Answer:
Step-by-step explanation:
Answer:
C, E
Step-by-step explanation:
Here, we want to change the equation of a circle from general form to standard form. This is done by making the leading coefficients 1, completing the squares, and then rewriting the equation in standard form.
The leading coefficients of the given equation are 2, so we first want to divide by 2. This gives ...
x² +y² -4x -6y +8 = 0
Subtracting 8 puts us in better position to complete the squares.
x² +y² -4x -6y = -8
Now, we can add the squares of half the coefficients of the linear terms.
(x² -4x +4) +(y² -6x +9) = -8 +13 . . . . . . matches C
And we can simplify this to the standard form equation:
(x -2)² +(y -3)² = 5 . . . . . matches E
Answer:
21
Step-by-step explanation:
Let's solve this problem step-by-step.
STEP-BY-STEP EXPLANATION:
Let's first establish that triangle BCD is a right-angle triangle.
Therefore, we can use Pythagoras theorem to find BC and solve this problem. Pythagoras theorem is displayed below:
a^2 + b^2 = c^2
Where c = hypotenus of right-angle triangle
Where a and c = other two sides of triangle
Now we can solve the problem by substituting the values from the problem into the Pythagoras theorem as displayed below:
Let a = BC
b = DC = 24
c = DB = 26
a^2 + b^2 = c^2
a^2 + 24^2 = 26^2
a^2 = 26^2 - 24^2
a = square root of ( 26^2 - 24^2 )
a = square root of ( 676 - 576 )
a = square root of ( 100 )
a = 10
Therefore, as a = BC, BC = 10.
If we want to check our answer, we can substitute the value of ( a ) from our answer in conjunction with the values given in the problem into the Pythagoras theorem. If the left-hand side is equivalent to the right-hand side, then the answer must be correct as displayed below:
a = BC = 10
b = DC = 24
c = DB = 26
a^2 + b^2 = c^2
10^2 + 24^2 = 26^2
100 + 576 = 676
676 = 676
FINAL ANSWER:
Therefore, BC is equivalent to 10.
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Answer: 3,130
Step-by-step explanation: 2,815 + 315 = 3,130
