Answer:
C(3,-4), r=4*sqrt(2)
Step-by-step explanation:
C(p, q)
x^2+y^2+dx+ey+f=0
p=-d/2, q=-e/2, r^2=p^2+q^2-f
x^2+y^2 - 6x+8y-7=0
p=-(-6)/2=6/2=3
q=-8/2=-4
r^2=3^2 +(-4)^2+7
r^2=9+16+7
r^2=32
r=sqrt(32)
r=sqrt(16*2)
r=4*sqrt(2)
Answer:
The vertex of the parabola = (-7 , -4)
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the parabola y = 4 x² + 56 x +192
y = 4 (x² + 14 x + 48 )
y = 4 ( x² + 2 × 7 (x) + 49-1)
y = 4 ( x² + 2 × 7 (x) + 49)- 4
we apply the formula
(a +b)² = a² + 2ab + b²
y = 4 ( x + 7 )² - 4
<u>Step(ii):-</u>
<em>The general form of the parabola in algebraically</em>
<em> y = a ( x-h)² +k</em>
<em>The equation </em>
<em> y = 4 ( x + 7 )² - 4</em>
y = 4 ( x-(-7))² - 4
The vertex of the parabola (h,k) = (-7 , -4)
<u>Final answer:-</u>
The vertex of the parabola = (-7 , -4)
QUESTION 12
The given figure has five unequal sides.
The perimeter is the distance around the figure.
So we add all the lengths of the sides of the rectangle to get,

We regroup the like terms to obtain,

This will simplify to give us,


QUESTION 13
The given figure has two pairs of sides that are equal in length and three unequal sides.
The perimeter can be found by adding all the lengths of the sides of the of the figure.
This will give us

We regroup like terms to obtain,

This finally simplifies to ,
.

QUESTION 14
This plane figure has four sides that are equal to 4j and two sides that are equal to 2h.
We add all the lengths of the sides of the plane figure to get,

This will simplify to give us,
21x-9+6y
combining terms: 4x+17x=21x