Is the function described by the points in this table linear or nonlinear?

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

Solve for x in this circle.

Katen [24]

Answer:

Step-by-step explanation:

7*(7 + x+1) = 6*(x + 5 + 6) {Intersecting secant theorem}

7 *(x + 8) = 6*(x + 11)

Distributive property,

7x + 56 = 6x + 66

Subtract 56 from both sides

7x = 6x + 66 - 56

7x = 6x + 10

Subtract 6x from both sides

7x - 6x = 10

x = 10

8 0

2 years ago

What number multiplied by itself 3 times equals 9?

Harlamova29_29 [7]

The answer is 3 3x3x3=9

Hope this helped:)

5 0

3 years ago

Read 2 more answers

you have a bag with 20 marbles 2 yellow 5 green 12 red and 1 blue which of the following statements are true? Select all that ap

NNADVOKAT [17]

An event has probability 1 if you're certain that it will happen. You are sure to pick a marble that's either yellow, green, red, or blue. So, this probability is 1.
There are more yellow marbles than blue marbles, so it's actually more likely that you'll pick a yellow one, rather than the blue one.
The probability of picking a green marble is given by the number of green marbles divided by the total number of marbles. Compute this ratio and see what you get.
Similarly, the probability of picking a black marble is given by the number of black marbles divided by the total number of marbles. There are no black marbles, so...

5 0

2 years ago

Extra points!! A candle is 17 in tall after burning for 3 hours. After 5

PIT_PIT [208]

Answer:

1) $h=-t+20$