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3 years ago

Solve 4x + 2 < 2x - 2

1 answer:

7 0

$4x+2 \ \textless \ 2x-2\ \ \ |subtract\ 2\ from\ both\ sides\\\\4x \ \textless \ 2x -4\ \ \ |subtract\ 2x\ from\ both\ sides\\\\2x \ \textless \ -2\ \ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{x \ \textless \ -2}\to\boxed{x\in(-\infty;-2)}$

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Find the equation of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit.

leonid [27]

Answer-

The equations of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit are

$12x-5y+14=0 \\ 12x-5y-14=0$

Solution-

Let a point which is 1 unit away from the line 12x-5y-1=0 is (h, k)

The applying the distance formula,

$\Rightarrow \left | \frac{12h-5k-1}{\sqrt{12^2+5^2}} \right |=1$

$\Rightarrow \left | \frac{12h-5k-1}{\sqrt{169}} \right |=1$

$\Rightarrow \left | \frac{12h-5k-1}{13} \right |=1$

$\Rightarrow 12h-5k-1=\pm 13$

$\Rightarrow 12h-5k=\pm 14$

$\Rightarrow 12h-5k=14,\ 12h-5k=-14$

$\Rightarrow 12h-5k-14=0,\ 12h-5k+14=0$

$\Rightarrow 12x-5y-14=0,\ 12x-5y+14=0$

Two equations are formed because one will be upper from the the given line and other will be below it.

4 0

3 years ago

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stiv31 [10]

Answer:

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Step-by-step explanation:

You simply divide them (remember the word "per" means divide).

$\dfrac{120}{1 \frac34} \approx 68.6$

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3 years ago

If the Federal Reserve sets the reserve rate to 2%, what is the resulting money

Yuliya22 [10]

Answer:A

Step-by-step explanation:

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3 years ago

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tangare [24]

Answer:

5 and 10

Step-by-step explanation:

You have all the information you need to find the area of the circle and then subtracting that from 77 you'll have the area of the rectangle and will be able to figure out the length and height by looking at the answer options.

So the area of a triangle is 1/2(b x h) or (b x h)/2 so the base is 6 and the height is 9 so the area is 54/2 which equals 27. 77 - 27 = 50 so the area of the rectangle is 50. With the answer options provided I can see that the height of the rectangle is 5 and the length is 10.

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3 years ago

Which equation represents the line that is perpendicular to the graph

ella [17]

Answer:

Here look at this graph this is your answer.

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3 years ago