Question

if $x=5$, triangle 2 has the greater perimeter.
8 essay 2 points
use the gcf to factor $16 + 48$
9 essay 1 point
use the distributive property to expand $9(3+x)$

Explanation:

Step1: Find GCF of 16 and 48

Factors of 16: $1, 2, 4, 8, 16$; Factors of 48: $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$. GCF = $16$

Step2: Factor out GCF from $16+48$

$\frac{16}{16} = 1$, $\frac{48}{16} = 3$. So $16+48 = 16(1+3)$

Step3: Apply Distributive Property to $9(3+x)$

Distributive Property: $a(b+c)=ab+ac$

Step4: Calculate expanded form

$9\times3 = 27$, $9\times x = 9x$. So $9(3+x)=27+9x$

Answer:

1. $16(1 + 3)$
2. $27 + 9x$