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4 years ago

Say I buy a violin for $860 and I have to pay 7% sales tax, how much do I pay in all

Mathematics

2 answers:

Natalija [7]4 years ago

6 0

$920.2 in all I believe

Alex_Xolod [135]4 years ago

6 0

$920.20 since the .2 is equal to 20 cents

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Find the range of p in equation p(x+1) (x-3)=x-4p-2 has no real roots.

Tanya [424]

Answer:

$\displaystyle p > \frac{1}{4}$ .

Step-by-step explanation:

Expand the left-hand side of this equation:

$p\, (x + 1)\, (x - 3) = p\, \left(x^2 - 2\, x - 3\right) = p\, x^2 - 2\, p\, x - 3\, p$ .

Collect the terms, so that this quadratic equation is in the form $a\, x^2 + b\, x+ c = 0$ :

$p\, x^2 - 2\, p\, x - 3\, p = x - 4\, p - 2$ .

$p\, x^2 - (2\, p + 1)\, x + (p + 2) = 0$ .

In this equation:

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$b = -(2\, p + 1)$ .
$c = p + 2$ .

Calculate the quadratic discriminant of this quadratic equation:

$\begin{aligned}b^2 - 4\, a\, c &= (-(2\, p + 1))^2 - 4\, p\, (p + 2) \\ &= 4\, p^2 + 4\, p + 1 - 4\, p^2- 8\, p = -4\, p + 1\end{aligned}$ .

A quadratic equation has no real root if its quadratic discriminant is less then zero. As a result, this quadratic equation will have no real root when $-4\, p + 1 < 0$ . Solve for the range of $p$ :

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