are these correct now i hope?
Problem #1
simplify
(m^2)/(8) divided by (m^5)/(16)
My answer: (2)/(m^4)
Problem #2
multiply
(3x-30)/(x^2-4x) times (8x)/(10-x)
My answer: (-6)/(x)
No. 2/m^3
(3x-30)/(x^2-4x)* (8x)/(10-x)
3*(x-10)*8x /(x-10)(-1)(x)(x-4)
x's divid out, the (x-10) divides out
3*8/(-1)(x-4)
and reduce. Check this.
Let's go through each problem to determine if the answers provided are correct.
Problem #1:
To simplify the expression (m^2)/(8) divided by (m^5)/(16), we can rewrite it as a multiplication by taking the reciprocal of the second fraction:
(m^2/8) * (16/m^5)
Now, we can simplify by canceling out common factors between the numerators and denominators:
(m^2 * 16) / (8 * m^5)
= (16m^2) / (8m^5)
= 2m^-3
From the provided answer of (2)/(m^4), it seems that there has been an error in the simplification. The correct answer should be 2m^-3.
Problem #2:
To multiply the expression (3x-30)/(x^2-4x) times (8x)/(10-x), we can simply multiply the numerators and the denominators:
[(3x-30) * (8x)] / [(x^2-4x) * (10-x)]
Next, we can simplify by canceling common factors:
[(3 * 8 * x * (x-10)) / (x * (x-4) * (-1) * (x-10))]
In this case, we can note that the "x-10" terms in the numerator and denominator cancel out:
[(3 * 8 * x) / (x * (x-4) * (-1))]
After simplifying further, we get:
(-24x) / (-x * (x-4))
= 24x / (x * (x-4))
= 24 / (x-4)
From the provided answer of (-6)/(x^3), it seems that there has been an error in the simplification. The correct answer should be 24 / (x-4).
Therefore, the provided answers for both problems are incorrect.