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n200080 [17]
3 years ago
14

Find the values of y for which the distance between the point p2,-3 and q 10, y is 10 units

Mathematics
1 answer:
lina2011 [118]3 years ago
7 0

Answer:

y = - 9, y = 3

Step-by-step explanation:

Calculate distance d using the distance formula

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (10, y)

d = \sqrt{(10-2)^2+(y+3)^2}

   = \sqrt{8^2+(y+3)^2}

Given distance between points is 10, then

\sqrt{64 +(y+3)^2} = 10 ( square both sides )

64 + (y + 3)² = 100 ( subtract 64 from both sides )

(y + 3)² = 36 ( take the square root of both sides )

y + 3 = ± \sqrt{36} = ± 6 ( subtract 3 from both sides )

y = - 3 ± 6 , thus

y = - 3 - 6 = - 9

y = - 3 + 6 = 3

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Answers:

  1. C) x = plus/minus 11
  2. B) No real solutions
  3. C) Two solutions
  4. A) One solution
  5. The value <u>  18  </u> goes in the first blank. The value <u>  17  </u> goes in the second blank.

========================================================

Explanations:

  1. Note how (11)^2 = (11)*(11) = 121 and also (-11)^2 = (-11)*(-11) = 121. The two negatives multiply to a positive. So that's why the solution is x = plus/minus 11. The plus minus breaks down into the two equations x = 11 or x = -11.
  2. There are no real solutions here because the left hand side can never be negative, no matter what real number you pick for x. As mentioned in problem 1, squaring -11 leads to a positive number 121. The same idea applies here as well.
  3. The two solutions are x = 0 and x = -2. We set each factor equal to zero through the zero product property. Then we solve each equation for x. The x+2 = 0 leads to x = -2.
  4. We use the zero product property here as well. We have a repeated factor, so we're only solving one equation and that is x-3 = 0 which leads to x = 3. The only root is x = 3.
  5. Apply the FOIL rule on (x+1)(x+17) to end up with x^2+17x+1x+17 which simplifies fully to x^2+18x+17. The middle x coefficient is 18, while the constant term is 17.
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How large in square meters is the land area of australia (2941526 mi 2)?
cluponka [151]
2941526 mi^2
 The first thing you should know to solve this problem is the following conversion:
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 Applying the conversion we have:
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 Answer: 
 The land area of Australia in square meters is:
 7.61848E + 12 m ^ 2
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Answer: a) 6, 0, 10       b) yellow/orange line  

Step-by-step explanation:

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