Answer:
C
Step-by-step explanation (A):
[tex]\frac{4}{5}(3x+5y)[/tex]
Apply the Distributive Property
[tex]\frac{4}{5}\times3x+\frac{4}{5}\times5y[/tex]
Cross out the common factor
[tex]\frac{4}{5}\times3x+4y[/tex]
Multiply the monomials
[tex]\frac{12}{5}x+4y[/tex]
Determine true/false
[tex]Determine\ whether\ \frac{12}{5}x+\frac{20}{3}y\ and\\ \frac{4}{5}(3x+5y)\ are\ equivalent\\ False[/tex]
Step-by-step explanation (B):
[tex]\frac{4}{15}(3x-5y)[/tex]
Apply the Distributive Property
[tex]\frac{4}{15}\times3x-\frac{4}{15}\times5y[/tex]
Cross out the common factor
[tex]\frac{4}{5}x-\frac{4}{15}\times5y\\ \frac{4}{5}\times-\frac{4}{3}y[/tex]
Determine true/false
[tex]Determine\ whether\ \frac{12}{5}x+\frac{20}{3}y\ and\ \frac{4}{15}(3x-5y)\ are\ equivalent:[/tex]
[tex]False[/tex]
Step-by-step explanation (C):
[tex]\frac{4}{15}(9x+25y)[/tex]
Apply the Distributive Property
[tex]\frac{4}{15}\times9x+\frac{4}{15}\times25y[/tex]
Cross out the common factor
[tex]\frac{4}{5}\times3x+\frac{4}{15}\times25y\\ \frac{4}{5}\times3x+\frac{4}{3}\times5y[/tex]
Multiply the monomials
[tex]\frac{12}{5}x+\frac{4}{3}\times5y\\ \frac{12}{5}x+\frac{20}{3}y[/tex]
Determine true/false
[tex]Determine\ whether\ \frac{12}{5}x+\frac{20}{3}y\ and\ \frac{4}{15}(9x+25y)\ are\ equivalent:\\ True[/tex]
Step-by-step explanation (D):
[tex]\frac{4}{3}(3x-5y)[/tex]
Apply the Distributive Property
[tex]\frac{4}{3}\times3x-\frac{4}{3}\times5y[/tex]
Cross out the common factor
[tex]4x-\frac{4}{3}\times5y[/tex]
Multiply the monomials
[tex]4x-\frac{20}{3}y[/tex]
Determine true/false
[tex]Determine\ whether\ \frac{12}{5}x+\frac{20}{3}y\ and\ \frac{4}{3}(3x-5y)\ are\ equivalent:\\ False[/tex]
I hope this helps you
:)
