Hey there! :)
Answer:
㏒
(1/25) = -2.
Step-by-step explanation:
Starting with:
㏒
(1/25) =
We can rewrite this expression as:
![5^{x} = 1/25](https://tex.z-dn.net/?f=5%5E%7Bx%7D%20%3D%201%2F25)
1/25 is equivalent to
, therefore:
![5^{x} = 5^{-2}](https://tex.z-dn.net/?f=5%5E%7Bx%7D%20%3D%205%5E%7B-2%7D)
x = -2.
Therefore, ㏒
(1/25) = -2.
The x-intercept is the point where the line intersects the x-axis which means that it is the value of x when y in the equation is set to be equal to zero. In the equation of the line given, setting the y value to zero will result to an x value of -1/2. Therefore, the x-intercept would be -1/2.
Answer:
7 and 8 would work
Step-by-step explanation:
just insert them as w and they have to be greater than 20. I hope this helps.
Answer:
![\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}](https://tex.z-dn.net/?f=%5Chuge%5Cunderline%7B%5Cred%7BA%7D%5Cblue%7Bn%7D%5Cpink%7Bs%7D%5Cpurple%7Bw%7D%5Corange%7Be%7D%5Cgreen%7Br%7D%20-%7D)
<h3><em>Topic </em><em>-</em><em> </em><em>Arithmetic</em><em> </em><em>Progression </em><em>(</em><em> </em><em>AP </em><em>)</em></h3>
- Given - <u>a </u><u>general </u><u>term </u><u>for </u><u>a </u><u>sequence.</u>
- To find - <u>the </u><u>1</u><u>5</u><u>0</u><u>t</u><u>h</u><u> </u><u>term </u><u>of </u><u>the </u><u>given </u><u>sequence</u>
so let's start ~
General term ,
= 3n + 10
let's consider certain values of n to get some information with us which will help us solve the problem further !
let's first consider , n = 1 ! then ,
![3n + 10 = 3(1) + 10 \\ \dashrightarrow \: 13](https://tex.z-dn.net/?f=3n%20%20%2B%2010%20%3D%203%281%29%20%20%2B%2010%20%5C%5C%20%5Cdashrightarrow%20%5C%3A%20%2013)
now , let's consider n = 2
![3n + 10 = 3(2) + 10 = 6 + 10 \\ \dashrightarrow \: 16](https://tex.z-dn.net/?f=3n%20%2B%2010%20%3D%203%282%29%20%2B%2010%20%3D%206%20%2B%2010%20%5C%5C%20%5Cdashrightarrow%20%5C%3A%2016)
then , let's consider n = 3
![3n + 10 = 3(3) + 10 = 9 + 10 \\ \dashrightarrow \: 19](https://tex.z-dn.net/?f=3n%20%20%2B%2010%20%3D%203%283%29%20%2B%2010%20%3D%209%20%2B%2010%20%5C%5C%20%5Cdashrightarrow%20%5C%3A%2019)
hence ,
now we've with us an AP which is as follows -
![13 \: , \: 16 \: , \: 19 \: ......](https://tex.z-dn.net/?f=13%20%5C%3A%20%2C%20%5C%3A%2016%20%5C%3A%20%2C%20%5C%3A%2019%20%5C%3A%20......)
from this Arithmetic Progression ,
we can know that
a = first term = 13
d = common difference = 16 - 13 = 19 - 16 = <u>3</u>
now ,
![A _{n} = a + (n - 1)d \\ \implies \: A _{150} = 13 + (149)(3) \\ \implies \: A _{150} = 13 + 447 \\ \pink{\implies \: A _{150} = 460}](https://tex.z-dn.net/?f=A%20_%7Bn%7D%20%3D%20a%20%2B%20%28n%20-%201%29d%20%5C%5C%20%5Cimplies%20%5C%3A%20A%20_%7B150%7D%20%3D%2013%20%2B%20%28149%29%283%29%20%5C%5C%20%5Cimplies%20%5C%3A%20A%20_%7B150%7D%20%3D%2013%20%2B%20447%20%5C%5C%20%20%5Cpink%7B%5Cimplies%20%5C%3A%20A%20%20_%7B150%7D%20%3D%20460%7D)
hope helpful :D
Check the picture below.
so, we have two points this line passes through, well, more than two points really, but let us use these two points to get its slope.
keeping in mind that the the constant of proportionality is simply the slope.
![\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0.7}~,~\stackrel{y_2}{0.3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0.3-0}{0.7-0}\implies \cfrac{0.3}{0.7}\implies \cfrac{~~\frac{03}{10}~~}{\frac{07}{10}} \\\\\\ \cfrac{3}{10}\cdot \cfrac{10}{7}\implies \cfrac{10}{10}\cdot \cfrac{3}{7}\implies \blacktriangleright \cfrac{3}{7} \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B0%7D~%2C~%5Cstackrel%7By_1%7D%7B0%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B0.7%7D~%2C~%5Cstackrel%7By_2%7D%7B0.3%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B0.3-0%7D%7B0.7-0%7D%5Cimplies%20%5Ccfrac%7B0.3%7D%7B0.7%7D%5Cimplies%20%5Ccfrac%7B~~%5Cfrac%7B03%7D%7B10%7D~~%7D%7B%5Cfrac%7B07%7D%7B10%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B3%7D%7B10%7D%5Ccdot%20%5Ccfrac%7B10%7D%7B7%7D%5Cimplies%20%5Ccfrac%7B10%7D%7B10%7D%5Ccdot%20%5Ccfrac%7B3%7D%7B7%7D%5Cimplies%20%5Cblacktriangleright%20%5Ccfrac%7B3%7D%7B7%7D%20%5Cblacktriangleleft)