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B3%7D%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B6%7D)
![\sin^{2}{\theta} + \cos^{2}{\theta} = 1](https://tex.z-dn.net/?f=%5Csin%5E%7B2%7D%7B%5Ctheta%7D%20%2B%20%5Ccos%5E%7B2%7D%7B%5Ctheta%7D%20%3D%201)
![\cos^{2}{\theta} = 1 - \sin^{2}{\theta}](https://tex.z-dn.net/?f=%5Ccos%5E%7B2%7D%7B%5Ctheta%7D%20%3D%201%20-%20%5Csin%5E%7B2%7D%7B%5Ctheta%7D)
![\cos^{2}{\theta} = 1 - (\frac{\sqrt{3}}{6})^2](https://tex.z-dn.net/?f=%5Ccos%5E%7B2%7D%7B%5Ctheta%7D%20%3D%201%20-%20%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B6%7D%29%5E2)
![\cos^{2}{\theta} = 1 - \frac{3}{36}](https://tex.z-dn.net/?f=%5Ccos%5E%7B2%7D%7B%5Ctheta%7D%20%3D%201%20-%20%5Cfrac%7B3%7D%7B36%7D)
![\cos^{2}{\theta} = \frac{33}{36}](https://tex.z-dn.net/?f=%5Ccos%5E%7B2%7D%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B33%7D%7B36%7D)
First quadrant, so the cosine is positive. Then
![\cos^{2}{\theta} = \sqrt{\frac{33}{36}} = \frac{\sqrt{33}}{6}](https://tex.z-dn.net/?f=%5Ccos%5E%7B2%7D%7B%5Ctheta%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B33%7D%7B36%7D%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B33%7D%7D%7B6%7D)
Tangent:
Sine divided by cosine. So
![\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{\frac{\sqrt{3}}{6}}{\frac{\sqrt{33}}{6}} = \frac{\sqrt{3}}{\sqrt{33}} = \frac{\sqrt{3}}{\sqrt{3}\sqrt{11}} = \frac{1}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{11}}{11}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csin%7B%5Ctheta%7D%7D%7B%5Ccos%7B%5Ctheta%7D%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B6%7D%7D%7B%5Cfrac%7B%5Csqrt%7B33%7D%7D%7B6%7D%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B33%7D%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B3%7D%5Csqrt%7B11%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B11%7D%7D%20%5Ctimes%20%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B%5Csqrt%7B11%7D%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B11%7D)
The answer is:
![\tan{\theta} = \frac{\sqrt{11}}{11}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B11%7D%7D%7B11%7D)
1)<span>
960 square feet</span>
2) B. 25 cm ^2The area of a regular pentagon can be found using the formula.
![A=\frac{1}{4} \sqrt{5(5+2 \sqrt{5})} *s^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B4%7D%20%5Csqrt%7B5%285%2B2%20%5Csqrt%7B5%7D%29%7D%20%2As%5E2)
s=side length
A≈960 square feet
The apothem of a square is half of the side length. 2.5*2=5. 5^2 = 25cm^2
Answer: 825 minutes
Step-by-step explanation: We know there is a total of 15 people in the book club. We also know that 10 people each read an average of 65 minutes each day, and the remaining 5 people read for an average of 35 minutes each day.
To find the total amount f minutes read, simply multiply the amount of people by the minutes read.
10 x 65 = 650 total minutes read if 10 people each read 65 minutes for one day.
5 x 35 = 175 total minutes read if 5 people each read for 35 minutes in one day.
Now, simply add the total minutes read to find the reading time fr the entire book club each day.
650 + 175 = 825 average reading time for the entire book club each day.
Answer:
185/9
Step-by-step explanation:
![20\frac{5}{9} \\\\20+\frac{5}{9}\\\\\frac{20*9}{9}+\frac{5}{9}\\\\\frac{180}{9}+\frac{5}{9}\\\\\frac{180+5}{9}\\\\\frac{185}{9}](https://tex.z-dn.net/?f=20%5Cfrac%7B5%7D%7B9%7D%20%5C%5C%5C%5C20%2B%5Cfrac%7B5%7D%7B9%7D%5C%5C%5C%5C%5Cfrac%7B20%2A9%7D%7B9%7D%2B%5Cfrac%7B5%7D%7B9%7D%5C%5C%5C%5C%5Cfrac%7B180%7D%7B9%7D%2B%5Cfrac%7B5%7D%7B9%7D%5C%5C%5C%5C%5Cfrac%7B180%2B5%7D%7B9%7D%5C%5C%5C%5C%5Cfrac%7B185%7D%7B9%7D)