Answer:
, option C.
Step-by-step explanation:
The parent function is ![f(x) = \sqrt{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7Bx%7D)
Function h:
Function h is function f shifted left 5 units.
Shifting a function f a units to the left is the same as finding ![f(x+a)](https://tex.z-dn.net/?f=f%28x%2Ba%29)
Thus:
![h(x) = f(x+5) = \sqrt{x+5}](https://tex.z-dn.net/?f=h%28x%29%20%3D%20f%28x%2B5%29%20%3D%20%5Csqrt%7Bx%2B5%7D)
The function is
, and thus, the correct answer is given by option C.
since the equation of the line passing through the given point is perpendicular to the given line(m2= -1/m1)
using the formula y=mx+c
y=2/3x +1
m1=2/3
m2= -1/2/3
m2= -3/2
the slope of the second line is -3/2 and it passes through the point(3,-2)
using the formula y-y1 = m(x-x1)
y-(-2)= -3/2(x-3)
y+2= -3/2(x-3)
multiply both sides by 2
2(y+2) = -3(x-3)
2y+4 = -3x+9
2y = -3x+5
y= -3/2x + 5/2
The answer is 5cm because 5 x 5 x 5 = 125
Answer:
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)
Step-by-step explanation:
The standard form of the equation of a parabola is (y - k)² = 4p (x - h), where
- The vertex of the parabola is (h , k)
- The focus is (h + p, k)
∵ The vertex of the parabola is (3 , -2)
∴ h = 3 and k = -2
∵ The focus is (5 , -2)
∴ h + p = 5
- Substitute h by 3 to find p
∵ 3 + p = 5
- Subtract 3 from both sides
∴ p = 2
∵ The standard form of the equation of the parabola is (y - k)² = 4p (x - h)
- Substitute the values of h , k , and p in the equation
∴ (y - -2)² = 4(2) (x - 3)
∴ (y + 2)² = 8 (x - 3)
The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)