The correct answer is: [D]: "17" .
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The radius is: " 17" .
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Note:
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The formula/equation for the graph of a circle is:
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(x − h)² +<span> </span> (y − k)² = r² ;
in which:
" (h, k) " ; are the coordinate of the point of the center of the circle;
"r" is the length of the "radius" ; for which we want to determine;
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We are given the following equation of the graph of a particular circle:
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→ (x − 4)² + (y + 12)² = 17² ;
which is in the correct form:
→ " (x − h)² + (y − k)² = r² " ;
in which: " h = 4 " ;
" k = -12" ;
"r = 17 " ; which is the "radius" ; which is our answer.
→ { Note that: "k = NEGATIVE 12" } ;
→ Since the equation <u>for this particular circle</u> contains the expression: _________________________________________________________
→ "...(y + k)² ..." ;
[as opposed to the standard form: "...(y − k)² ..." ] ;
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→ And since the coordinates of the center of a circle are represented by:
" (h, k) " ;
→ which are: " (4, -12) " ; (<u>for this particular circle</u>) ;
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→ And since: " k = -12 " ; (<u>for this particular circle</u>) ;
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then:
" [y − k ] ² = [ y − (k) ] ² = " [ y − (-12) ] ² " ;
= " ( y + 12)² " ;
{NOTE: Since: "subtracting a negative" is the same as "adding a positive" ;
→ So; " [ y − (-12 ] " = " [ y + (⁺ 12) ] " = " (y + 12) "
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Note: The above explanation is relevant to confirm that the equation is, in fact, in "proper form"; to ensure that the: radius, "r" ; is: "17" .
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→ Since: "r = 17 " ;
→ The radius is: " 17 " ;
which is: Answer choice: [D]: "17" .
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It would be the first one (x,-y) because say for example you take the point of v1 (4,-1) and reflect across x axis you get (4,1) for v
Answer:
5.5
Step-by-step explanation:
57-29.5 / 10-5 = 5.5
Answer:
x=4 cm
Step-by-step explanation:
x=smallest side
4x=hypotenuse
4√15=third side
use the Pythagorean Theorem
(4x)^2=x^2+(4√15)^2
16x^2=x^2+240
16x^2-x^2=240
15x^2=240
x^2=240/15
x^2=16
x=√16
x=4 cm is the smallest side
the hypotenuse is 16 cm
the third side is 4√15 cm
10 and 12 you never get the number that’s on the slanted side I learned this but I forgot if u add or multiply but the digits that should be used r 10 and 12
