Answer:
The sum of a number and 7 multiplied by 2 is increased by 10
Step-by-step explanation:
Remark
Many calculators have a key that will do this in one step. Mine is one of them. So let's start with the answer and then we'll do it the long way.
9C3 = 84. You put it into your calculator as 9 2nF nCr 3 =
Solution
![\dfrac{9!}{(n - 3)!3!} = \dfrac{9*8*7*6!}{6!*3!}=\dfrac{9*8*7}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%21%7D%7B%28n%20-%203%29%213%21%7D%20%3D%20%5Cdfrac%7B9%2A8%2A7%2A6%21%7D%7B6%21%2A3%21%7D%3D%5Cdfrac%7B9%2A8%2A7%7D%7B6%7D)
3*4*7 = 84 which is what you set out to show.
A quadratic equation is one in which the highest exponent of x is 2.
![7x^2+14x=0](https://tex.z-dn.net/?f=7x%5E2%2B14x%3D0)
is quadratic; the highest exponent is 2.
x³-3x²+1=0 is NOT quadratic. The highest exponent of x is 3, not 2.
5x-7=0 is NOT quadratic. The highest exponent of x is 1, not 2.
x²+3x-5=0 is quadratic; the highest exponent of x is 2.
x-5=9x+7 is NOT quadratic. The highest exponent of x is 1, not 2.
x²-x=3x+7 is quadratic; the highest exponent of x is 2.
Answer: ![7\times10^{19} buckets](https://tex.z-dn.net/?f=7%5Ctimes10%5E%7B19%7D%20buckets)
Step-by-step explanation:
Given: A cubic kilometer=
cubic centimeters
The volume of world’s oceans=
cubic kilometers of water.
⇒ The volume of world’s oceans=
cubic centimeters of water.
Volume of a bucket = 20,000 cubic centimeters of water.
The number of bucket-loads would it take to bucket out the world’s oceans
![n=\frac{\text{volume of ocean}}{\text{volume of bucket}}=\frac{1.4\times10^{9}\times10^{15}}{20000}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B%5Ctext%7Bvolume%20of%20ocean%7D%7D%7B%5Ctext%7Bvolume%20of%20bucket%7D%7D%3D%5Cfrac%7B1.4%5Ctimes10%5E%7B9%7D%5Ctimes10%5E%7B15%7D%7D%7B20000%7D)
![\Rightarrow\ n=\frac{1.4\times10^{9+15}}{0.2\times10^5}......[a^n\times a^m=a^{m+n}]\\\Rightarrow\ n=7\times10^{24-5}.....[\frac{a^m}{a^n}=a^{m-n}]\\\Rightyarrow\ n=7\times10^{19}](https://tex.z-dn.net/?f=%5CRightarrow%5C%20n%3D%5Cfrac%7B1.4%5Ctimes10%5E%7B9%2B15%7D%7D%7B0.2%5Ctimes10%5E5%7D......%5Ba%5En%5Ctimes%20a%5Em%3Da%5E%7Bm%2Bn%7D%5D%5C%5C%5CRightarrow%5C%20n%3D7%5Ctimes10%5E%7B24-5%7D.....%5B%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D%5D%5C%5C%5CRightyarrow%5C%20n%3D7%5Ctimes10%5E%7B19%7D)
hence,
bucketloads would it take to bucket out the world’s oceans.