Could someone just double check my work
sqrt280x^6/sqrt7x
I got 2x^3 sqrt10\sqrtx
Also 1/5(30y+40)+2/3(9y-27)=18
I got 7/3
Both answers is correct but you can simplify answer 1.
sqrt ( 280 x ^ 6 ) / sqrt ( 7 x ) =
sqrt ( 280 x ^ 6 / 7 x ) =
sqrt [ ( 280 / 7 ) * x ^ 6 / x ] =
sqrt ( 40 * x ^ 5 ) =
sqrt ( 40 ) * sqrt ( x ^ 5 ) =
sqrt ( 4 * 10 ) * sqrt ( x ^ 5 ) =
sqrt ( 4 ) * sqrt ( 10 ) * sqrt ( x ^ 5 ) =
2 * sqrt ( 10 ) * sqrt ( x ^ 5 ) =
2 * sqrt ( 10 ) * x ^ ( 5 / 2 )
If you'll allow one more step,
2x^2 sqrt(10x)
1. 2x sqrt(10x^3)
2. 7/3
By the way, 2x^3 sqrt(10/x) is also correct. So, good work, I think.
Let's break down the expressions step by step to double-check your work.
For the first expression, we have:
√(280x^6) / √(7x)
To simplify, you can multiply the numerators and denominators by the square root of 7, which will eliminate the square root in the denominator:
(√(280x^6) / √(7x)) * (√(7) / √(7))
Now, simplify each term separately:
√(280x^6) * √(7) = √(1960x^6) = √(1960) * √(x^6) = 14√(10) * x^3
√(7x) * √(7) = √(49x) = 7√(x)
Combining these results, we get:
(14√(10) * x^3) / (7√(x))
Reduce the expression further by canceling out the common factors:
(14/7) * (√(10)/√(1)) * (x^3/x)
Simplifying this, we have:
2 * √(10) * x^2 = 2x^2√10
Therefore, the correct simplified expression is 2x^2√10.
Now let's move on to the second expression:
1/5(30y + 40) + 2/3(9y - 27) = 18
First, simplify the terms within parentheses:
1/5 * (30y + 40) = (1/5) * 30y + (1/5) * 40 = 6y + 8
2/3 * (9y - 27) = (2/3) * 9y + (2/3) * (-27) = 6y - 18
Now rewrite the equation using the simplified terms:
6y + 8 + 6y - 18 = 18
Combine like terms:
12y - 10 = 18
Now, isolate the variable by adding 10 to both sides:
12y = 28
Finally, divide both sides by 12 to solve for y:
y = 28/12 = 7/3
Therefore, the correct solution for the second equation is y = 7/3.
I have double-checked your work, and it appears that your answers are correct. Well done!