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Helen [10]
3 years ago
14

Which statement is true about the equations –3x + 4y = 12 and 1/4x –1/3 y = 1?The system of the equations has exactly one soluti

on at (–8, 3). The system of the equations has exactly one solution at (–4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.
Mathematics
1 answer:
iren [92.7K]3 years ago
4 0

Answer:

The system of the equations has no solution; the two lines are parallel.

Step-by-step explanation:

The equations have the same slope. In standard form, this can be seen as the same coefficients for x and y. We will multiply the second equation by -12 to reveal this.

\frac{1}{4} x-\frac{1}{3}y=1 \\-12(\frac{1}{4} x-\frac{1}{3}y=1)\\\frac{-12}{4} x-\frac{-12}{3}y=-12\\-3x+4y=-12

This means the equations are parallel and will never cross. There is no solution.

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Answer:  The required scale factor of the dilation is 4.  

Step-by-step explanation:  Given that the parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.

We are to find the scale factor of the dilation.

From the graph, we note that

JH = 2 units   and   J'H' = 8 units.

We know that

\textup{Scale factor of dilation}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the correponding side of the original figure}}.

Therefore, the scale factor of the given dilation is

S=\dfrac{J'H'}{JH}\\\\\\\Rightarrow S=\dfrac{8}{2}\\\\\Rightarrow S=4.

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Step-by-step explanation:

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First multiply ¹/₄ times 16. that is the same as dividing 16/4 = 4

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Another way is to change 2¹/₄ to an improper fraction and multiply

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Given :  f(x) = 5x – 2 and g(x) = 2x + 1

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Consider  (f + g)(x) = f(x) + g(x)

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