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AVprozaik [17]
3 years ago
15

Which values for A and B will create infinitely many solutions for this system of equations

Mathematics
1 answer:
nikdorinn [45]3 years ago
8 0

Answer:

  A = 6, B = -15

Step-by-step explanation:

In order for there to be infinitely many solutions, the equations must be dependent. That is, one of them must be a multiple of the other. Here, the multiplier is apparently -1.

Comparing coefficients on the left, we see that the bottom equation has an x-coefficient that is the opposite of the one in the top equation. So, to make y-coefficients opposite, the top equation should read ...

  4x -6y = 15 . . . . . A = 6

Carrying that through, the bottom equation should read ...

  -4x +6y = -15 . . . . . B = -15

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Jobisdone [24]

Answer:

Length of Shorter leg = 27 feet

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Length of Hypotenuse = 45 feet

Step-by-step explanation:

Given:

Let,

    Length of Shorter leg = x,

According to the given condition we have

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(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}

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By using Identity (A ± B)² = A² ± 2AB +B²  we get

4x^{2} -36x+81=x^{2} +(x^{2} +18x+81)\\\\4x^{2} -2x^{2} -36x-18x=81-81\\\\2x^{2} -54x=0\\2x(x-27)=0\\2x=0 or x-27=0\\\therefore x\ cannot\ be \ zero\\\therefore x = 27 \feet

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∴  Length of Hypotenuse = 2x - 9 = 2×27 -9 = 45 feet

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Solve for A if F=MA and F=10 and M=2.5
gogolik [260]

Answer:

\boxed{\sf A = 4}

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F = MA

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Step-by-step explanation:

\sf Substituting \ values \ of \ F \ and \ M \ in \ F = MA:

\sf \implies 10 = 2.5A

\sf \implies 2.5A = 10

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\sf \implies \frac{2.5}{2.5} A  =  \frac{10}{2.5}

\sf \frac{2.5}{2.5}  = 1 :

\sf \implies  A  =  \frac{10}{2.5}

\sf \frac{4 \times  \cancel{2.5}}{ \cancel{2.5}}  = 4 :

\sf \implies A = 4

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