Which two expressions are equivalent to 9(2 + n)?ResponsesA 9 + 2 • 9 + n9 + 2 • 9 + nB 2(9 + n)2(9 + n )C 9 • 2 + 9 • n9 • 2 + 9 • nD 9 • (n + 2)9 • ( n + 2)E n • 9 + n • 2
Question
Which two expressions are equivalent to 9(2 + n)?ResponsesA 9 + 2 • 9 + n9 + 2 • 9 + nB 2(9 + n)2(9 + n )C 9 • 2 + 9 • n9 • 2 + 9 • nD 9 • (n + 2)9 • ( n + 2)E n • 9 + n • 2
Solution
The two expressions equivalent to 9(2 + n) are:
C 9 • 2 + 9 • n D 9 • (n + 2)
This is because of the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, the equation a(b + c) = ab + ac holds. In this case, a is 9, b is 2, and c is n. So, 9(2 + n) = 92 + 9n, which is option C. Option D is simply a reordering of the original expression, so it is also equivalent.
Similar Questions
Which two expressions are equivalent to 9(2 + n)?ResponsesA 9 + 2 • 9 + n9 + 2 • 9 + nB 2(9 + n)2(9 + n )C 9 • 2 + 9 • n9 • 2 + 9 • nD 9 • (n + 2)9 • ( n + 2)E n • 9 + n • 2
Which expression is equivalent to (n ÷ 14) + 11?ResponsesA 14 ÷ (n + 11)14 ÷ ( n + 11)B n ÷ (14 + 11)n ÷ (14 + 11)C 11 + (n ÷ 14)11 + ( n ÷ 14)D (14 ÷ n) + 11
Which two expressions are equivalent?ResponsesA (9 + 4) • x and 9 + (4 • x)(9 + 4) • x and 9 + (4 • x )B (11 – 6) ÷ x and x ÷ (6 – 11)(11 – 6) ÷ x and x ÷ (6 – 11)C 7 + (6 • x) and 7 + (x • 6)7 + (6 • x ) and 7 + ( x • 6)D (x – 11) ÷ 7 and x – (11 ÷ 7)
Which two expressions are equivalent?ResponsesA (14 – 6) – y and 14 – (6 – y)(14 – 6) – y and 14 – (6 – y )B y ÷ (16 ÷ 4) and (y ÷ 4) ÷ 16y ÷ (16 ÷ 4) and ( y ÷ 4) ÷ 16C (9 + 7) • y and 9 + (7 • y)(9 + 7) • y and 9 + (7 • y )D (11 • 2) • y and 11 • (2 • y)(11 • 2) • y and 11 • (2 • y )
Which expression is equivalent to 2(6b+9)?
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