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Stolb23 [73]
3 years ago
7

Compare 8 ⋅ 107 to 2 ⋅ 104.

Mathematics
1 answer:
Alex73 [517]3 years ago
6 0
107 x 8 is 856 compared to 2 x 104 which is 208
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Step-by-step explanation:

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Read 2 more answers
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}

Only x=4 works when plugged in the original equation. Therefore, x=24 is extraneous and the only solution is \boxed{x=4}

4 0
2 years ago
A car travels 2 1/3 miles in 3 1/2 minutes at a constant speed. Write an equation to represent the car travels in miles and minu
Flura [38]

Answer:

The speed of car in miles per minute is  \frac{2}{3} miles per minute and

The speed of car in mile per hour is 40 miles per hour,

Step-by-step explanation:

Given as :

The distance cover by car = 2 \frac{1}{3} = \frac{7}{3} miles

The Time taken by car to cover distance =  3 \frac{1}{2} min =  \frac{7}{2} min

The speed o car in miles per minute = S miles/min

So, Speed = \dfrac{\textrm Distance}{\textrm Time}

Or, S = \frac{\frac{7}{3}}{\frac{7}{2}} mie per min

∴  S = \frac{2}{3} miles per minute

Now, Let The speed of car in miles per hour = x miles/h

So, Time in hour = \frac{7}{2} × \frac{1}{60} = \frac{7}{120} hours

So ,  Speed = \dfrac{\textrm Distance}{\textrm Time}

Or, x = \frac{\frac{7}{3}}{\frac{7}{120}} miles per hours

Or, x = 40 miles per hours

Hence The speed of car in miles per minute is  \frac{2}{3} miles per minute and the speed of car in mile per hour is 40 miles per hour, answer

7 0
3 years ago
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