Answer:
B: |8| + (-7)
Step-by-step explanation:
When you are looking for the distance between two numbers, always add. The distance between 8 and -7 is 15 (|8| = 8). If, for instance, the answer was negative, which it is now, just find the absolute value of -15 which equals 15. The answer is B.
9.) 1 / [3]
When you set the denominators of 2 / 5 and 1 / 3, equal to each other, you receive a denominator of 15, the only denominator the two have in common
Answer:perimeter
Step-by-step explanation:20+20+4=44 and u multiply 3/5x times 2 it equals 6/10x+44
Given:
![\bold{t_2=5}\\\\\bold{t_8=15}\\\\](https://tex.z-dn.net/?f=%5Cbold%7Bt_2%3D5%7D%5C%5C%5C%5C%5Cbold%7Bt_8%3D15%7D%5C%5C%5C%5C)
To find:
![\bold{T_n=?}\\\\\bold{S_{10}=?}](https://tex.z-dn.net/?f=%5Cbold%7BT_n%3D%3F%7D%5C%5C%5C%5C%5Cbold%7BS_%7B10%7D%3D%3F%7D)
Solution:
![\to \bold{t_2=5}\\\\ \bold{a+d=5} \\\\ \bold{a=5-d} ................(i)\\\\ \to \bold{t_8=15}\\\\ \bold{a+ 7d=15}.................(ii)\\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cbold%7Bt_2%3D5%7D%5C%5C%5C%5C%20%20%5Cbold%7Ba%2Bd%3D5%7D%20%5C%5C%5C%5C%20%20%5Cbold%7Ba%3D5-d%7D%20................%28i%29%5C%5C%5C%5C%20%5Cto%20%5Cbold%7Bt_8%3D15%7D%5C%5C%5C%5C%20%5Cbold%7Ba%2B%207d%3D15%7D.................%28ii%29%5C%5C%5C%5C)
Putting the equation (i) value into equation (ii):
![\to \bold{5-d+7d=15}\\\\\to \bold{5+6d=15}\\\\\to \bold{6d=15-5}\\\\\to \bold{6d=10}\\\\\to \bold{d=\frac{10}{6}}\\\\\to \bold{d=\frac{5}{3}}\\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cbold%7B5-d%2B7d%3D15%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7B5%2B6d%3D15%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7B6d%3D15-5%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7B6d%3D10%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Bd%3D%5Cfrac%7B10%7D%7B6%7D%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Bd%3D%5Cfrac%7B5%7D%7B3%7D%7D%5C%5C%5C%5C)
Putting the value of (d) into equation (i):
![\to \bold{a=5-\frac{5}{3}}\\\\\to \bold{a=\frac{15-5}{3}}\\\\\to \bold{a=\frac{10}{3}}\\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cbold%7Ba%3D5-%5Cfrac%7B5%7D%7B3%7D%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Ba%3D%5Cfrac%7B15-5%7D%7B3%7D%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Ba%3D%5Cfrac%7B10%7D%7B3%7D%7D%5C%5C%5C%5C)
Calculating the ![\bold{t_n :}](https://tex.z-dn.net/?f=%5Cbold%7Bt_n%20%3A%7D)
![\to \bold{t_n=a+(n-1)d}\\\\\to \bold{t_n=\frac{10}{3}+(n-1)\frac{5}{3}}\\\\\to \bold{t_n=\frac{10}{3}+\frac{5}{3}n-\frac{5}{3}}\\\\\to \bold{t_n=\frac{10}{3}-\frac{5}{3} +\frac{5}{3}n}\\\\\to \bold{t_n=\frac{10-5}{3} +\frac{5}{3}n}\\\\\to \bold{t_n=\frac{5}{3} +\frac{5}{3}n}\\\\ \to \bold{t_n=\frac{5}{3}(1+n)}\\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cbold%7Bt_n%3Da%2B%28n-1%29d%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Bt_n%3D%5Cfrac%7B10%7D%7B3%7D%2B%28n-1%29%5Cfrac%7B5%7D%7B3%7D%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Bt_n%3D%5Cfrac%7B10%7D%7B3%7D%2B%5Cfrac%7B5%7D%7B3%7Dn-%5Cfrac%7B5%7D%7B3%7D%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Bt_n%3D%5Cfrac%7B10%7D%7B3%7D-%5Cfrac%7B5%7D%7B3%7D%20%2B%5Cfrac%7B5%7D%7B3%7Dn%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Bt_n%3D%5Cfrac%7B10-5%7D%7B3%7D%20%2B%5Cfrac%7B5%7D%7B3%7Dn%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7Bt_n%3D%5Cfrac%7B5%7D%7B3%7D%20%2B%5Cfrac%7B5%7D%7B3%7Dn%7D%5C%5C%5C%5C%20%5Cto%20%5Cbold%7Bt_n%3D%5Cfrac%7B5%7D%7B3%7D%281%2Bn%29%7D%5C%5C%5C%5C)
Formula:
![\bold{S_n = \frac{n}{2}[2a + (n - 1)d ] }\\](https://tex.z-dn.net/?f=%5Cbold%7BS_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B2a%20%2B%20%28n%20-%201%29d%20%5D%20%7D%5C%5C)
Calculating the ![\bold{S_{10}} :](https://tex.z-dn.net/?f=%5Cbold%7BS_%7B10%7D%7D%20%3A)
![\to \bold{S_{10} = \frac{10}{2}[2\frac{10}{3} + (10- 1)\frac{5}{3} ] }\\\\\to \bold{S_{10} = 5[\frac{20}{3} + (9)\frac{5}{3} ] }\\\\\to \bold{S_{10} = 5[\frac{20}{3} + 9 \times \frac{5}{3} ] }\\\\\to \bold{S_{10} = 5[\frac{20}{3} + 3\times 5 ] }\\\\\to \bold{S_{10} = 5[\frac{20}{3} + 15 ] }\\\\\to \bold{S_{10} = 5[\frac{20+ 45}{3} ] }\\\\\to \bold{S_{10} = 5[\frac{65}{3} ] }\\\\\to \bold{S_{10} = 5 \times \frac{65}{3} }\\\\\to \bold{S_{10} = \frac{325}{3} }\\\\\to \bold{S_{10} =108.33 }](https://tex.z-dn.net/?f=%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%20%5Cfrac%7B10%7D%7B2%7D%5B2%5Cfrac%7B10%7D%7B3%7D%20%2B%20%2810-%201%29%5Cfrac%7B5%7D%7B3%7D%20%5D%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%205%5B%5Cfrac%7B20%7D%7B3%7D%20%2B%20%289%29%5Cfrac%7B5%7D%7B3%7D%20%5D%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%205%5B%5Cfrac%7B20%7D%7B3%7D%20%2B%209%20%5Ctimes%20%5Cfrac%7B5%7D%7B3%7D%20%5D%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%205%5B%5Cfrac%7B20%7D%7B3%7D%20%2B%203%5Ctimes%205%20%5D%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%205%5B%5Cfrac%7B20%7D%7B3%7D%20%2B%2015%20%5D%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%205%5B%5Cfrac%7B20%2B%2045%7D%7B3%7D%20%5D%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%205%5B%5Cfrac%7B65%7D%7B3%7D%20%5D%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%205%20%5Ctimes%20%5Cfrac%7B65%7D%7B3%7D%20%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D%20%20%5Cfrac%7B325%7D%7B3%7D%20%20%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7BS_%7B10%7D%20%3D108.33%20%7D)
Therefore, the final answer is "
"
Learn more:
brainly.com/question/11853909