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babunello [35]
3 years ago
15

Solve the equations for all values of x by completing the square x^2+62=-16x

Mathematics
1 answer:
lorasvet [3.4K]3 years ago
4 0

Answer:

x =  \sqrt{2} - 8\\x =  -\sqrt{2} - 8

Step-by-step explanation:

To complete the square, we first have to get our equation into ax^2 + bx = c form.

First we add 16x to both sides:

x^2 + 16x + 62 = 0

And now we subtract 62 from both sides.

x^2 + 16x = -62

We now have to add (\frac{b}{2})^2 to both sides of the equation. b is 16, so this value becomes (16\div2)^2 = 8^2 = 64.

x^2 + 16x + 64 = -62+64

We can now write the left side of the equation as a perfect square. We know that x+8 will be the solution because 8\cdot8=64 and 8+8=16.

(x+8)^2 = -62 + 64

We can now take the square root of both sides.

x+8 = \sqrt{-62+64}\\\\ x+8 = \pm \sqrt{2}

We can now isolate x on one side by subtracting 8 from both sides.

x = \pm\sqrt{2} - 8

So our solutions are

x =  \sqrt{2} - 8\\x =  -\sqrt{2} - 8

Hope this helped!

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(12x + y + z = 26
mel-nik [20]

Option D. D has the matrix of constants [[12], [11], [4]].

Step-by-step explanation:

Step 1:

With the given equations, we can form matrices to represent them.

The coefficients of x, y, and z form a matrix of order 3 ×3, the variables x, y, and z form a matrix of order 1 ×3 and the constants form a matrix of order 1 ×3.

Step 2:

The linear system A is represented as

\left[\begin{array}{ccc}12&1&1\\1&-11&0\\1&-1&4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}26\\17\\23\end{array}\right].

Step 3:

The linear system B is represented as

\left[\begin{array}{ccc}4&1&1\\1&-11&0\\1&-1&12\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}23\\17\\26\end{array}\right].

Step 4:

The linear system C is represented as

\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\11\\12\end{array}\right].

Step 5:

The linear system D is represented as

\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}12\\11\\4\end{array}\right].

Step 6:

Of the four options, the linear system D has the matrix of constants [[12], [11], [4]]. So the answer is option D. D.

4 0
3 years ago
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Answer:

false

Step-by-step explanation:

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This gives Katie 6083.26-5000 = 1083.26 in interest (1083, to the nearest dollar).

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This means she earned 11248.64-10000=1248.64 in interest (1249, to the nearest dollar).

The difference in interest is given by 1249-1083=166
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