Answer:
The coordinates of the circumcenter of this triangle are (3,2)
Step-by-step explanation:
we know that
The circumcenter is the point where the perpendicular bisectors of a triangle intersect
we have the coordinates

step 1
Find the midpoint AB
The formula to calculate the midpoint between two points is equal to

substitute the values


step 2
Find the equation of the line perpendicular to the segment AB that passes through the point (-2,2)
Is a horizontal line (parallel to the x-axis)
-----> equation A
step 3
Find the midpoint BC
The formula to calculate the midpoint between two points is equal to

substitute the values


step 4
Find the equation of the line perpendicular to the segment BC that passes through the point (3,-1)
Is a vertical line (parallel to the y-axis)
-----> equation B
step 5
Find the circumcenter
The circumcenter is the intersection point between the equation A and equation B
-----> equation A
-----> equation B
The intersection point is (3,2)
therefore
The coordinates of the circumcenter of this triangle are (3,2)
Answer:
∠ADB ≅ ∠CBD
Step-by-step explanation:
The three arcs at each of D and B identify congruent angles. However, the angles cannot be identified by their vertices alone. The 3-letter designations of the congruent angles are ...
∠ADB ≅ ∠CBD
Answer and explanation:
To solve the inequality x-2/x + x+2/x+3 < 3/2 we have to first simplify the expressions on the left side of the inequality sign. And so we multiply x by the expressions on the left side to eliminate fractions:
=x(x-2/x)+x(x+2/x)+x(3)< 3/2
=x-2+x+2+3x < 3/2
=5x < 3/2
x < 3/2/5
x < 3/2×5/1
x < 15/2
x < 7 1/2 or 7. 5
Total number of trees n = 4 + 3 + 3 = 10. Count the number of each different trees. n1=4, n2=3, n3=3. Number of ways the landscaper plant the trees in a row is = 10 ! / ( 4! * 3! * 3! ) = 3628800 / ( 24 * 6 * 6 ) = 3628800 / 864 = 4200 ways.
Therefore, the trees can be planted 4200 ways