When you round you have to check the number to the right of the number you are rounding. If the number to the right is 0-4 then you keep the number the same. 5-9 the number you are rounding goes up by one. Now the 4 before the decimal point is in the ones spot. The 5 to the right of the 4 is the tenth spot and the 6 to the right of that is in the hundredth spot. so this is where we need to round. To the right of the 6 is a 4 so the number would stay the same. Now when you round you drop all the numbers after it so the number is 3184.56

6 0

3 years ago

use the discriminant to determine how many and what kind of solutions the quadratic equation x²-x=-1/4 has

pantera1 [17]

$\bf x^2-x=-\cfrac{1}{4}\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4x^2-4x=-1}\implies 4x^2-4x+1=0$

$\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+1} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} \boxed{0}&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-4)^2-4(4)(1)\implies 16-16\implies \boxed{0}$

4 0

3 years ago