Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this firm use the method of completing the square
Factor out - 1 from each term
y = - (x² - 9x + 12)
To complete the square
add/subtract (half the coefficient of the x- term )² to x² - 9x
y = - (x² + 2( - 
)x + 
- + 12 )
= - ( (x - )² - )
y = - (x - )² + ← in vertex form
Answer:
(x - 7)² + (y - 4)² = 49
Step-by-step explanation:
Given
Equation: x² + y² = 49
Required:
New Equation when translated 7 units right and 4 units up
Taking it one step at a time.
When the equation is translated 7 units right, this implies a negative unit along the x axis.
The equation becomes
(x - 7)² + y² = 49
When the equation is translated 4 units up, this implies a negative unit along the y axis.
(x - 7)² + (y - 4)² = 49
The expression can be further simplified but it's best left in the form of
(x - 7)² + (y - 4)² = 49
Answer:
The range interval is: (7, -1)
Step-by-step explanation:
Given the function
g(x) = -2r+5
Let us put the domain values in the interval (-1, 3)
Putting x = -1
g(x)=-2r+5
= -2(-1)+5
= 2+5
= 7
Putting x = 0
g(x)=-2r+5
= -2(0)+5
=0+5
= 5
Putting x = 1
g(x)=-2r+5
= -2(1)+5
=-2+5
= 3
Putting x = 2
g(x)=-2r+5
= -2(2)+5
=-4+5
= 1
Putting x = 3
g(x)=-2r+5
= -2(3)+5
=-6+5
= -1
Thus the range interval is: (7, -1)
Gradient = 7-(-1)/4-3
= 8
when x = 3, y = -1,
y = 8x + c
-1 = 8(3) + c
c = -1 - 24
= -25
the equation of the line is y = 8x - 25.
Answer:
70m²
Step-by-step explanation:
Area of the plot=½×28×15
= 210m²
Area used by rose plants=⅔×210 =140m²
Area used by marigold=210-140
=70m²
