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3 years ago

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Sammy's mother bought 2 1/2 pounds of blueberries on monday. Sammy ate 1/4 of the blueberries before be went to bed. How many po

unds did he eat on monday? 2. How many pounds were left? 3 on tuesday sammy ate 1/3 of the remaining blueberries how may pounds did he eat on tuesday? 4 did sammy eat more on monday or tuesday explain your reasoning. Thanks!

1 answer:

erma4kov [3.2K]3 years ago

3 0

1. on monday he ate .625 pounds of blueberries
2. there was 1.875 pounds of blueberries left
3.on teusday he ate 0.625 pounds again because that is a third of what was left from monday
4. sammy ate the same amount of blueberries on monday and teusday because one fourth was 0.625 and one third of what was left over was also 0.625

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3 years ago

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3 years ago

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$x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

Step-by-step explanation:

Considering the equation

$2x^2\:-\:5x\:+\:67\:=\:0$

The first step is to divide all the terms by the coefficient of $x^{2}$ which is 2.

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$\mathrm{Add\:}a^2=\left(-\frac{5}{4}\right)^2\mathrm{\:to\:both\:sides}$

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Completing the square

$\left(x-\frac{5}{4}\right)^2=-\frac{511}{16}$

Since, you had required to know the first step in completing the square for the equation above, I hope you have got the point, but let me quickly solve the remaining solution.

For $f^2\left(x\right)=a$ the solution are $f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

Solving

$x-\frac{5}{4}=\sqrt{-\frac{511}{16}}$

$x-\frac{5}{4}=\sqrt{-1}\sqrt{\frac{511}{16}}$

$x-\frac{5}{4}=i\sqrt{\frac{511}{16}}$ ∵ Applying imaginary number rule $\sqrt{-1}=i$

$x-\frac{5}{4}=i\frac{\sqrt{511}}{\sqrt{16}}$

$-\frac{5}{4}=i\frac{\sqrt{511}}{4}$

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4}$

Similarly, solving

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$x-\frac{5}{4}=-i\frac{\sqrt{511}}{4}$ ∵ Applying imaginary number rule $\sqrt{-1}=i$

$x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

Therefore, the solutions to the quadratic equation are:

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

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