Answer:
The equation is ( x² / 9 ) - ( y² / 7 ) = 1
Step-by-step explanation:
Given the data in question;
hyperbola is centered at the origin, this means h and k are all equals to 0.
Vertices: (-3,0) and (3,0)
Since y-coordinates are constant, this implies it is a hyperbola with horizontal transverse axis.
h - a = -3
0 - a = -3
a = 3
Foci: (-4,0) and (4,0)
h - c = -4
0 - c = -4
c = 4
we know that, for a hyperbola
c² = a² + b²
so
⇒ ( 4 )² = ( 3 )² + b²
16 = 9 + b²
b² = 16 - 9
b² = 7
So the equation for the hyperbola will be;
⇒ ( (x-h)² / a² ) - ( (y-k)² / b² ) = 1
so we substitute
⇒ ( (x-0)² / 3² ) - ( (y-0)² / 7 ) = 1
⇒ ( x² / 3² ) - ( y² / 7 ) = 1
⇒ ( x² / 9 ) - ( y² / 7 ) = 1
Therefore, The equation is ( x² / 9 ) - ( y² / 7 ) = 1
Principal , P =$800
Rate , r = 6% = 0.06
Time , t = 3 years
Simple Interest = P*r*t = 800*0.06*3 = $144
Total Interest plus Principal = $800 + $144 = $944
Answer: Side QR
Step-by-step explanation: The sum of a triangle internal angles is 180°. So to determine the angles, we calculate x:
5x - 27 +4x - 7 + 3x + 10 = 180
12x = 204
x = 17
With x, solve for the angles:
m∠P = 5(17) - 27 = 58
m∠Q = 4(17) - 7 = 61
m∠R = 3(17) + 10 = 61
The relationship between angles and sides in any triangle:
- the largest angle is opposite the largest side;
- the middle angle is opposite to the middle-sized side;
- the shortest angle and side are opposite to each other;
So, the shortest side of PQR is the side opposite to the shortest angle.
The shortest angle is m∠P = 58°. Therefore, the shortest side is QR
623,901 is less than 692,281
Answer:
6
Step-by-step explanation:
We know that the area of a circle is equal to 
.
A semi-circle is a half-circle, meaning that it will have half of the area of a full circle.
Therefore, a semi-circle's area is equivalent to 
.
Set this equation equal to 18.
Solve for r.
We then find that r = 6.
Now, we need to find the circumference. We know that the equation for the circumference of a circle is 2r. Since we only need the perimeter of half of a circle, our circumference equation will equal r.
Plug 6 in for r.
The perimeter of the garden is equal to 6.
