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tigry1 [53]
2 years ago
6

Point B has coordinates (−4, −2). The x-coordinate of point A is 5. The distance between points A and B is 15 units. What are th

e possible coordinates of point A?
Mathematics
1 answer:
GaryK [48]2 years ago
7 0

~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{y})\qquad B(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{AB}{15}=\sqrt{[-4 - 5]^2 + [-2 - y]^2}\implies 15^2=(-9)^2+(-2-y)^2

225=81+(-2-y)(-2-y)\implies 225=81+\stackrel{F~O~I~L}{(4+4y+y^2)} \\\\\\ 144=4+4y+y^2\implies 0=y^2+4y-140\implies 0=(y-10)(y+14) \\\\\\ y= \begin{cases} 10\\ -14 \end{cases}\qquad \qquad \qquad A(5~~,~~10)\qquad A(5~~,~~-14)

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Answer:

A) 3 in

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Geometry</u>

  • Surface Area of a Sphere: SA = 4πr²
  • Diameter: d = 2r

Step-by-step explanation:

<u>Step 1: Define</u>

SA = 23 in²

<u>Step 2: Find </u><em><u>r</u></em>

  1. Substitute [SAS]:                    23 in² = 4πr²
  2. Isolate <em>r </em>term:                         23 in²/(4π) = r²
  3. Isolate <em>r</em>:                                  √[23 in²/(4π)] = r
  4. Rewrite:                                   r = √[23 in²/(4π)]
  5. Evaluate:                                 r = 1.35288 in

<u>Step 3: Find </u><em><u>d</u></em>

  1. Substitute [D]:                    d = 2(1.35288 in)
  2. Multiply:                              d = 2.70576 in
  3. Round:                                d ≈ 3 in
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