Please correct me if I am wrong! I got A,A,B,B?

Question

15. The quadratic equation x^2 + 9 = 0, where a>0, ___________ has at least one real number solution.
a. always
b.sometimes
c.never
27. Divide. (8y^3 - 30x + 21) *divided by* (4x - 6)
a.2x^2 + 3y - 3+ 3/4x - 6
b. 2x^2 + 3x - 3 - 3 /x.
c. 2x^2 - 3x + 3 + 3/4x - 6.
d.2y^2 - 3x + 3 - 3 / 4x - 6.
28. Add -c + 6/ -12x + -x-6/-12x
a.1/3
b.x/6
c.-x - x/ - 24x
d. 1/6
29.Find the LCD of the pair of expressions 5/6x^7y^4 , 5/3x^6y^3.
a.18x^6y^3
b.6x^6y^3
c.6x^7y^4
d.18x^7y^4.

Answer 1

15) The quadratic equation x² + 9 = 0

Compare it to quadratic equation ax² + bx + c = 0

a = 1, b = 0, c = 9

Discriminant  b² - 4ac = 0 - 4(1)(9)

= - 9

since discriminant is negative, the roots are imaginary.

Option C is correct.

Answer 2

29)

Find the prime factorization of each denominator.

Multiply greatest power of each prime factor.

Option C is correct answer.

Answer 3

27) Assume the expression is

By using long division.

Divide the first term of the dividend by the first term of the divisor 8x³/4x = 2x².

So,the first term of the quotient is 2x². Multiply (4x - 6) by 2x² and subtract.

Divide the first term of the last row by first term of the divisor 12x²/4x = 3x.

So,the second term of the quotient is 3x. Multiply (4x - 6) by 3x and subtract.

Divide the first term of the last row by first term of the divisor  (- 12x)/4x = - 3.

So,the third term of the quotient is (- 3). Multiply (4x - 6) by (- 3) and subtract.

The remainder is the last entry in the last row.There fore, R = 3.

The result of the division is (8x³ - 30x + 21)/(4x - 6) = (2x² + 3x - 3) + 3/(4x - 6).

Answer 4

Assume the expression is

Option d is correct choice.