How many thirds in 10?
1 answer:
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Answer:
Circumcenter =(-1,0)
Orthocenter =(2,-3)
Step-by-step explanation:
Given : Points A = (2,3), B = (-4,-3), C = (2,-3)
Formula used :
→Mid point of two points-
→Slope of two points -
→Perpendicular of a line =
Circumcenter- The point where the perpendicular bisectors of a triangle meets.
Orthocenter-The intersecting point for all the altitudes of the triangle.
To find out the circumcenter we have to solve any two bisector equations.
We solve for line AB and AC
So, mid point of AB =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of the perpendicular bisector = -1
Equation of AB with slope -1 and the coordinates (-1,0) is,
(y – 0) = -1(x – (-1))
y+x=-1………………(1)
Similarly, for AC
Mid point of AC =
Slope of AC =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of the perpendicular bisector = 0
Equation of AC with slope 0 and the coordinates (2,0) is,
(y – 0) = 0(x – 2)
y=0 ………………(2)
By solving equation (1) and (2),
put y=0 in equation (1)
y+x=-1
0+x=-1
⇒x=-1
So the circumcenter(P)= (-1,0)
To find the orthocenter we solve the intersections of altitudes.
We solve for line AB and BC
So, mid point of AB =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of CF = -1
Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF
(y – 0) = -1(x – (-1))
y+x=-1………………(3)
Similarly, mid point of BC =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of AD = 0
Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD
(y-(-3)) = 0(x – (-1))
y+3=0
y=-3………………(4)
Solve equation (3) and (4),
Put y=-3 in equation (3)
y+x=-1
-3+x=-1
x=2
Therefore, orthocenter(O)= (2,-3)
Answer:
D).
Step-by-step explanation:
For better clarity let us re write the options
A).
B).
C).
D).
To express polynomial with mixed variables in standard form, we begin by the highest coefficient of x to the smallest (we place high precedence on the coefficient x terms)
The correct question is
<span>If you are paid $5.50/hour for mowing yards, and you take 3 1/3 hours to mow a yard, how much money are you owed
see the attached figure
we know that
3 1/3 hours-----> (3*3+1)/3----> 10/3 hours
Multiply </span>$5.50/hour by (10/3) hour
so
5.5*10/3----> $18.33
the answer is
$18.33
<span>If you are paid $5.50/hour for mowing yards, and you take 3 1/3 hours to mow a yard, how much money are you owed
see the attached figure
we know that
3 1/3 hours-----> (3*3+1)/3----> 10/3 hours
Multiply </span>$5.50/hour by (10/3) hour
so
5.5*10/3----> $18.33
the answer is
$18.33