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3 years ago

Explain algebraplz help

Mathematics

1 answer:

julsineya [31]3 years ago

8 0

Algebra is really easy when you try your hardest. What seems to be troubling you friend?

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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

Use a graphing calculator to graph the function and its parent function. Then describe the transformations, f(x)=(x+3)+1/4

nlexa [21]

Most of the graphing resources used shows that the graph is translated up by 3.25 (3 + 1/4). If you add the 3 and the 1/4, you get the equation of a line:

f(x) = x + 3.25,

which means that the graph of f(x)= x now has a y intercept of 3.25.

The graphs are below. The red line represents f(x) = x, and the green line represents (x+3)+1/4. Hope this helps!

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3 years ago

How did you get 0.36 from 7/20

Tema [17]

I'm confused when I did it I got .35 and you divide
hope it helped

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4 years ago

Brainliest + Points. <br><br> Can someone please help me I'm confused

mezya [45]

A would be (-3, 6).

B would be (-6, 3).

Anytime something is asking you to reflect off of the Y-axis, you put the original but flipped. Also, your answer will always be straight across vertically.

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3 years ago

HELP ME PLEASEEEEEEEEEEEEEEEE

hoa [83]

90 mm ..................

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3 years ago

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