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3 years ago

The value of y varies directly as x, with a constant of variation of -8. What is the value of y when x is 7?

Mathematics

2 answers:

slega [8]3 years ago

6 0

Answer:

y = -56

Step-by-step explanation:

The equation for direct variation is

y = kx where k is the constant of variation

y = -8 x

We know x =7

y = -8*7

y = -56

denis-greek [22]3 years ago

6 0

Answer:

-56

Step-by-step explanation:

y = kx,

Where k = -8

y = -8x

y = -8(7)

y = -56

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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:

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

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

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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

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

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3 years ago

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Stels [109]

Answer:

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Step-by-step explanation:

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