What is the area of a circle with a radius of 11 meters? Round your answers to the nearest tenth.
A. 34.6 m2
B. 121.0 m2
C. 380.1 m2
D. 760.3 m2

[tex]\left\{\begin{array}{ccc}y=2x&(1)\\3x+4y=22&(2)\end{array}\right[/tex]

Put (1) to (2):

[tex]3x+4(2x)=22\\3x+8x=22\\11x=22\qquad|\text{divide both sides by 11}\\\boxed{x=2}[/tex]

Substitute the value of x to (1):

[tex]y=2\cdot2\\\boxed{y=4}[/tex]

Solution:

[tex]\huge\boxed{\left\{\begin{array}{ccc}x=2\\y=4\end{array}\right}[/tex]

System A has 2 real solutions, System B has 0 real solutions and System C has 1 real solution.

Given a system of equations for A is x²+y²=17 and y=-(1÷2)x, a system of equations for B is y=x²-7x10 and y=-6x+5 and a system of equations for C is y=-2x²+9 and 8x-y=-17.

For system A,

The two systems of equations are

x²+y²=17            ......(1)

y=-1÷2x             ......(2)

Substitute the value of equation (2) into equation (1) as

x²+(-x÷2)²=17

x²+(x²÷4)=17

Simplify the above equation by taking L.C.M. as

(4x²+x²)÷4=17

5x²=68

x²=68÷5

x=±3.688

Find the value of y by substituting the value of x in equation (2).

When x=3.688 then y is

y=-(1÷2)×3.688

y=-1.844

And When x=-3.688 then y is

y=-(1÷2)×(-3.688)

y=1.844

Thus, the points where the equations of system A intersect each other is (3.688,-1.844) and (-3.688,1.844)

So, the system of equations of A has 2 real solutions.

For system B,

The two systems of equations are

y=x²-7x+10            ......(3)

y=-6x+5                ......(4)

Substitute the value of equation (4) into equation (3) as

-6x+5=x²-7x+10

x²-7x+10+6x-5=0

x²-x+5=0

Simplify the above quadratic equation using the discriminant rule,

x=(-b±√(b²-4ac))÷(2a)

Here, a=1, b=-1 and c=5

Substitute the values in the discriminant rule as

x=(1±√(1-4\times 5\times 1))÷2

x=(1±√(-19))÷2

x=(1±√(19)i)÷2

Here, the value of x goes into the complex.

So, the system of equations of B has 0 real solutions.

For system C,

The two systems of equations are

y=-2x²+9            ......(5)

8x-y=-17            ......(6)

Substitute the value of equation (6) into equation (5) as

8x-(-2x²+9)=-17

8x+2x²-9+17=0

2x²+8x+8=0

Simplify the above quadratic equation using factorization method as

2x²+4x+4x+8=0

2x(x+2)+4(x+2)=0

(2x+4)(x+2)=0

x=-2,-2

Find the value of y by substituting the value of x in equation (5).

When x=-2 then y is

y=-2(-2)²+9

y=-8+9

y=1

Thus, the point where the equations of system C intersect each other is (-2,1)

So, the system of equations of C has 1 real solutions.

Hence, the system of equations for A is x²+y²=17 and y=-(1÷2)x having 2 real solution, a system of equations for B is y=x²-7x10 and y=-6x+5 having 0 real solution and a system of equations for C is y=-2x²+9 and 8x-y=-17 having 1 real solution.

Learn about system of equations from here brainly.com/question/12962074

#SPJ4

Answer:

28

Step-by-step explanation:

2x + 7 = 4x - 7

14 = 2x

x = 7

BC = 4x = 4(7) = 28

Using the binomial distribution, it is found that there is a 0.9815 = 98.15% probability that at least one of them has been vaccinated.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are:

n = 5, p = 0.55

The probability that at least one of them has been vaccinated is given by:

[tex]P(X \leq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.55)^{0}.(0,45)^{5} = 0.0185[/tex]

Then:

[tex]P(X \leq 1) = 1 - P(X = 0) = 1 - 0.0185 = 0.9815[/tex]

0.9815 = 98.15% probability that at least one of them has been vaccinated.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

#SPJ1

Answer:

3. n>or=0

5. n>or=0

Step-by-step explanation:

3. -1<or=2n+4-5

    =-1<or=2n-1

    =1-1<or=2n

    =0<or=2n

     =n>or=0.

5. 0<or=2n+3n

  =0<or5n

  =n>or=0

The equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30 so the correct answer is option C.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Diving is the art of going down to the depth of the ocean. Divers usually go deep down in the ocean to study the dynamics of ocean life.

The equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30

Therefore the equation that can be used to describe the minimum and maximum depths Laurie wants to stay between is x + 10 = 30 and x + 10 = –30 so the correct answer is option C.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ1

Answer: 12/5

Step-by-step explanation:

[tex]3 \frac{3}{5}=\frac{18}{5}\\\\\implies \frac{2}{3} \times 3 \frac{3}{5}=\frac{2}{3} \times \frac{18}{5}\\\\=\frac{36}{15}\\\\=\boxed{\frac{12}{5}}[/tex]

Using it's concept, it is found that the inverse function is [tex]y = \sqrt{9 - x}[/tex], and the domain is [tex]x \leq 9[/tex].

The inverse of a function y = f(x) is found exchanging x and y and isolating y. The domain of the inverse is the range of the original function f(x).

In this problem, the function is:

y = 9 - x²

Then, we exchange and isolate y, hence:

[tex]x = 9 - y^2[/tex]

[tex]y² = 9 - x[/tex]

[tex]y = \sqrt{9 - x}[/tex]

The domain is [tex]9 - x \geq 0 \rightarrow x \leq 9[/tex], as looking at the graph of y = 9 - x², the range is [tex]y \leq 9[/tex].

More can be learned about inverse functions at https://brainly.com/question/8824268

#SPJ1

Answer:

The answer is A

Step-by-step explanation:

They both have a maximum of 5!

The value of the angle AED = 99 degree , Angle BEC is 99 degree , angle DEC = 81 degree , angle AEB is 81 degree

The straight line has an angle of 180 degree.

The two lines AC and BD intersects such that

∠AEB:∠BEC = 9 : 11

Let angle BEC be x

Then

Angle AEB is 9x/11

and angle AEC + BEC = 180 degree

(9x/11) + x = 180

9x +11x = 11 * 180

20x = 11 * 180

x = 99 degree

Angle BEC is 99 degree

and angle AEB is 81 degree

As Angle AED is vertically opposite to angle BEC

Therefore angle AED = 99 degree

As Angle DEC is vertically opposite to angle AEB

Therefore angle DEC = 81 degree.

To know more about Angle of Straight line

https://brainly.com/question/13037238

#SPJ1

Answer:

Option B and D

Step-by-step explanation:

Subtract 9 from both sides :

4x² + 4x - 8 = 0

Divide both sides by 4 :

x² + x - 2 = 0

Factorise using factorisation method :

x² - x + 2x -2 = 0

x(x - 1) +2(x-1) = 0

(x+2)(x-1) = 0

Solve for x

x +2 = 0   OR     x - 1 = 0        

x = -2       OR     x = 1

Answer will be Option B and D

Hope this helped and have a good day

Answer:

option b. –2 and d. 1 are correct.

*For detailed explanation refer to the attachment

Answer:

rate = 0.4 %

Step-by-step explanation:

Interest = principal x rate x time

33549 = 8635 x r x 11

33549 = 94985r

r = 33549/94985

r = 0.3532

r = 0.4

rate = 0.4 %

The measure of angle 7 is 82°.

A transversal is defined as a line that passes through two lines in the same plane at two distinct points in the geometry

Given:

angle 6= 98°

As, angle 6 and 7 forms a linear pair then

angle 6 + angle 7 = 180

98 +  angle 7= 180

angle= 180-98

angle 7 = 82°

Hence, angle 7 is 82°.

Learn more about linear pair here:

https://brainly.com/question/1757859

#SPJ1

Answer:

£196 and 400cm

Step-by-step explanation:

3.5^2 = 12.25 will give the whole floor

12.25 × 16 = 196

20^2= 400cm is the front cover of the book

The expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]

Difference of polynomials

A polynomial is a function that has a leading degree of 3 and above.

Given the expression below

(10m – 6) – (7m – 4)

Expand

10m - 6 - 7m  + 4

Collect the like terms

10m - 7m - 6 + 4

Simplify

3m -2

Hence the expression can be used to find the difference of the polynomials is [10m (–7m)] [(–6) 4]

learn more on difference of polynomial here: https://brainly.com/question/2516456

#SPJ1

If the value of the z-score is 1. Then the probability that a cat will weigh less than 11 pounds will be 0.84134.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The weight of a cat is normally distributed with a mean of 9 pounds and a standard deviation of 2 pounds.

Then the probability that a cat will weigh less than 11 pounds will be

The value of z-score will be

z = (11 – 9) / 2

z = 1

Then the probability will be

P(x < 11) = P(z < 1)

P(x < 11) = 0.84134

Thus, the probability that a cat will weigh less than 11 pounds will be 0.84134.

More about the z-score link is given below.

https://brainly.com/question/15016913

#SPJ1

ответ: д
-1/2 * 16 = -8
или 16/(-2) = -8

Answer: by rewriting equation in the form, / 1\2 16 X 4X 4 f=~1_~) (Do-2)2=g=~

Step-by-step explanation: hope this helps

Answer:

133 inches

Step-by-step explanation:

First, you need to do 22 + 17 which is 39
Next, you need to do 39 + 12 which is 51.
Next, you need to do 51 + 12 which is 63.
Next, you need to do 63 + 30 which is 93.
Lastly, you need to do 93 + 40 which is 133.

Remember This:
Perimeter is adding up all the side lengths to get your answer.


I Hope This Helped :D

Answer:

133

Step-by-step explanation:

Answer:

Option A: circle

Step-by-step explanation:

A circle is a set of points in a plane that are equidistant from a common center point.

A fraction is a way to describe a part of a whole. The value of x is 6.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The value of x can be written as,

[tex]\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{x}}} = \dfrac{7}{13}\\\\\\\dfrac{1}{1+\dfrac{1}{\dfrac{x+1}{x}}} = \dfrac{7}{13}\\\\\\\dfrac{1}{1+\dfrac{x}{x+1}} = \dfrac{7}{13}\\\\\\\dfrac{1}{\dfrac{x+1+x}{x+1}}= \dfrac{7}{13}\\\\\\\dfrac{x+1}{x+1+x}= \dfrac{7}{13}\\\\[/tex]

13x + 13 = 7x + 7 + 7x

13x + 13 = 14x + 7

x = 6

Hence, the value of x is 6.

Learn more about Fraction:

https://brainly.com/question/1301963

#SPJ1

Answer:

x < -6

Step-by-step explanation:

x -3x > 12

Combine like terms

-2x>12

Divide by -2, remembering to flip the inequality

-2x/-2 < 12/-2

x < -6

Answer:

x < -6

Step-by-step explanation:

The volume of the prism as given with dimensions is; 840cm³.

The prism given in the task content can be further subdivided to be represented by two rectangular prisms as follows;

First prism = 10cm by 6cm by 8cm.

Second prism = 5cm by 12cm by 6cm

Hence, the volume of the prism is; (10×6×8) + (5×12×6) = 840cm³.

Read more on volume of a prism;

https://brainly.com/question/4192447

#SPJ1

Coplanar points are those that are all in the same PLANE. The other point that lies on line AC is B.

Collinear Points: Points are collinear if they are all in the same straight line.

Coplanar points: Coplanar points are those that are all in the same PLANE.

A.) Another way to label KF is F K.

B.) The other point that lies on line AC is B.

C.) Yes, Any two points can form a line, thus, A and D are colinear.

D.) Coplanar points are those points that lie in the same place. Although D and K lie on the same plane,j; the point E does not lie on the same plane. Thus, points E, D, and K are not coplanar points.

Learn more about Collinear Points and Coplanar points:

https://brainly.ph/question/13096098

#SPJ1

Answer:

A

Step-by-step explanation:

guessing

He should evaluate the function f(x)=−1/3 x+4 for x=3  , Option D is the correct answer.

Interpolation is when the line of best fit is used to determine the value of a point that is within the range of plotted points.

It is given to find the value at Day 3 which lies in the range of the points used for plotting

The line for best fit is

f(x) = (-1/3)x +4

At x = 3

f(3) = (-1/3) * 3 +4

f(3) = -1+4 = 3

Therefore He should evaluate the function f(x)=−1/3 x+4 for x=3

Option D is the correct answer.

To know more about Interpolation

https://brainly.com/question/18768845

#SPJ1

Yes, because 16 divided by 4 is 4, and 12 divided by 3 is also 4

Answer: You didn't give any data about the cylinder

Step-by-step explanation:

The cylinder is just an extruded circle. To calculate the cylinder's volume you need to multiply its base circle by the cylinder's height.

To do that, get the circle's radius and square it. Multiply the squared radius by 3.14.

After that, multiply the result by the cylinder's height

Answer: 8788

Step-by-step explanation:

Use the formula and use 3 for pi

13cm is the radius

[tex]13^{3\\[/tex] = 2197

2197 x 3 = 6591

6591 x 4/3 = 8788