Find an equation of the tangent line to the circle x^2 +y^2=24 at the point (-2 square root 5, 2).

Answers

Answer 1
Answer: Circle:\n(x-a)^2+(y-b)^2=r^2\n\nPoint:\nP(x_P;\ y_P)\n\ntangent\ line\ to\ the\ circle:\n\nk:(x_p-a)(x-a)+(y_p-b)(y-b)=r^2


Circle:\nx^2+y^2=24\n\ncenter\ of\ circle:S(0;\ 0)\n\nradius:r=√(24)\n\nPoint:P(-2\sqrt5;\ 2)

tangent\ line\ to\ the\ circle:\n\nk:(-2\sqrt5-0)(x-0)+(2-0)(y-0)=(√(24))^2\n\n-2\sqrt5x+2y=24\n\n2y=2\sqrt5x+24\ \ \ \ /:2\n\ny=\sqrt5x+12-answer

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If the width and length of a rectangle are both increased by 10%, by what percent does the area of the rectangle increase? By what percent does the perimeter of the rectangle increase?

Answers

Answer:

10%

Step-by-step explanation:

We know Perimeter of rectangle

= 2 (Length + Width)

If width and length are increased by 10%

New length= L + 10/100L = (1.1) L

New width = W + 10/100W = (1.1) W

Perimeter = 2 [(1.1) L + (1.1) W]

Perimeter = 2 (1.1) (L + W)

Perimeter = (2.2) (L + W)

Increase in perimeter = 2.2 (L + W) - 2 (L + W)

The increase in Perimeter = 0.2 (L + W)

Percent increase

= 0.2 (L + W)/2 (L + W) × 100

= 0.2/2 × 100

= 0.1 × 100

= 10%

I hope this helped and if it did, please mark as Brainliest.

Final answer:

When the length and width of a rectangle are increased by 10%, the area increases by 21% and the perimeter increases by 10%.

Explanation:

The area of a rectangle is calculated by the formula Length × Width. If both the length and width are increased by 10%, the new area would be 1.1(length) × 1.1(width), which is 1.21(length × width) or 121% of the original area. So the area increases by 21%. The perimeter of a rectangle is calculated by the formula 2(Length + Width). If both the length and width increase by 10%, the new perimeter would be 2(1.1 Length + 1.1 Width) = 2.2 Length + 2.2 Width, which is 110% or 1.1 times the original perimeter. So the perimeter increases by 10% when you increase the length and width by 10%.

Learn more about Increase in Rectangle Dimensions here:

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Need help with this problem

Answers

Answer:

39°

Step-by-step explanation:

Internal angles of the triangle are:

  • x, 60° and (180° -99°)

Angle x is:

  • x = 180° - (60° + 81°)
  • x = 180° - 141°
  • x = 39°

If 4x - 3 = 5, then x=

Answers

Answer:

x=2

Step-by-step explanation:

4x-3=5

4x-3 plus 3 and 5 plus 3

4x=8

Divide both sides by 4

x=2

Answer:

X = 2

Step-by-step explanation:

This is how I got the answer:

Move constant to the right-hand + change signs

4x = 5 + 3

add

4x =5 + 3

4x = 8

Divide by both sides to get the answer of;

X = 2

The price of a gallon of unleaded gas was $2.80 yesterday. Today, the price rose to $2.87 . Find the percentage increase. Round your answer to the nearest tenth of a percent.

Answers

Earlier price is 2.80
Current price is 2.87

Increment is 
2.87 - 2.80
0.07

Increment percentage is
(0.07 / 2.80) * 100
2.5 %

List all the angles that are congruent to the given angle (72 degrees).1/2
72°
3
d
4/5
7/6
HELP!

Answers

Answer:

<2, <5, and <7.

Step-by-step explanation:

<2 and 72°, are vertical angles. Vertical angles are congruent. Therefore, <2 ≅ 72°.

<7 and 72° are corresponding angles. Corresponding angles are congruent, therefore, <7 ≅ 72°.

<5 and 72° are alternate interior angles. Alternate interior angles are congruent, therefore, <5 ≅ 72°.

Angles that are congruent to 72° are <2, <5, and <7.

Which of the following statements contains a quotient? A. 7 + 6 = 13 B. 7 × 6 = 42 C. 42 ÷ 6 = 7 D. 7 – 6 = 1

Answers

Mathematically, quotient means the solution you get when solving a division problem.

The only reliable choice is C)

Choice A) is called "the sum or total"
Choice B) is called "the product."
Choice D) is called the "the difference"

The quotient is the answer to a division problem. Therefore, C is the correct answer.