Step-by-step explanation:
Take the LCM of the denominators:
=> LCM = 18
=> -7/9 x 2/2 = -14/18
=> -4/9 x 2/2 = -8/18
=> 1/9 x 2/2 = 2/18
=> 1/2 x 9/9 = 9/18
When the number is negative, the greater the number, the smaller it is.
So, -14 is smaller than -8.
< = smaller than
=> -14/18 < -8/18 < 2/18 < 9/18
=> -7/9 < -4/9 < 1/9 < 1/2
<u>Given</u>:
Let x represents the number of weeks.
Let y represents the amount of money.
Given that you are saving money for a new cell phone.
At week 0 you have saved $20 and at week 10 you have $100.
Writing this as coordinates, we get;
(0,20) and (10,100)
We need to determine the slope of the linear equation.
<u>Slope</u>:
The slope of the equation can be determined using the formula,
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substituting the coordinates, we get;
![m=\frac{100-20}{10-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B100-20%7D%7B10-0%7D)
![m=\frac{80}{10}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B80%7D%7B10%7D)
![m=8](https://tex.z-dn.net/?f=m%3D8)
Thus, the slope of the linear equation is $8.
Hence, $8 is put away each week.
2/5 more i believe!
basically just subtract 4/5 and 2/5 and you get 2/5
feel free to mark brainliest, hope this helps!
Answer:
2, 6, 10, 14
or
14, 10, 6, 2.
Step-by-step explanation:
Let the four consecutive numbers in A.P. be a - 3d, a - d, a + d, a + 3d
According to the first condition:
a - 3d + a - d + a + d + a + 3d =32
4a = 32
a = 32/4
a = 8
According to the second condition:
![\frac{(a - 3d)(a + 3d)}{(a - d)(a + d)} = \frac{7}{15} \\ \\ \frac{ {a}^{2} - (3d)^{2} }{ {a}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ {a}^{2} - 9d^{2} }{ {a}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ {8}^{2} - 9d^{2} }{ {8}^{2} - {d}^{2} } = \frac{7}{15} \\ \\ \frac{ 64 - 9d^{2} }{ 64 - {d}^{2} } = \frac{7}{15} \\ \\ 15(64 - 9 {d}^{2} ) = 7(64 - {d}^{2} ) \\ \\ 960 - 135 {d}^{2} = 448 - 7 {d}^{2} \\ \\ 960 - 448 = 135 {d}^{2} - 7 {d}^{2} \\ \\ 512 = 128 {d}^{2} \\ \\ {d}^{2} = \frac{512}{128} \\ \\ {d}^{2} = 4 \\ \\ d = \pm 2 \\ \\ when \: d = 2 \\ a - 3d = 8 - 3 \times 2 = 8 - 6 = 2 \\ a - d = 8 - 2 = 6 \\ a + d = 8 + 2 = 10 \\ a + 3d = 8 + 3 \times 2 = 8 + 6 = 14 \\\\ when \: d = - 2 \\ a - 3d = 8 - 3 \times ( -2 ) = 8 + 6 = 14 \\ a - d = 8 -( - 2 )= 8 + 2 = 10 \\ a + d = 8 + ( - 2 )= 8 - 2 = 6\\ a + 3d = 8 + 3 \times ( - 2 )= 8 - 6 = 2 \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28a%20-%203d%29%28a%20%2B%203d%29%7D%7B%28a%20-%20d%29%28a%20%2B%20d%29%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7B15%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B%20%7Ba%7D%5E%7B2%7D%20-%20%283d%29%5E%7B2%7D%20%20%7D%7B%20%7Ba%7D%5E%7B2%7D%20-%20%20%7Bd%7D%5E%7B2%7D%20%20%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7B15%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B%20%7Ba%7D%5E%7B2%7D%20-%209d%5E%7B2%7D%20%20%7D%7B%20%7Ba%7D%5E%7B2%7D%20-%20%20%7Bd%7D%5E%7B2%7D%20%20%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7B15%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B%20%7B8%7D%5E%7B2%7D%20-%209d%5E%7B2%7D%20%20%7D%7B%20%7B8%7D%5E%7B2%7D%20-%20%20%7Bd%7D%5E%7B2%7D%20%20%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7B15%7D%20%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B%2064%20-%209d%5E%7B2%7D%20%20%7D%7B%2064%20-%20%20%7Bd%7D%5E%7B2%7D%20%20%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7B15%7D%20%20%5C%5C%20%20%5C%5C%2015%2864%20-%209%20%7Bd%7D%5E%7B2%7D%20%29%20%3D%207%2864%20-%20%20%20%7Bd%7D%5E%7B2%7D%20%29%20%5C%5C%20%20%5C%5C%20960%20-%20135%20%7Bd%7D%5E%7B2%7D%20%20%3D%20448%20-%207%20%7Bd%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20960%20-%20448%20%3D%20135%20%7Bd%7D%5E%7B2%7D%20%20-%207%20%7Bd%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20512%20%3D%20128%20%7Bd%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%7Bd%7D%5E%7B2%7D%20%20%3D%20%20%5Cfrac%7B512%7D%7B128%7D%20%20%5C%5C%20%20%5C%5C%20%20%7Bd%7D%5E%7B2%7D%20%20%3D%204%20%5C%5C%20%20%5C%5C%20d%20%3D%20%20%5Cpm%202%20%5C%5C%20%20%5C%5C%20when%20%5C%3A%20d%20%3D%202%20%5C%5C%20a%20-%203d%20%3D%208%20-%203%20%5Ctimes%202%20%3D%208%20-%206%20%3D%202%20%5C%5C%20a%20-%20d%20%3D%208%20-%202%20%3D%206%20%5C%5C%20a%20%2B%20d%20%3D%208%20%2B%202%20%3D%2010%20%5C%5C%20a%20%2B%203d%20%3D%208%20%2B%203%20%5Ctimes%202%20%3D%208%20%2B%206%20%3D%2014%20%5C%5C%5C%5C%20when%20%5C%3A%20d%20%3D%20%20-%202%20%5C%5C%20a%20-%203d%20%3D%208%20-%203%20%5Ctimes%20%28%20-2%20%29%20%3D%208%20%20%2B%20%206%20%3D%2014%20%5C%5C%20a%20-%20d%20%3D%208%20-%28%20-%20%202%20%29%3D%208%20%2B%202%20%3D%2010%20%5C%5C%20a%20%2B%20d%20%3D%208%20%2B%20%28%20-%202%20%29%3D%208%20-%202%20%3D%206%5C%5C%20a%20%2B%203d%20%3D%208%20%2B%203%20%5Ctimes%20%28%20-%202%20%29%3D%208%20%20-%20%206%20%3D%202%20%5C%5C)
Thus the four consecutive numbers of the A. P. are 2, 6, 10, 14 or 14, 10, 6, 2.
Answer:
d = -1/2
Step-by-step explanation:
I got a negative answer, I'm not sure if that's what you are looking for. But Hope this helps!