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3 years ago

What is the solution-|-x|=-12

Mathematics

1 answer:

andreev551 [17]3 years ago

7 0

The solution to the equation includes both the positive and negative portions of the solution. x = 12, -12

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For what value of k is there one solution to the given quadratic equation (k+1)x²+4kx+2=0.

andriy [413]

Answer:

If $k = 1$ or $k = -\frac{1}{2}$ , there is only one solution to the given quadratic equation.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

The signal of $\bigtriangleup$ determines how many real roots an equation has:

$\bigtriangleup > 0$ : Two real and different solutions

$\bigtriangleup = 0$ : One real solution

$\bigtriangleup < 0$ : No real solutions

In this problem, we have the following second order polynomial:

$(k+1)x^{2} + 4kx + 2 = 0$ .

This means that $a = k+1; b = 4k; c = 2$

It has one solution if

$\bigtriangleup = 0$

$b^{2} - 4ac = 0$

$16k^{2} -8(k+1) = 0$

$16k^{2} - 8k - 8 = 0$

We can simplify by 8

$2k^{2} - k - 1 = 0$

The solution is:

$k = 1$ or $k = -\frac{1}{2}$

So, if $k = 1$ or $k = -\frac{1}{2}$ , there is only one solution to the given quadratic equation.

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3 years ago

The diameter of a circle is 10 in. Find its area in terms of pie.

kumpel [21]

Answer:

The diameter of the circle = 10 cm

The radius of the circle= 10/2= 5 cm

Step-by-step explanation:

Area of the circle = pi r^2

= pi 5^2

=3.14 *25

= 78.5 cm ^2

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2 years ago

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tankabanditka [31]

Answer:

Step-by-step explanation:

8 to the second power is 64

6 to the second power is 36

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so 10 is the length of the hypotenuse

Hope this helps!

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pochemuha

Answer:

Step-by-step explanation:

You just have to try it out for some points. I tried it for (-4,-3), (0,0), (7,0)

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2 years ago