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igomit [66]
3 years ago
6

Hiii I need help with this question!! 1.10.4 TEST coordinate geometry!

Mathematics
1 answer:
KatRina [158]3 years ago
6 0

<u>F</u><u>o</u><u>r</u><u>m</u><u>u</u><u>l</u><u>a</u>

\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}

<h3><u>S</u><u>o</u><u>l</u><u>u</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u><u>-</u><u>1</u></h3>

  • (5,7)
  • (-4,-2)

\\ \sf\longmapsto m=\dfrac{-2-7}{-4-5}

\\ \sf\longmapsto m=\dfrac{-9}{-9}

\\ \sf\longmapsto m=1

<h3><u>S</u><u>o</u><u>l</u><u>u</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u><u>-</u><u>2</u></h3>

  • (1,3)
  • (1,-10)

\\ \sf\longmapsto m=\dfrac{-10-3}{1-1}

\\ \sf\longmapsto m=\dfrac{-13}{0}

\\ \sf\longmapsto m=0

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Answers and Step-by-step explanations:

(a) We want to find the slope-intercept equation (y = mx + b), where m is the slope and b is the y-intercept. We already have two points: (2, 6200) and (7, 21200). The slope is change in y over change in x so:

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(b) We want a quadratic formula in vertex form because the problem says that Kat's account maxes out at 44100 on her 25th birthday, indicating that's the vertex. Our vertex point is (20, 44100); note that it's 20 and not 25 because she starts the account at age 5, not age 0. The generic vertex form of a quadratic is:

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Plug in our vertex:

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(c) In order to find the age when they have the same amount, we set the two equations equal:

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t = 13 or t = -3   --   obviously, years can't be negative, so t = 13.

Note, however, that t is the number of years <em>after</em> Kat and Nat are 5, so we need to add 13 to 5:

13 + 5 = 18

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