Answer:

Step-by-step explanation:
A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.
The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:

The coordinates of the foci is at (±c, 0), where c² = a² + b²
Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:
I don't feel like explaining so...
a. = 4
The foci c is at +/-2√5, using c² = a² + b²:
B = 2
Substituting the value of a and b to get the equation of the hyperbola:

On #29 x = 12 and <apb = 90° and <dcb = 40° and on #30 all I dont even understand, sorry
Answer:
∠ABC= 45°
Step-by-step explanation:
∠ABC= ∠BCD (alt. ∠s, AB//CD)
(2x +15)°= (3x)°
2x +15= 3x
3x-2x= 15 <em>(</em><em>-2x </em><em>on </em><em>both </em><em>sides)</em>
x= 15
Substituting the value of x:
∠ABC
= ∠BCD
= [3(15)]°
= 45°
Solution :
It is given that four different prizes were awarded. So,
a). 4 ways for person 47 to win a prize
99 ways to give out the 2nd prize
98 ways to give the 3rd prize
97 ways to give the last prize
∴ P(99,3) = 99 x 98 x 97
b). 1 way to give person 47 their prize
1 way to give person 19 their prize
98 ways to give out the 3rd prize
97 ways to give out the last prize
So, P(98,2) = 98 x 97