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3 years ago

Which of the following are solutions to the equation below? (4x - 1)2 = 11

Mathematics

1 answer:

babunello [35]3 years ago

3 0

(4x - 1)2 = 11
(4x - 1) = 22
4x - 1 = 22
4x = 23
x = 5.75

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Write the equation of the sphere in standard form. x^2 + y^2 + z^2 + 2x − 4y − 6z = 22

madam [21]

The equation $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ in standard form looks like $(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$ .

Given equation of sphere be $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ .

We are required to express the given equation in the standard form of the equation of sphere.

Equation is basically relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation,quadratic equation, cubic equation or many more depending on the powers of variables. The standard form of the equation of sphere looks like $x^{2} +y^{2} +z^{2} =r^{2}$ .

The given equation is $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ .

We have to break 22 which is in right side into various parts according to the left side of the equation.

$x^{2} +y^{2} +z^{2} +2x-4y-6z=-1-4-9+36$

$x^{2} +y^{2} +z^{2} +2x-4y-6z+1+4+9=36$

$x^{2} +1+2x+y^{2}+4-4y+z^{2} +9-6z=36$

$x^{2} +(1)^{2} +2*1*x+y^{2} +(2)^{2} -2*2y+z^{2} +(3)^{2} -2*3z=36$

$(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$

Hence the equation $x^{2} +y^{2} +z^{2} +2x-4y-6z=22$ in standard form looks like $(x+1)^{2} +(y-2)^{2} +(z-3)^{2} =(6)^{2}$ .

Learn more about equations at brainly.com/question/2972832

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1 year ago

What is the slope of the line.

irina [24]

Answer:

Step-by-step explanation:

I believe it's A. Hope this helps.

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2 years ago

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7hr= how many minutes

denis-greek [22]

Answer:

420 minutes

Step-by-step explanation:

1 hour = 60 minutes

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2 years ago

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(08.01)Consider the following system of equations:

amid [387]

The first one is correct.

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3 years ago

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PLEASE HELP!

____ [38]

<h3>Answer:</h3>

A. x = -2
B. (-2, -3), (-3, -1)
C. x = 0

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

Part A. The solution is represented by the point at which the graphs intersect: (-2, -3). The x-value that makes p(x) = f(x) is x = -2.

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Part B. The point found in Part A is one solution to f(x). The graph shows the line has a slope of -2, so another point will be 1 to the left and 2 up: (-3, -1). So, two solutions are ...

... (-2, -3) and (-3, -1)

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Part C. The graphs of p(x) and g(x) intersect at the point (0, 2). This means

... p(0) = g(0) = 2

So, x = 0 is the solution to the equation p(x) = g(x).

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3 years ago