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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Exponential form is when a certain number is raised to the power of a certain number or also known as exponents. Exponents signifies that the base or the number that is being raised to a certain powers will be multiplied a number of times, based on the exponents).
Exponential form is defined as repeated multiplication of the base.
The value of the <em>a, </em>in the provided quadratic equation for which Nancy found one solution as x=1 is 9.
<h3>What is the solution of equation?</h3>
The solution of the quadratic equation is the solution of the variable of the equation, for which the equation satisfies.
Nancy found that x=1 is one solution to the quadratic equation. The quadratic equation is,
For this equation, one solution is <em>x</em>=1. Put this value in the above equation to get the value of <em>a,</em>
Thus, the value of the <em>a, </em>in the provided quadratic equation for which Nancy found one solution as x=1 is 9.
Learn more about the solution of the equation here;
brainly.com/question/21283540
Answer:
The line is y=1x+8
Step-by-step explanation:
We can use point-slope form of a line to make an equation. Point-slope form is as follows:
y-y₁=m(x-x₁)
**The variables y₁ and x₁ are where we will plug in our given coordinates and the variable m is your slope.
1. Plug in the given info:
y-10=1(x-2)
2. Distribute the 1:
y-10=1x-2
3. Add 10 to both sides:
y=1x+8
