All categories

3 years ago

NEEED HELP ASSSSAAAAPPPPP PLEASE

Mathematics

1 answer:

boyakko [2]3 years ago

4 0

Answer:

Option 2 - square root 5, 5 over 2, 2.71 repeating 71, 2 and 3 over 4.

Step-by-step explanation:

Given : Numbers 2.71 repeating 71, 2 and 3 over 4, square root 5, 5 over 2

To find : Order the set of numbers from least to greatest ?

Solution :

First we write numbers in one form i.e. in decimals,

2.71 repeating 71 = $2.7171....$

2 and 3 over 4 = $2\frac{3}{4}=\frac{11}{4}=2.75$

square root 5 = $\sqrt{5}=2.2360....$

5 over 2 = $\frac{5}{2}=2.5$

Arranging from least to greatest,

$2.2360.. < 2.5 < 2.7171.. < 2.75$

or $\sqrt{5}< \frac{5}{2} < 2.7171.. < 2\frac{3}{4}$

or square root 5, 5 over 2, 2.71 repeating 71, 2 and 3 over 4.

Therefore, Option 2 is correct.

You might be interested in

Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$