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Luden [163]
3 years ago
5

Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589.

Mathematics
1 answer:
KatRina [158]3 years ago
5 0
AB = AU + UB = 20x + 108 + 273 = 20x + 381

\cfrac{AU}{AB} =\cfrac{UV}{BC}    \\  \\  \cfrac{20x+108}{20x+381} =\cfrac{444}{703}   \\  \\ 703(20x+108)=444(20x+381)\\\\14060x+75924=8880x+169164 \\  \\ 14060x-8880x = 169164 - 75924 \\  \\ 5180x = 93240 \\  \\ x=93240/5180 \\  \\ x=18
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The solution of the system of equations is (-3 , -2)

Step-by-step explanation:

Steps for Using Linear Combinations Method)

  • Arrange the equations with like terms in columns
  • Analyze the coefficients of x or y
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∵ 3 x - 8 y = 7 ⇒ (1)

∵ x + 2 y = -7 ⇒ (2)

- Multiply equation (2) by 4 to make the coefficients of y are equal in

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∴ 4 x + 8 y = -28 ⇒ (3)

Add equations (1) and (3)

∵ 3 x - 8 y = 7 ⇒ (1)

∵ 4 x + 8 y = -28 ⇒ (3)

∴ 7 x = -21

- Divide both sides by 7

∴ x = -3

Substitute the value of x in equation (2) to find y

∵ x + 2 y = -7 ⇒ (2)

∵ x = -3

∴ -3 + 2 y = -7

- Add 3 to both sides

∴ 2 y = -4

- Divide both sides by 2

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The solution of the system of equations is (-3 , -2)

Learn more:

You can learn more about the system of the linear equations in brainly.com/question/13168205

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In essence; to determine the constant of proportionality, k in this case;

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Since the company charges, $55.50 for 3 days; we have;

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A constant rate of change means the variation in the dependent variable as dependent on the independent variable is constant

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