Question

question #4
what is the value of $3^{2}+36div4 - 1$?
a 17
b 14
c 16.25
d 9.5
question #5
which expression correctly represents $5^{6}$?
a $5\times6$
b $5 + 6$
c $5\times5\times5\times5\times5\times5$
d $(5 + 6)\times(5 + 6)\times(5 + 6)\times(5 + 6)\times(5 + 6)$
question #6
the length and width of a rectangle are shown in the table.
which can represent the perimeter of the rectangle?
a 2 times the sum of a number n and 10.
b 6 times the sum of a number n and 4.
c the sum of 6 times a number n and 24
d the sum of 12 times a number n and 48

Explanation:

Question #4

Step1: Calculate the exponent

According to the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), first calculate \(3^{2}\).
\(3^{2}=3\times3 = 9\)

Step2: Calculate the division

Next, calculate \(36\div4\).
\(36\div4 = 9\)

Step3: Perform addition and subtraction

Now, substitute the values back into the original expression \(3^{2}+36\div4 - 1\).
\(9 + 9-1=(9 + 9)-1=18 - 1=17\)

The exponent \(a^{n}\) means \(a\) multiplied by itself \(n\) times. For \(5^{6}\), \(a = 5\) and \(n=6\), so \(5^{6}=5\times5\times5\times5\times5\times5\). Option A (\(5\times6\)) is incorrect as it represents \(5\) added \(6\) times (in a non - exponent sense). Option B (\(5 + 6\)) is just addition. Option D \((5 + 6)\times(5 + 6)\times(5 + 6)\times(5 + 6)\times(5 + 6)\) is \((11)^{5}\), not \(5^{6}\).

Step1: Recall the perimeter formula for a rectangle

The perimeter formula of a rectangle is \(P=2(l + w)\), where \(l\) is the length and \(w\) is the width. Given \(l = 6\) and \(w=n + 4\).

Step2: Substitute into the formula

\(P=2(6+(n + 4))\). Simplify the expression inside the parentheses first: \(6+(n + 4)=n+(6 + 4)=n + 10\). So \(P = 2(n + 10)\), which means \(2\) times the sum of a number \(n\) and \(10\).

Answer:

A. 17

Question #5