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2 years ago

Given the following equation of a circle in general form, find the equation in standard form by completing the square.

Mathematics

1 answer:

Artist 52 [7]2 years ago

3 0

The standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²

<h3>What is a circle?</h3>

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have an equation that represents the circle:

4x² + 8x + 4y² + 32y +52 = 0

Divide by 4 on both the sides:

x² + 2x + y² + 8y + 13 = 0

x² + 2x + 1 - 1 + y² + 8y + 4² - 4² + 13 = 0

x² + 2x + 1 + y² + 8y + 4² - 1 - 16 + 13

(x + 1)² + (y + 4)² = 4

(x + 1)² + (y + 4)² = 2²

Thus, the standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²

Learn more about circle here:

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Law Incorporation [45]

Hello there! The value of x is 20 or -20

"20 or - 20" is one answer so you are supposed to answer 20 or -20, not choose only one.

Step-by-step explanation:

$\large{ \frac{ {x}^{2} }{ {5}^{2} } = {4}^{2} }$

First, we simplify 5² and 4²

$\large{ \frac{ {x}^{2} }{25} = 16}$

Multiply the whole equation by 25 to get rid of the denominator.

$\large{ \frac{ {x}^{2} }{25} (25) = 16(25)} \\ \large{ {x}^{2} = 400}$

Square both sides and solve the equation.

$\large{ \sqrt{ {x}^{2} } = \pm{ \sqrt{400} }}$

Also don't forget to write "plus or minus" symbol when we are solving a quadratic equation by squaring both sides.

$\large{x = \pm{20}}$

4 0

3 years ago

Today Ian wants to run less than 7/12 mile. Write a fraction with a denominator of 4 to respresent a distance that is less than

Mkey [24]

Lan wants to run less than 7/12 miles. It says to find out a fraction with a denominator of 4 and which is less than 7/12.

Let's assume the required fraction to be x/4 such that x/4 is less than 7/12.

$\frac{x}{4} < \frac{7}{12} \\\\ 3*\frac{x}{4} < \frac{7}{12}*3 \\\\ \frac{3x}{4} < \frac{21}{12} \\\\ \frac{3x}{4} < \frac{7}{4} \\\\ 3x < 7$

So we must have multiples of 3's that should be less than 7, we have only two choices 3 < 7 or 6 < 7.

It means x = 1 or x = 2, and the required fraction would be 1/4 or 2/4.

2/4 is simplified to 1/2 and the question says to have denominator 4.

Hence, final answer is 1/4

5 0

3 years ago

*Check Photo

MaRussiya [10]

Answer:

i forgot but i did this earler

Step-by-step explanation:

5 0

3 years ago

I really need help with this question. Can I get a explanation too?

aniked [119]

Answer:

Step-by-step explanation:

Find the surface area:

Bottom base: 57 × 27 = 1,539

Top base: 21 × 27 = 567

Rectangular face: 23 × 27 = 621

Trapezoidal face: (21 + 57) ÷ 2 × 15 = 585

1,539 + 567 + 621 + 621 + 585 + 585 = 4,518

The surface area is 4,518 square inches

3 0

3 years ago

Based on a kc value of 0.200 and the given data table, what are the equilibrium concentrations of xy, x, and y, respectively?

MariettaO [177]

There is no given data table but based on the question, the reaction is
xy <=> x + y
If we let M as the initial concentration of xy and c as the in the concentration after the dissociation, then we can use the ICE method
xy <=> x + y
I M
C -c c c
-----------------------------
E M-c c c

Solve for c using
Kc = c(c) / (M - c)
And the concentration of the xy, x, and y can then be determined

3 0

3 years ago