Find the volume of the sphere

Consider a circle whose equation is x2 + y2 + 4x – 6y – 36 = 0. Which statements are true? Check all that apply. To begin conver

umka21 [38]

Answer:

1) False, to begin converting the equation to standard form, each side must be added by 36. 2) True, to complete the square for the x terms, add 4 to both sides, 3) True, the center of the circle is at (-2, 3), 4) False, the center of the circle is at (-2, 3), 5) False, the radius of the circle is 7 units, 6) False, the radius of the circle is 7 units.

Step-by-step explanation:

Let prove the validity of each choice:

1) To begin converting the equation to standard form, subtract 36 from both sides:

Let consider the following formula and perform the following algebraic operations:

(i) $x^{2} + y^{2} + 4\cdot x - 6\cdot y - 36 = 0$ Given

(ii) $x^{2} + 4\cdot x + y^{2} - 6\cdot y - 36 = 0$ Commutative Property

(iii) $(x^{2} + 4\cdot x + 4) - 4 + (y^{2} - 6\cdot y + 9) - 9 -36 = 0$ Modulative/Associative Property/Additive Inverse Existence

(iv) $(x+ 2)^{2} - 4 + (y - 3)^{2} - 9 - 36 = 0$ Perfect Trinomial Square

(v) $(x+2)^{2} +(y-3)^{2} = 4 + 9 + 36$ Commutative Property/Compatibility with Addition/Additive Inverse Existence/Modulative Property

(vi) $(x+2)^{2} + (y-3)^{2} = 49$ Definition of Addition/Result

False, to begin converting the equation to standard form, each side must be added by 36.

2) True, step (iii) on exercise 1) indicates that both side must be added by 4.

3) The general equation for a circle centered at (h, k) is of the form:

$(x-h)^{2}+ (y-k)^{2} = r^{2}$

Where $r$ is the radius of the circle.

By direct comparison, it is evident that circle is centered at (-2,3).

True, step (vi) on exercise 1) indicates that center of the circle is at (-2, 3).

4) False, step (vi) on exercise 1) indicates that the center of the circle is at (-2, 3), not in (4, -6).

5) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

6) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

5 0

2 years ago

Read 2 more answers

(5+3√2)² simplify the following

madam [21]

Answer:

$(5+3\sqrt{2} )^{2} =43+30\sqrt{2}$

≈85.43

Step-by-step explanation:

apply the binomial theorem to the square

$=(5)^{2} +2(5)(3\sqrt{2} )+(3\sqrt{2} )^{2}$

$=25+30\sqrt{2} +18\\$

$=43+30\sqrt{2}$

≈85.43

Hope this helps

3 0

2 years ago

Read 2 more answers

What is -(11+2b) in simplified form?

Stella [2.4K]

Answer and Step-by-step explanation:

To simplify, distribute the negative number.

-(11 + 2b)

-11 - 2b is the answer.

#teamtrees #PAW (Plant And Water)

I hope this helps!

3 0

3 years ago

Read 2 more answers

What is the difference between the smallest six-digit whole number and the greatest 4-digit number

spin [16.1K]

What's the smallest six-digit whole number possible?
It is 100000

try counting, six digits, right? if you even take 1 off from it, it's no longer six digits, so it is the smallest six-digit whole number possible.

what's the greatest 4-digit number?
It should be 9999
try adding 1 to it, it becomes five-digit number.

So, 9999 is the greatest 4-digit whole number possible.

To get a difference, subtraction.
100000 - 9999 = 90001

Just as a tip, for six digit number, 000000 does not work, as it is same as 0

8 0

3 years ago

You have $400 saved in your banking account. You save $50 a week. Mr Brierley has $2000 in his bank account but only saves $25 a

lakkis [162]

Answer:

64 weeks

Step-by-step explanation:

Given that you already have $400 saved and you save $50 per week, in x weeks, you would have saved:

400 + (50 * x)

Also, given that Mr Brierley has $2000 in his bank account and he saves $25 per week, in x weeks, he would have:

2000 + (25 * x)

You and Mr Brierley would have the same amount of money when:

400 + (50 * x) = 2000 + (25 * x)

Solving for number of weeks, x, we have:

400 + 50x = 2000 + 25x

Collecting like terms:

50x - 25x = 2000 - 400

25x = 1600

x = 1600 / 25

x = 64

Hence, it will take 64 weeks for you and Mr Brierley to have the same amount of money.

4 0

3 years ago