Please help with these three questions

Step-by-step explanation:

44). Given function is,

      f(x) = 7x² - 3x - 1

      x intercept means value x at f(x) = 0.

      Therefore, for f(x) = 0

       7x² - 3x - 1 = 0

       By quadratic formula,

       x =

          =

          =

       Therefore, x - intercepts are x = ≈ -0.22, 0.65

45). f(x) = x² + 4x + 7

      For x intercepts, f(x) = 0

      x² + 4x + 7 = 0

      By quadratic formula,

      x =

         =

         = (-2 ± i)

      Since, x intercepts are imaginary, there are no x-intercepts.

46). Given formula for the projectile is,

      s = 96t - 16t²

      For s = 96 ft

      96 = 96t - 16t²

      6 = 6t - t²

      0 = -t² + 6t - 6

      t² - 6t + 6 = 0

      By quadratic formula,

      t =

      t =    

      t =

      t = (3 ± √3) ≈ 1.27 seconds, 4.73 seconds

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

ab will be equal to