All categories

3 years ago

Find the center and the radius of the circle with the equation x^2+6x+y^2+4y+12=0

Mathematics

1 answer:

Aneli [31]3 years ago

4 0

Answer:

(x + 3)² + (y+ 2)² = 1²

Step-by-step explanation:

The standard form for the equation of a circle with centre (a, b) and radius r is

(x - a)² + (y - b)² = r²

x² + 6x + y² + 4y + 12 = 0

Step 1. Subtract the constant from each side

x² + 6x + y² + 4y = -12

Step 2. Complete the squares for x and y

Square half the coefficients of x and y

(x² + 6x + 3²) + (y² + 4y + 2²) = -12 + 3² + 2²

Step 3. Write the lhs as squares of binomials

(x + 3)² + (y+ 2)² = -12 + 3² + 2²

Step 4. Convert the rhs to a square

(x + 3)² + (y+ 2)² = -12 + 9 + 4

(x + 3)² + (y+ 2)² = 1

(x + 3)² + (y+ 2)² = 1²

The graph below shows that this is the equation for a circle with

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

You might be interested in

Helppppppppppppp!!!!!!

skelet666 [1.2K]

Answer:

1. V(12) = $ 1200

2. V(20) = $ 4800

Step-by-step explanation:

The following data were obtained from the question:

V(t) = 150 × 2ᵗ/⁴

V(12) =?

V(20) =?

1. Determination of V(12)

Time (t) = 12 years

V(12) =?

V(t) = 150 × 2ᵗ/⁴

V(12) = 150 × 2¹²/⁴

V(12) = 150 × 2³

V(12) = 150 × 8

V(12) = $ 1200

2. Determination of V(20)

Time (t) = 20 years

V(20) =?

V(t) = 150 × 2ᵗ/⁴

V(20) = 150 × 2²⁰/⁴

V(20) = 150 × 2⁵

V(20) = 150 × 32

V(20) = $ 4800

4 0

3 years ago

Josue is at the Falls Church foot football game and wants to buy bags of tacos for his friends and $2 for himself. If each bag o

kondaur [170]

Ig 8 bags

explanation

6 0

3 years ago

Evaluate A 2-B 2 for A = 3 and B = -4

r-ruslan [8.4K]

Hello there, and thank you for posting your question here on brainly.

Since we know what both of the exponents are, we can rewrite the equation for it.

3 * 2 - (-4)

We can evaluate from here.

I can see we have a positive number subtracting a negative number.

Use the rule where x - (-y) = x + y

2 * 3 + 4

Now we can get solving.

2 * 3 ==> 6

6 + 4 ==> 10

10 is the final answer.

Hope this helps! ☺♥

4 0

3 years ago

The total charge that has entered a circuit element is q(t) = 6 (1 - e-7t) when t ≥ 0 and q(t) = 0 when t < 0. The current in

Bess [88]

Answer:

$A=42, B=-7$

Step-by-step explanation:

The current function of time is defined as follows:

$I(t)=\frac{dq(t)}{dt}$

where $q(t)$ is the charge function.

For the given charge function of time $q(t)=6\left( 1-e^{-7t}\right)$ we have the following current function:

$I(t)=\frac{d}{dt} \left(6\left( 1-e^{-7t}\right)\right)=42e^{-7t}$

In the problem it is proposed that $I(t)=Be^{-At}$ .

Examining the expression of $I(t)$ we obtained by deriving $q(t)$ with the expression proposed by the problem and comparing term by term:

$I(t)=Be^{-At}=42e^{-7t}$

We conclude that $A=-7$ and $B=42$ .

4 0

3 years ago

Which congruency statements could be correct for the figures? Check all that apply. MNOP ≅ STUV MNPO ≅ TSVU NPOM ≅ VUTS OPNM ≅ T

jeka94

Answer:

NPOM ≅ VUTS

OPNM ≅ TUVS

Step-by-step explanation: Given: two quadrilaterals having verticals P, N, O,M and S,T,V,U are congruent, where, OM is congruent or equal to TS and in quadrilaterals NPOM and VUTS-

since, the condition and, side UV=side OM follow for the above quadrilateral. (According to the figure)

then we can say according to the property of quadrilateral, their corresponding sides must be congruent. so they are congruent.

7 0

3 years ago

Read 2 more answers