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2 years ago

7

What is the solution to the equation? √x+3=12

2 answers:

djyliett [7]2 years ago

5 0

<h3>Answer:</h3>

3

<h3>Step-by-step explanation:</h3>

$\sf \sqrt{x + 3 = 12}$

$\sf = \sqrt{x = 12 - 3}$

$\sf = \sqrt{x = 9}$

$\sf = \sqrt{9}$

$\sf = \sqrt{3 \times 3}$

= 3

Paha777 [63]2 years ago

3 0

Answer:

x = 81

Step-by-step explanation:

Combine like terms: √x+3=12 becomes √x+3- 3= 12 - 3, or √x = 9.

Square both sides to obtain x: x = 81

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The given system of linear equations is expressed as

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3 years ago

Dada la ecuacion 25x2 + 4y2 = 100, determina las coordenadas de los vertices, focos, las longitudes de los respectivos ejes mayo

Likurg_2 [28]

Answer:

The given equation is

$25x^{2} +4y^{2}=100$

Which represents an elipse.

To find its elements, we need to divide the equation by 100

$\frac{25x^{2} +4y^{2} }{100} =\frac{100}{100} \\\frac{x^{2} }{4} +\frac{y^{2} }{25} =1$

Where $a^{2} =25$ and $b^{2}=4$ . Remember that the greatest denominator is $a$ , and the least is $b$ . So, we extract the square root on each equation.

$a=5$ and $b=2$ .

In a elipse, we have a major axis and a minor axis. In this case, the major axis is vertical and the minor axis is horizontal, that means this is a vertical elipse.

The length of the major axis is $2a=2(5)=10$ .

The length of the minor axis is $2b=2(2)=4$ .

The vertices are $(0,5);(0,-5)$ and $(2,0);(-2,0)$ .

Now, the main parameters of an elipse are related by

$a^{2}=b^{2} +c^{2}$ , which we are gonna use to find $c$ , the parameter of the focus.

$c=\sqrt{a^{2}-b^{2} }=\sqrt{25-4}=\sqrt{21}$

So, the coordinates of each focus are $(0,\sqrt{21})$ and $(0,-\sqrt{21})$

The eccentricity of a elipse is defined

$e=\frac{c}{a}=\frac{\sqrt{21} }{5} \approx 0.92$

The latus rectum is defined

$L=\frac{2b^{2} }{a}=\frac{2(4)}{5} =\frac{8}{5} \approx 1.6$

Finally, the graph of the elipse is attached.

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