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Ira Lisetskai [31]
3 years ago
12

Abc is equilateral with AB=3x-2,BC=2x+4, and CA= x+10

Mathematics
1 answer:
yan [13]3 years ago
7 0
AB = BC, so 3x-2 = 2x+4.  Also, BC = CA, so 2x+4=x+10.

Solve this system of linear equations:

3x-2 = 2x+4
2x+4=x+10 => x=6

Check:  Does AB=BC?  Does AB=BC?

Does 3(6)-2 = 2(6)+4?  Does 16=16?  YES.
Does BC = CA?  Does 2(6)+4 = 6+10?  YES

x = 6 (answer)
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Step-by-step explanation:

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6(x + 4) = 2(y + 5) ← distribute parenthesis on both sides of the equation

6x + 24 = 2y + 10 ( subtract 10 from both sides )

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After finishing the prep work, Gilberta and María start removing wallpaper at the same time. Gilberta removes the paper at a con
Alexxx [7]

Using linear functions, the inequality that represents when Gilberta has more wallpaper left in her room than María has in hers is: t < 5.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, we consider:

  • The initial amount as the y-intercept.
  • The rate as the slope.

Hence the amounts Gilberta and Maria have left after t hours are given by:

  • G(t) = 35 - 4.3t.
  • M(t) = 30.5 - 3.4t.

Gilberta has more papers when:

G(t) > M(t).

Hence:

35 - 4.3t > 30.5 - 3.4t

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Multiplying by -1:

0.9t < 4.5

t < 4.5/0.9

t < 5.

Hence the inequality is:

t < 5.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

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