Add. what is the sum (2 x 10") + (7 x 1016) in scientific notation? plz

9 x 10¹⁶.

To sum two numbers in scientific notation  it must be taken into account that the power of 10 has the same number and the numbers are normally added and the power of 10 is maintained.

a x 10ⁿ + b x 10ⁿ = (a + b) x 10ⁿ

Then, sum the numbers shown in the image:

(2 x 10¹⁶) + (7 x 10¹⁶) = (2 + 7) x 10¹⁶ = 9 x 10¹⁶

9 times 10^16

Explanation:

when adding or subtracting in standard form (aka scientific notation), the powers of  

10

 need to be the same. If they are just add the numbers and keep the same power of  

10

#2xx10^(16)+7xx10^(16)

= ( 2 + 7 ) × 10 ^16

=9 × 10 ^16

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.