1.
<span>1.5x-1 > 6.5
1.5x>1+6.5
</span>1.5x>7.5, divide by 1.5
x>5, is represented by the region to the right of the vertical line x=5
2.
<span>7x+3 < -25
7x<-25-3
7x<-28, divide by 4:
x<-4
</span>x<-4, is represented by the region to the left of the vertical line x=-4
Answer: check the picture
The sum of 3 products...there r 3 terms
0.75
Explanation:
Every 1/4 is 25. If you want to calculate them, then you're going to need 1/4 to find 25. In some other cases, 25, can also be written as another decimal. Such as, 4/100.
100/4 is 25. For example:
Woah! You have 3/4 of a dollar. You're really saving up money fast!
This example means that the person has 75 cents.
For an ounce, that would mean 0.04 pounds.
Answer:
0.032
Step-by-step explanation:
Divide each term by 0.032 and simplify
Answer:
S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5
Step-by-step explanation:
Given the sequence to find the sum up-to 12 terms
![(-7.5) + 15 + (-30) + ...](https://tex.z-dn.net/?f=%28-7.5%29%20%2B%2015%20%2B%20%28-30%29%20%2B%20...)
As we know that
A geometric sequence has a constant ratio 'r' and is defined by
![a_n=a_1\cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1%5Ccdot%20r%5E%7Bn-1%7D)
![\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}](https://tex.z-dn.net/?f=%5Cmathrm%7BCompute%5C%3Athe%5C%3Aratios%5C%3Aof%5C%3Aall%5C%3Athe%5C%3Aadjacent%5C%3Aterms%7D%3A%5Cquad%20%5C%3Ar%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D)
![\frac{15}{\left(-7.5\right)}=-2,\:\quad \frac{\left(-30\right)}{15}=-2](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B%5Cleft%28-7.5%5Cright%29%7D%3D-2%2C%5C%3A%5Cquad%20%5Cfrac%7B%5Cleft%28-30%5Cright%29%7D%7B15%7D%3D-2)
![\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Aratio%5C%3Aof%5C%3Aall%5C%3Athe%5C%3Aadjacent%5C%3Aterms%5C%3Ais%5C%3Athe%5C%3Asame%5C%3Aand%5C%3Aequal%5C%3Ato%7D)
![r=-2](https://tex.z-dn.net/?f=r%3D-2)
![\mathrm{The\:first\:element\:of\:the\:sequence\:is}](https://tex.z-dn.net/?f=%5Cmathrm%7BThe%5C%3Afirst%5C%3Aelement%5C%3Aof%5C%3Athe%5C%3Asequence%5C%3Ais%7D)
![a_1=\left(-7.5\right)](https://tex.z-dn.net/?f=a_1%3D%5Cleft%28-7.5%5Cright%29)
![a_n=a_1\cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1%5Ccdot%20r%5E%7Bn-1%7D)
![\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:](https://tex.z-dn.net/?f=%5Cmathrm%7BTherefore%2C%5C%3Athe%5C%3A%7Dn%5Cmathrm%7Bth%5C%3Aterm%5C%3Ais%5C%3Acomputed%5C%3Aby%7D%5C%3A)
![a_n=\left(-7.5\right)\left(-2\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D%5Cleft%28-7.5%5Cright%29%5Cleft%28-2%5Cright%29%5E%7Bn-1%7D)
![a_n=-\left(-2\right)^{n-1}\cdot \:7.5](https://tex.z-dn.net/?f=a_n%3D-%5Cleft%28-2%5Cright%29%5E%7Bn-1%7D%5Ccdot%20%5C%3A7.5)
![\mathrm{Geometric\:sequence\:sum\:formula:}](https://tex.z-dn.net/?f=%5Cmathrm%7BGeometric%5C%3Asequence%5C%3Asum%5C%3Aformula%3A%7D)
![a_1\frac{1-r^n}{1-r}](https://tex.z-dn.net/?f=a_1%5Cfrac%7B1-r%5En%7D%7B1-r%7D)
![\mathrm{Plug\:in\:the\:values:}](https://tex.z-dn.net/?f=%5Cmathrm%7BPlug%5C%3Ain%5C%3Athe%5C%3Avalues%3A%7D)
![n=12,\:\spacea_1=\left(-7.5\right),\:\spacer=-2](https://tex.z-dn.net/?f=n%3D12%2C%5C%3A%5Cspacea_1%3D%5Cleft%28-7.5%5Cright%29%2C%5C%3A%5Cspacer%3D-2)
![=\left(-7.5\right)\frac{1-\left(-2\right)^{12}}{1-\left(-2\right)}](https://tex.z-dn.net/?f=%3D%5Cleft%28-7.5%5Cright%29%5Cfrac%7B1-%5Cleft%28-2%5Cright%29%5E%7B12%7D%7D%7B1-%5Cleft%28-2%5Cright%29%7D)
![=-7.5\cdot \frac{1-\left(-2\right)^{12}}{1+2}](https://tex.z-dn.net/?f=%3D-7.5%5Ccdot%20%5Cfrac%7B1-%5Cleft%28-2%5Cright%29%5E%7B12%7D%7D%7B1%2B2%7D)
![\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}](https://tex.z-dn.net/?f=%5Cmathrm%7BMultiply%5C%3Afractions%7D%3A%5Cquad%20%5C%3Aa%5Ccdot%20%5Cfrac%7Bb%7D%7Bc%7D%3D%5Cfrac%7Ba%5C%3A%5Ccdot%20%5C%3Ab%7D%7Bc%7D)
∵ ![\left(1-\left(-2\right)^{12}\right)\cdot \:7.5=-30712.5](https://tex.z-dn.net/?f=%5Cleft%281-%5Cleft%28-2%5Cright%29%5E%7B12%7D%5Cright%29%5Ccdot%20%5C%3A7.5%3D-30712.5)
![=-\frac{-30712.5}{3}](https://tex.z-dn.net/?f=%3D-%5Cfrac%7B-30712.5%7D%7B3%7D)
![=\frac{30712.5}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B30712.5%7D%7B3%7D)
![=10237.5](https://tex.z-dn.net/?f=%3D10237.5)
Thus, S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5