Answer:
(x − 4)² + (y − 3)² = 25
Step-by-step explanation:
The equation of a circle is:
(x − h)² + (y − k)² = r²
Given three points on the circle, we can write three equations:
(1 − h)² + (7 − k)² = r²
(8 − h)² + (6 − k)² = r²
(7 − h)² + (-1 − k)² = r²
Expanding:
1 − 2h + h² + 49 − 14k + k² = r²
64 − 16h + h² + 36 − 12k + k² = r²
49 − 14h + h² + 1 + 2k + k² = r²
Simplifying:
50 − 2h + h² − 14k + k² = r²
100 − 16h + h² − 12k + k² = r²
50 − 14h + h² + 2k + k² = r²
Subtracting the first equation from the second and third equations:
50 − 14h + 2k = 0
-12h + 16k = 0
Solving the system of equations, first reduce:
25 − 7h + k = 0
-3h + 4k = 0
Solve with substitution or elimination. Using substitution, solve for k in the first equation and substitute into the second.
k = 7h − 25
-3h + 4(7h − 25) = 0
-3h + 28h − 100 = 0
25h = 100
h = 4
k = 7h −25
k = 7(4) − 25
k = 3
Now plug these into any of the original three equations to find r.
(1 − h)² + (7 − k)² = r²
(1 − 4)² + (7 − 3)² = r²
9 + 16 = r²
25 = r²
The equation of the circle is:
(x − 4)² + (y − 3)² = 25
Graph: desmos.com/calculator/ctoljeqhnp
Answer:
We are given that triangle PQR is an isosceles triangle in which PQ = PR .
Since the base angles of an isosceles triangle are equal,
angle PQR = angle PRQ
Also, And we are given that
angle MRQ = angle NQR
In ΔQNR and ΔRMQ
∠NQR=∠MRQ (given)
QR = QR (common)
-triangles QNR is congruent to triangles RMQ - ASA - angle side angle
all even numbers
hope it really helps...!!!
Answer:
Use the given slope and point to substitute into the point-slope formula y−y1=m(x−x1).
Slope-intercept form:
y=3x²+4x−25
Point-slope form:
y+5=(3x+10)⋅(x−2)
Step-by-step explanation:
Answer:
40 N
Step-by-step explanation:
To know which bag is cheaper, you have to compare both package price as cost per kilograms of sugar. Then we can find how much we can save by finding the difference between the two values
The 500g sugar package cost is N195. Every kg is equal to 1000g, so the price will be: 195N/ (500g*1kg/1000g)= 390 N/kg
The 25kg sugar package cost is N8750. so the price will be: 8750N/25kg= 350 N/kg
The amount you save per kg if you buy 25kg package instead of 500g will be: 390 N/kg - 350N/kg = 40 N/kg
