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Readme [11.4K]
3 years ago
10

Solve the simultaneous equation:

Mathematics
1 answer:
Lesechka [4]3 years ago
7 0

I don't approximate.  To me that's like turning a correct answer into a wrong answer.

y = 3x+5

y = 4x^2 + x

3x + 5 = 4x^2 + x

0 = 4x^2 - 2x - 5

x = \frac 1 4 (1 \pm \sqrt{1^2 - (4)(-5)})

x = \frac 1 4 (1 \pm \sqrt{21})

So there are two values for x.  Each has an associated y.  Since our quadratics have integer coefficients, the pair of ys, like the pair of xs, will be quadratic conjugates:

y_+ = 3x_++5 = \frac 3 4(1 + \sqrt{21}) + 5 = \frac 1 4(23 + 3\sqrt{21})

y_- = 3x_- +5 = \frac 3 4(1 - \sqrt{21}) + 5 = \frac 1 4(23 - 3\sqrt{21})

Answer:

(x,y) = \left( \frac 1 4 (1 + \sqrt{21}), \frac 1 4(23 + 3\sqrt{21})\right) \textrm{ or } \left( \frac 1 4 (1 - \sqrt{21}), \frac 1 4(23 - 3\sqrt{21})\right)

You're on your own for the calculate work.

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Step-by-step explanation:

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Why do the functions f(x) = sin−1(x) and g(x) = cos−1(x) have different ranges?
Gnom [1K]
We Know that
For a function to have an inverse function, it must be one-to-one—that is, it must pass the Horizontal Line Test.

1. On the interval [–pi/2, pi/2], the function y = sin x is increasing
2. On the interval [–pi/2, pi/2], y = sin x takes on its full range of values, [–1, 1]
3. On the interval [–pi/2, pi/2], y = sin x is one-to-one
sin x has an inverse function on this interval [–pi/2, pi/2]

On the restricted domain [–pi/2, pi/2]  y = sin x has a unique inverse function called the inverse sine function. <span>f(x) = sin−1(x)
</span>the range of y=sin x  in the domain [–pi/2, pi/2]  is [-1,1] 
the range of y=sin-1  x  in the domain [-1,1]  is [–pi/2, pi/2]  

1. On the interval [0, pi], the function y = cos x is decreasing
2. On the interval [0, pi], y = cos x takes on its full range of values, [–1, 1]
3. On the interval [0, pi], y = cos x is one-to-one
cos x has an inverse function on this interval [0, pi]

On the restricted domain [0, pi]  y = cos x has a unique inverse function called the inverse sine function. f(x) = cos−1(x)
the range of y=cos x  in the domain [0, pi]  is [-1,1] 
the range of y=cos-1  x  in the domain [-1,1]  is [0, pi] 

the answer is

<span>the values ​​of the range are different because the domain in which the inverse function exists are different</span>  
8 0
3 years ago
The Gleason family has a monthly budget of $4,500. Mr. Gleason has a full-time job and takes home $900 each week. Mrs. Gleason w
lana [24]

Answer:

The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month. 

Step-by-step explanation:

To answer this item, we let x be the number of hours per month that Mrs. Gleason should work. The total budget is equal to sum of the amount acquired by Mr. Gleason and Mrs. Gleason. The equation that would express this is,

                         4,500 = 900(4) + 9x

The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month. 

I am sorry if you get this wrong.

4 0
4 years ago
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