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3 years ago

Please help i cant get this one

Mathematics

1 answer:

klasskru [66]3 years ago

3 0

(2x+11) = ( 5x-19)
subtract 2x from each side. So 2x - 2x =0 and 5x - 2x = 3x.
Now your equation is 11 = 3x- 19.
Next, add 19 to each side. - 19 + 19 = 0 and 11 + 19 = 30.
Your equation is now 30 = 3x.
Now divide by 3x on each side. 3x / 3x= x and 30 / 3 = 10.
<em>So your answer would be x = 10</em>.

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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

The length and width or a rectangular courtyard is 40 feet and 30 feet, respectively. In order to make the courtyard larger, an

SpyIntel [72]

Answer:

The new area is 1800feet^2

Step-by-step explanation:

Step one:

Given data

The length and width or a rectangular courtyard is 40 feet and 30 feet

we can calculate the area of the courtyard as

Area= 40*30

Area= 1200 feet^2

when the extra 15 feet is added to the width

the new width is= 30+15= 45feet

The new area is

Area= 40*45

Area= 1800 feet^2

in all the area will increase by 1800-1200= 600feet

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3 years ago

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bixtya [17]

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3 years ago

Read 2 more answers

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MakcuM [25]

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= 1/2 * 10^2 - 1/2 pi *5^2 = 50 - 12.5pi

So area of shaded parts = area of square - 4 (50 - 12.5pi)
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6 0

4 years ago