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3 years ago

Can someone please help?

Mathematics

1 answer:

PIT_PIT [208]3 years ago

4 0

Step-by-step explanation:

are this form 1 question???

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Show work please \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

Right triangle ABC is isosceles and point M is the midpoint of the hypotenuse.

kotykmax [81]

Answer:

Step-by-step explanation:

I need this to ekk

8 0

3 years ago

Read 2 more answers

What is the value of x for which m || n? x = 40 x = 5 x = 105 x = 30

QveST [7]

Answer:

(A) x=40

Step-by-step explanation:

Given: It is given that m is parallel to n.

To find: The value of x.

Proof: It is given that m is parallel to n, from the figure it can be seen that 105° and (3x-15)° forms alternate exterior angles which are equal in measure because m is parallel to n.

Thus, $105^{\circ}=3x-15^{\circ}$

⇒ $105^{\circ}+15^{\circ}=3x$

⇒ $120^{\circ}=3x$

⇒ $\frac{120}{3}=x$

⇒ $x=40$

Thus, the value of x is 40, hence option A is correct.

4 0

3 years ago

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#22 im not sure what the first step is

swat32

To rotate a point 180° about the origin, you simply have to multiply -1 to the first and second coordinate. For your problem, just do that for all the points and list them out.

8 0

4 years ago

What is the to m(3 +m)

ella [17]

Answer:

3m+m^2

Step-by-step explanation:

3 0

3 years ago

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