Question

1. give an example of an irrational number____ 5) simplify: 8÷(6 - 4) 6) simplify: (6)(2)+4 - 2^3 7) simplify (finding the error) explain your reasoning: (9-(6 - 1))÷4 (3 - 1)÷4 (2)÷4 2/4 = 1/2 8) find the hypotenuse: 9 12 9)find the missing leg show your work:

Explanation:

Step1: Answer question 4

An irrational number cannot be written as a fraction. $\pi$ is a common example.

Step2: Simplify 8÷(6 - 4) in question 5

First, solve the parentheses.
$6-4 = 2$
Then, perform the division.
$8\div2=4$

Step3: Simplify (6)(2)+4 - 2³ in question 6

First, calculate the exponent.
$2^3=2\times2\times2 = 8$
Then, calculate the multiplication.
$(6)(2)=12$
Now, perform the addition - subtraction.
$12 + 4-8=8$

Step4: Find error in (9-(6 - 1))÷4 in question 7

The error is in the first - step calculation. First, solve the innermost parentheses: $6 - 1=5$, then $9-5 = 4$, and $4\div4=1$. The original solution wrongly calculated $9 - 6$ first.

Step5: Find the hypotenuse in question 8

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 9$, $b = 12$.
$c=\sqrt{9^{2}+12^{2}}=\sqrt{81 + 144}=\sqrt{225}=15$

Step6: Assume the ladder problem in question 9 is a right - triangle problem

Let the length of the ladder be the hypotenuse $c = 15$, and one leg $a$ (height on the wall) be unknown, and the other leg $b = 9$.
Using the Pythagorean theorem $a=\sqrt{c^{2}-b^{2}}$.
$a=\sqrt{15^{2}-9^{2}}=\sqrt{225 - 81}=\sqrt{144}=12$

Answer:

1. $\pi$
2. 4
3. 8
4. The correct answer is 1. The error was in not solving the innermost parentheses first.
5. 15
6. 12