<span>Jessica pays $10 more for membership. The function for the amount that Jessica pays in dollars, y, for renting x number of video games would be y = 5x + 40. To determine how much more a membership costs for Jessica, subtract 30 from 40 to get 10.</span>
4/18 are yellow, you add up all of the marbles, and then put the number of yellow marbles over
Answer: ![\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}](https://tex.z-dn.net/?f=%5Cbold%7BS_%7B%5Cinfty%7D%3D%5Cdfrac%7B3125%7D%7B2%7D%3D1562.5%7D)
<u>Step-by-step explanation:</u>
a₁, 375, a₃, a₄, 81
First, let's find the ratio (r). There are three multiple from 375 to 81.
![375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}](https://tex.z-dn.net/?f=375r%5E3%3D81%5C%5C%5C%5Cr%5E3%3D%5Cdfrac%7B81%7D%7B375%7D%5C%5C%5C%5C%5C%5Cr%5E3%3D%5Cdfrac%7B27%7D%7B125%7D%5Cqquad%20%5Cleftarrow%20simplied%5C%5C%5C%5C%5C%5C%5Csqrt%5B3%5D%7Br%5E3%7D%20%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B27%7D%7B125%7D%7D%5C%5C%20%5C%5C%5C%5Cr%3D%5Cdfrac%7B3%7D%7B5%7D)
Next, let's find a₁
![a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625](https://tex.z-dn.net/?f=a_1%5Cbigg%28%5Cdfrac%7B3%7D%7B5%7D%5Cbigg%29%3D375%5C%5C%5C%5C%5C%5Ca_1%3D375%5Cbigg%28%5Cdfrac%7B5%7D%7B3%7D%5Cbigg%29%5C%5C%5C%5C%5C%5Ca_1%3D125%285%29%5C%5C%5C%5C%5C%5Ca_1%3D625)
Lastly, Use the Infinite Geometric Sum Formula to find the sum:
![S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}](https://tex.z-dn.net/?f=S_%7B%5Cinfty%7D%3D%5Cdfrac%7Ba_1%7D%7B1-r%7D%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Cdfrac%7B625%7D%7B1-%5Cfrac%7B3%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%5Cdfrac%7B625%7D%7B%5Cfrac%7B2%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%20%5Cdfrac%7B625%285%29%7D%7B2%7D%5C%5C%5C%5C%5C%5C.%5Cquad%20%3D%20%5Clarge%5Cboxed%7B%5Cdfrac%7B3125%7D%7B2%7D%7D)
Answer:
64/5 pi
Step-by-step explanation:
Answer: the angle is 1°+n×120°
1°, 121°, 241°
Step-by-step explanation:
Angles are taken modulo 360°, so 363° = 3°.
Angle plus supplement gives 180°.
Let a be angle, s be supplement of a.
So s = 180-a. Given a = 3 + 2s
a = 3 + 2(180 - a)
a = 3 + 360 - 2a = 363 - 2a
3a = 363° or 3° or 723°
a = 121° or 1° or 241°
a = 1°
s = 179°
2s = 358°
2s+3 = 361° = 1° (modulo 360)
a = 121°
s = 180-121 = 59°
2s = 118°
2s + 3 = 121°, as required.
a = 241°
s = 360+180-241 = 540-241 = 299
2s = 598
2s + 3 = 601 = 241 (modulo 360)