Question

1. if a={5, 6, 7, 8, 9} and b={prime numbers}, what is a∩b?
2. (2a)(-5a)(4a²) =
3. what is the solution of |x| > 5?

a. all numbers greater than 5
b. all numbers less than 5
c. all numbers greater than 5 and all numbers less than -5

1. (1/2) ÷ (2a/3) =
2. if jill is n years old and jack is 3 years older, which one of the following equations describes jack’s age?

a. n - 3
b. 3n
c. n + 3
d. n²

1. what is the coefficient in 6y⁴?
2. what is the exponent in 6y⁴?
3. evaluate 25 - 4y, when y = 5.
4. is n² always greater than n? circle: yes or no
5. is n² always greater than n for all whole numbers? circle: yes or no

Explanation:

Step1: Identify primes in set A

Prime numbers in $A=\{5,6,7,8,9\}$ are 5,7.

Step2: Compute intersection $A\cap B$

$A\cap B = \{5,7\}$

Step3: Multiply coefficients and variables

Multiply constants: $2\times(-5)\times4=-40$; multiply variables: $a\times a\times a^2=a^{1+1+2}=a^4$. Result: $-40a^4$

Step4: Solve absolute value inequality

For $|x|>5$, split into $x>5$ or $x<-5$.

Step5: Rewrite division as multiplication

$\frac{1}{2}\div\frac{2a}{3}=\frac{1}{2}\times\frac{3}{2a}=\frac{3}{4a}$

Step6: Express Jack's age

Jack is 3 years older than Jill ($n$): $n+3$

Step7: Identify coefficient in $6y^4$

Coefficient is the numerical factor: 6

Step8: Identify exponent in $6y^4$

Exponent is the power of $y$: 4

Step9: Substitute $y=5$ into expression

$25-4\times5=25-20=5$

Step10: Test $n^2 > n$ for counterexample

If $n=0.5$, $n^2=0.25<0.5$, so answer is No.

Step11: Test whole numbers for $n^2 > n$

If $n=0$, $n^2=0$ which is not greater than 0; if $n=1$, $n^2=1$ which is equal to 1. So answer is No.

Answer:

1. $\{5, 7\}$
2. $-40a^4$
3. c. All numbers greater than 5 and all numbers less than -5
4. $\frac{3}{4a}$
5. c. $n + 3$
6. 6
7. 4
8. 5
9. No
10. No