3x + 9 + 3x =15
6x + 9 = 15
- 9 = -9
6x = 6
/6 /6
X =1
The sum of 31/4+42/4= 18.25
<u>Step-by-step explanation</u>:
- The denominators are same.
- Then add the numerators and keep the denominators same.
The sum of (31/4) + (42/4) = (31+42)/4
⇒ 73/4
⇒ 18.25
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Answer:
x=9
Step-by-step explanation:
We can use similar triangles and ratios. Put the small triangle side over the large triangle side.
9cm 3x -20
---------- = ---------------- We need to add the sides to get to the larger triangle
72+9 cm 3x-20 + 56
We can cross multiply to solve
9 * (3x-20+56) = (72+9) * (3x-20)
Simplify
9*(3x+36) = 81*(3x-20)
Distribute
27x +324 = 243x -1620
Subtract 27x from each side
27x-27x +324 = 243x-27x -1620
324 = 216x-1620
Add 1620 to each side
324+1620 = 216x
1944 = 216x
Divide each side by 216
1944/216 = 216x/216
9=x
Answer:
15.98
Step-by-step explanation:
∑₁¹⁰ 
![=8[1+\frac{1}{4} +\frac{1}{16} + ........ +t_{10}]](https://tex.z-dn.net/?f=%3D8%5B1%2B%5Cfrac%7B1%7D%7B4%7D%20%2B%5Cfrac%7B1%7D%7B16%7D%20%2B%20........%20%2Bt_%7B10%7D%5D)
We have to use the formula of sum of a G.P. series with common ratio r < 1.
If the first term is a, the common ratio is r and the number of terms is n then the sum [a + ar + ar² + ar³ + ......... up to n terms] is given by
![[a \times\frac{1-r^{n} }{1-r}]](https://tex.z-dn.net/?f=%5Ba%20%5Ctimes%5Cfrac%7B1-r%5E%7Bn%7D%20%7D%7B1-r%7D%5D)
![= 8[1 \times \frac{1-\frac{1}{2^{10} } }{1-\frac{1}{2} } ]](https://tex.z-dn.net/?f=%3D%208%5B1%20%5Ctimes%20%5Cfrac%7B1-%5Cfrac%7B1%7D%7B2%5E%7B10%7D%20%7D%20%7D%7B1-%5Cfrac%7B1%7D%7B2%7D%20%7D%20%5D)
(Answer)
