PDF File For Algebra2 Questions?

1. ⁴√400/ ⁴√5 = ⁴√(400/5) = ⁴√80 = ⁴√(16 * 5)  = (2)⁴√5 = "b"

2. We can use logic to solve this one....this parabola must turn "downward"  since at  x = 1, y +2 and at x = 3, y = -10. The only  two equations that fit are either "A" or "D".......but when x = 0, "A" = -2 and that doesn't work. So "D" is correct. And f(6) = -2(6)^2 +2(6) + 2 = -72 + 12 + 2 = -58.

3. (5a + 4b)^3 = (using the binomial theorem) =

(5a)^3*b^0 + 3(5a)^2*(4b)^1 + 3(5a)^1*(4b)^2 + (5a)^0*(4b)*3 =

125a^3 + 3(25a^2*4b) + 3( 5a*16b^2) + 64b^3 =

125a³ + 300a²*b + 240ab² + 64b³  = B

3.  A

4.  A is correct .....

Sales - Costs = Profit  

12x - (8x + 20) ≥ 100    

4x - 20   ≥ 100

4x  ≥ 100 + 20

4x ≥ 120

x ≥ 30

6.  329 = 20(273 + t)^(1/2)      divide both sides by 20

(329/20) = (273 + t)^(1/2)   square both sides

(329/20)^2 = 273 + t       subtract 273 from both sides

(329/20)^2 - 273 = t  = -2C

7. 𝑥^3 − 6𝑥^2 + 8𝑥    factoring, we have

x(x^2 - 6x + 8)  = x(x-2)(x-4) = x(2-x)(4-x)  and dividing by (2-x) we have x and (4-x) for the height and length (or the length and height, as the case may be)

8. √(2𝑥 + 8) − 6 = 4   Add 6 to both sides and then square both sides....so we have

2x + 8 = 100

2x = 92

x = 46

9.  |4𝑥 + 3| = 9 + 2𝑥     We have that either   4x + 3 = 9 + 2x   or  -(4x + 3) = 9 + 2x

Solving the first, we have   2x = 6     x = 3

Solving the second, we have  -6x = 12      x = -2

10.  V = pi* (r)^2 * (r+7)

11. log₈₁ 3      says   81^x = 3      so   ( 3⁴)^x = 3¹  so  3^4x = 3¹     so 4x = 1   so x = 1/4   so  log₈₁ 3 = 1/4

12.  ??????

13. 4(3ℎ − 6)/ (1 + ℎ); ℎ = −2:    4(3(-2) − 6) / (1 + (-2)) =  4(-12)/ (-1) = -48/-1 = 48

14. Again we can use some logic here....when x = 0, y = -4    and that's "c" in ax^2 + bx + c

Also......this parabola must turn  "downward".....because at x = 4, y = -20.......so the lead coeedicient on "a" must be negative........"D" is the only possibility.....

15.    -13    (that's too easy)

16. The shaded area  = (x^2) - (3^2)   = x^2 - 9   =   (x+3)(x-3)

17.  𝑎(𝑏𝑥 + 2) = 𝑐𝑥 − 12

abx + 2a  = cx - 12

abx - cx  = -2a - 12

x (ab - c) = -(2a + 12)

x = -(2a + 12) / (ab-c)       note ......ab ≠ c  because that would nake the denominator 0 ...."A"

18.  Function....each x is matched with a different y....(.if one x were matched to two different y's......it wouldn't pass the "vertical line" test)

19. √(7x) (√x - 7√7)  =  x√7 - 7√(7x*7) =  x√7 - 7√(49*x) = x√7 - 7*7√(x) = x√7 - 49√(x) ...."a"

20.  Since we have an odd power and an odd exponent in the lead term .......when x is a large negative,,,,the graph is positive....when x is a large positive......the graph is negative.....thus, up and down......'c"

I think you should at least give yourself some points here Chris.  You put a lot of effort into this one!