can a theorem easily be proved by using corollary

Answer:

1. The center is (-5, 6)

The radius is 11

2. The center is (3, -9)

The radius is 6

3. The center of the circle is (-4, -2)

The radius is 3

4. The coordinate of the center of the circle is (2, 2)

The radius of the circle is 4

5. The equation of the circle is (x - 4)² + (y + 3)² = 2²

6. The equation of the circle is (x + 1)² + (x - 10)² = 7²

7. The given point (6, 8) does not lie on the circumference of the circle

8. Yes, the point (√17, 4) lies on the circumference of the circle

9. Please find the attached graph created with the aid of MS Excel

10 Please find the attached graph created with the aid of MS Excel

11. The equation of the circle is (x - a)² + (y - b)² = c²

12. The equation of the circle is x² + y² = 1

Step-by-step explanation:

1. The equation of the circle is (x + 5)² + (y - 6)² = 121

The standard form of the equation of a circle is (x - h)² + (y - k)² = r²

Where;

The center of the circle = (h, k)

The radius of the circle = r

By comparison we have;

h = -5, k = 6, and r = √121 = 11

The center of the circle, (h, k) = (-5, 6)

The radius of the circle, r = 11

2. (x - 3)² + (x + 9)² = 36

Similar to question 1, above, we have by comparison;

h = 3, k = -9, r = √36 = 6

The center of the circle, (h, k) = (3, -9)

The radius of the circle, r = 6

3. From the graph of the circle on the coordinate plane, we have;

The center of the circle = (-4, -2)

The radius of the circle =  -1 - (-4) = 3

4. From the graph of the locus of the circle, we have;

The coordinate of the center of the circle, r = (2, 2)

The length of the radius of the circle = The distance from the center  to the point (-2, 2)

Therefore, the radius of the circle, r = 2 - (-2) = 4

5. The given radius of the circle, r = 2

The center of the circle, (h, k) = (4, -3)

The equation of a circle in standard form is  (x - h)² + (y - k)² = r²

By comparison, we have the equation of the circle given as follows;

(x - 4)² + (y - (-3))² =  (x - 4)² + (y + 3)² = 2²

The equation of the circle is (x - 4)² + (y + 3)² = 2²

6. The given radius of the circle, r = 7

The center of the circle, (h, k) = (-1, 10)

The equation of a circle in standard form is  (x - h)² + (y - k)² = r²

By comparison, we have the equation of the circle given as follows;

(x - (-1))² + (y - 10)² = (x + 1)² + (y - 10)² = 7²

The equation of the circle is (x + 1)² + (x - 10)² = 7²

7. The given point = (6, 8)

The radius, r = 4

The center of the circle = (3, 5)

The point lies on the circle if the distance. 'd', from the point to the center of the circle = The radius of the circle

∴ d = √((6 - 3)² + (8 - 5)²) = √((3² + 3²) = √(18) = 3·√2

Given that the distance from the point to the center of the circle, d = 3·√2 ≠ 4 = r, the point (6, 8), does not lie on the circumference of the circle

8. The point = (√17, 4)

Radius, r: 9

The center: (0, -4)

The distance from the point to the center of the circle, d = √((√17 - 0)² + (4 - (-4))²) = 9 = r, the radius of the circle

Therefore, given that the distance of the point from the center of the circle = The radius of the circle, the point, (√17, 4), lies on the circumference of the circle

9. The given equation of the circle is (x - 5)² + (y - 1)² = 49

Comparing with the equation of a circle in standard form, we have;

The center of the circle, (h, k) = (5, 1)

The radius of the circle, r = √49 = 7

Please find the attached graph created with the aid of MS Excel

10. The given equation of the circle is x² + (y - 3)² = 25

The center of the circle, (h, k) = (0, 3)

The radius of the circle, r = √25 = 5

Please find the attached graph created with the aid of MS Excel

11. Given that the center of the circle is (a, b) and the radius of the circle is c, the equation of a circle in standard form, (x - h)² + (y - k)² = r², becomes;

(h, k) = (a, b)

r = c

∴ (x - a)² + (y - b)² = c²

12. The diameter of the circle, d = 2 in.

The center of the circle = The origin with coordinates, (0, 0)

Therefore;

The radius of the circle. r = d/2 = 2 in./2 = 1 in.

The center of the circle, (h, k) = (0, 0)

The equation of the circle is therefore;

(x - 0)² + (y - 0)² = 1²

Which gives the equation of the circle as x² + y² = 1.

Answer:

12.05

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(2 - 1)² + [4 - (-8)]²

√(1)² + (12)²

√(1) + (144)

√145

12.05

Answer:

length = 15 feet.

Step-by-step explanation:

This paper is 15 feet across on any side. Who will deliver this monster?

Area = s^2 where s is the length of 1 side.

Area = 225 feet^2  (You sure this isn't inches).

s^2 = area

s^2 = 225        Take the square root of both sides of the equation.

sqrt(s^2) = sqrt(225)

s = 15

Answer:

120 ft

Step-by-step explanation:

Find c and multiply it by 4. You're working with one triangle only at first.

The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

cos(B)=adj/hyp

Cos(60) = 15 / hyp

hyp = 15/cos(60)

hyp = 30

Answer:

∠ a = 119°

Step-by-step explanation:

Supplementary angles sum to 180° , then

6x + 17 + 3x + 10 = 180, that is

9x + 27 = 180 ( subtract 27 from both sides )

9x = 153 ( divide both sides by 9 )

x = 17

Then

∠ a = 6x + 17 = 6(17) + 17 = 102 + 17 = 119°

Answer:

You can't find the probibilty of the event because it doesn't exist

Step-by-step explanation:

Answer:

v = 12cm³

Step-by-step explanation:

v = lwh

v= 6 * 2 * 1

v = 12cm³

Answer:

its 9?

Step-by-step explanation:

Answer:

184 m²

Step-by-step explanation:

Surface Area = 2(10*2) + 2(10*6) + 2(2*6)

Surface Area = 2(20 + 60 + 12)

Surface Area = 2(92)

Surface Area = 184 m²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

c=3

Step-by-step explanation:

8=-5(-1)^2-10(-1)+c

8=5+c

c=3

Answer:

[tex]Max\ Area = \frac{x^2}{16}[/tex]

Step-by-step explanation:

Given

[tex]P = x[/tex] ---- the perimeter of fencing

Required

The maximum area

Let

[tex]L \to Length[/tex]

[tex]W \to Width[/tex]

So, we have:

[tex]P = 2(L + W)[/tex]

This gives:

[tex]2(L + W) = x[/tex]

Divide by 2

[tex]L + W = \frac{x}{2}[/tex]

Make L the subject

[tex]L = \frac{x}{2} - W[/tex]

The area (A) of the fence is:

[tex]A = L * W[/tex]

Substitute [tex]L = \frac{x}{2} - W[/tex]

[tex]A = (\frac{x}{2} - W) * W[/tex]

Open bracket

[tex]A = \frac{x}{2}W - W^2[/tex]

Differentiate with respect to W

[tex]A' = \frac{x}{2} - 2W[/tex]

Set to 0

[tex]\frac{x}{2} - 2W = 0[/tex]

Solve for 2W

[tex]2W = \frac{x}{2}[/tex]

Solve for W

[tex]W = \frac{x}{4}[/tex]

Recall that:

[tex]L = \frac{x}{2} - W[/tex]

[tex]L = \frac{x}{2} - \frac{x}{4}[/tex]

[tex]L = \frac{2x- x}{4}[/tex]

[tex]L = \frac{x}{4}[/tex]

So, the maximum area is:

[tex]A = L * W[/tex]

[tex]A = \frac{x}{4}*\frac{x}{4}[/tex]

[tex]Max\ Area = \frac{x^2}{16}[/tex]

Answer:

$986.84

Step-by-step explanation:

exchange rate is the rate at which one currency is exchanged for another currency

Amount of dollars bought = amount of RS / selling rate

75,000 / 76 = $986.84

Answer:

1/5, 0.63, 0.71, 0.78

Step-by-step explanation:

1/5 = 0.2

Answer:

f(x)= 1/4

(4)

x

for x=1→f(1)=

4

1

⋅4

1

=1→(1; 1)

for x=2→f(2)=

4

1

⋅4

2

=

4

1

⋅16=4→(2; 4)

Answer: The graph nr 4.

Other method:

f(x)=\dfrac{1}{4}\cdot4^x=4^{-1}\cdot4^x=4^{x-1}f(x)=

4

1

⋅4

x

=4

−1

⋅4

x

=4

x−1

Used:

\begin{gathered}a^{-1}=\dfrac{1}{a}\\\\a^n\cdot a^m=a^{n\cdot m}\end{gathered}

a

−1

=

a

1

a

n

⋅a

m

=a

n⋅m

Draw the graph of y = 4^x and next shift it 1 unit right.

Answer:

For the first circle: x=40°

For the second circle: x=94°

Step-by-step explanation:

First circle:

Second circle:

Answer:

[tex]A=60m^2[/tex]

Step-by-step explanation:

formula for area of a parallelogram is [tex]A=bh[/tex] where [tex]b[/tex] stands for base and [tex]h[/tex] stands for height.

[tex]A=12(5)[/tex]

[tex]A=60[/tex]

Answer:

18 Pages are filled with photos because you do 800÷8 and you get 100 coins then since it says 82% of the album is empty since the album has 100 coins it makes it easy and you subtract 82 from 100 therefore you get 18 coins that are filled

Step-by-step explanation:

Because you do 800÷8 and you get 100 coins then since it says 82% of the album is empty since the album has 100 coins it makes it easy and you subtract 82 from 100 therefore you get 18 coins that are filled

Answer:

let the number be x.

hope it helps

Answer:

C: m∠WXY + m∠YXZ = 180°

Step-by-step explanation:

edu is annoying to do, i got you :)

Answer:

-1

Step-by-step explanation:

in negative numbers, it goes the opposite of positive numbers

15

Answer:

Solution given;

m = -7/2 , T(13, 2), W(_x, -5)

m=(y2-y1)/(x2-x1)

-7/2=(-5-2)/(x-13)

-7/2=-7/(x-13)

doing crisscrossed multiplication

x-13=2

x=2+13

x=15

Answer:

the answer is 15

Step-by-step explanation:

correct me if I'm wrong thanks

Answer:

The answer is -40 and -20

Answer:

29.6925

Step-by-step explanation:

Answer:mj,bhvb n

mnbnmb mbnmbnb

Step-by-step explanation:

Answer:

ab^2-(a-c)b-c

ab^2-ab+bc-c

ab(b-1)+c(b-1)

(b-1)(ab+c)

Answer:

Answer is 3 because

Step-by-step explanation:

a=2

20*2= 40

40-1 = 39

b = 13

so 39/13 = 3

Answer:

He sold 12 chocolates for 1 Re.

Step-by-step explanation:

He bought 15 chocolates for 1 Rupee

He sold for a profit of 25%

Sale price = profit + cost price

SP= 25%of 1 + 1 Re

SP = 0.25*1+ 1

SP = 1.25 Rs

He sold 15 chocolates fro 1.25 Rs

Chocolates            Rupees

15                            1.25

x                                1

Applying cross product

x*1.25= 15*1

x= 15*1/1.25

x= 12

He sold 12 chocolates for 1 Re.