Consider this system of equations.
What is the solution to the system of equations?
2.1 + y = 11
2x - 5y = 8

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06\)

Given statement solution is :- a) The area of one semi-circle at one end is  58.09 square feet.

b) The area of the garden is 274.42 square feet.

c) The area in square metres is approximately 58.09 square feet.

The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.

Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.

Now we can calculate the area of the semi-circle:

A = (π * 4.3²) / 2

A ≈ 58.09 square feet

b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.

Area of the rectangular portion = length * width

Area of the rectangular portion = 18.4 feet * 8.6 feet

Area of the rectangular portion ≈ 158.24 square feet

Area of the two semi-circles = 2 * (area of one semi-circle)

Area of the two semi-circles ≈ 2 * 58.09 square feet

Area of the two semi-circles ≈ 116.18 square feet

Total area of the garden = area of the rectangular portion + area of the two semi-circles

Total area of the garden ≈ 158.24 square feet + 116.18 square feet

Total area of the garden ≈ 274.42 square feet

c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.

Area in square meters = Total area of the garden * (0.3048)²

Area in square meters ≈ 274.42 square feet * 0.3048²

Area in square meters ≈ 25.49 square meters

Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

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Yes, Matrix B is invertible.

And, The eigenvalues of B−1 are;

⇒ (5 ± 7.68) / 14 - 1

An Invertible Matrix is a square matrix defined as invertible if the product of the matrix and its inverse is the identity matrix.

Given that;

B be a 2 ×2 matrix such that;

⇒ 7B² −5B + 3I = 0

Now,

Since, B be a 2 ×2 matrix.

And, The expression is,

⇒ 7B² −5B + 3I = 0

⇒ B² −5/7B + 3I/7 = 0

Multiply by B⁻¹, we get;

⇒ B - 5/7 + 3B⁻¹ = 0

Solve for B⁻¹;

⇒ 3B⁻¹ = - B + 5/7

⇒ B⁻¹ = - B/3 + 5/21

Thus, The matrix B is invertible.

And, The eigen value of B are;

⇒ 7B² −5B + 3I = 0

⇒ 7B² −5B + 3I = 0

⇒ B = - (-5) ± √(-5)² - 4×7×3 / 2×7

⇒ B = 5 ± √25 - 84/14

⇒ B = 5 ± √- 59 / 14

⇒ B = 5 ± 7.68 i / 14

⇒ B - 1 = (5 ± 7.68) / 14 - 1

Thus, Matrix B is invertible.

The eigenvalues of B−1 are = (5 ± 7.68) / 14 - 1

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Answer:

\(Area = 153.938040026m^2\)

\(Circumference= 43.9822971503m\)

Step-by-step explanation:

Area

\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)

Circumference

\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)

Answer:

Step-by-step explanation:

The angle bisector in this isosceles triangle is also its altitude. It meets the base segment at right angles.

  x° = 90°

__

The acute angles in a right triangle are complementary.

  y° = 90° -47°

  y° = 43°

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

22.5 \(m^{2}\)

Explanation:

The equation for the area of a triangle is \(\frac{1}{2}\)bh

In this case, the base is 9 m and the height is 5 m

9x5=45

45/2= 22.5

Answer:

23

Step-by-step explanation:

just used a calculator

Answer:

angle 1 and 3 are equal by vertically opp. angle

3x-1 = 2x +9

3x-2x = 9+1

x = 10

put the value of x in any equation

3(10)-1 = 29

angle 1 = angle 3 = 29

angle 2 + angle 3 = 180 ° (linear pair)

angle 2 = 180 -29

angle 2 = 149

angle = angle 3 = 149.

Hope it helps

Answer:2x+1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Definitions

Find the prime factorization of 6750

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 6750, start by dividing 6750 by the first prime number, 2:

⇒ 6750 ÷ 2 = 3375

As 3375 is not a prime number, we need to divide again.  3375 is not divisible by 2, so let's try dividing it by the next prime number, 3:

⇒ 3375 ÷ 3 = 1125

Continue like this until the end result is a prime number:

⇒ 1125 ÷ 3 = 375

⇒ 375 ÷ 3 = 125

⇒ 125 ÷ 5 = 25

⇒ 25 ÷ 5 = 5

As 5 is a prime number, we can stop.

Therefore, 6750 is the product of:

⇒ 6750 = 2 × 3 × 3 × 3 × 5 × 5 × 5

As 3 and 5 appear three times, we can write this using exponents:

⇒ 6750 = 2 × 3³ × 5³

3³ and 5³ are perfect cubes.  If they are multiplied together they make another perfect cube:

⇒ 3³ × 5³ = (3 × 5)³ = 15³

Therefore:

\(\sf \implies 6750=2 \times 15^3\)

\(\sf \implies \dfrac{6750}{2}=15^3\)

Therefore, the least number by which 6750 may be divided so that the quotient (result) is a perfect cube is 2.

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Answer:

Obtuse - over 90°

Acute - less than 90°

Right - 90°

Straight - 180°

1. Obtuse

2. Acute

3. Right

Answer:

Step-by-step explanation:

The cube has 6 equal faces.

Total surface area:

Answer:

A cubic function

Step-by-step explanation:

I graphed it and connected the lines on desmos then compared to the types of calculus graphs on the search engine.

The lateral surface area of a cylinder is given by the expression:

Solution

Therefore for all values of n ≥ 2

Answer:

2/3x

Step-by-step explanation:

Answer:

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hello :

note :

an equation of the circle Center at the w(a,b) and ridus : r is :

(x-a)² +(y-b)² = r²  

in this exercice : x²+y²-16x+6y+53=0

(x²-16x) +( y²+6y ) +53 = 0

(x² -2(8)x +8² -  8²) +(y² +2(3)x -3²+3² ) +53=0

(x² -2(8)x +8²) -  8² +(y² +2(3)x +3²)-3²  +53=0

(x-8)² +( y+3)² = 20

the center is :  w(8,-3) and ridus : r  = √20

Still stuck? Get 1-on-1 help from an expert tutor now.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

10 x \(5\frac{1}{3}\) x \(4\frac{1}{5}\) = 224

Step-by-step explanation:

It is B, hope this helps & please give me brainliest.

Using a system of equations, the rental cost for a movie and a video game is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is also described as simultaneous equations.

                                  Movies   Video     Total

                                                Games    Cost

First month rental           3          5          $32

Second month rental    12          2          $29

Let the rental cost per movie = x

Let the rental cost per video game = y

3x + 5y = 32 ... Equation 1

12x + 2y = 29 ... Equation 2

Multiply Equation 1 by 4:

12x + 20y = 128 ... Equation 3

Subtract Equation 2 from Equation 3:

12x + 20y = 128

-

12x + 2y = 29

18y = 99

y = 5.5

Substitute y = 5.5 in Equation 1 or 2:

12x + 2y = 29

12x + 2(5.5) = 29

12x + 11 = 29

12x = 18

x = 1.5

Thus, based on simultaneous equations, the rental cost for a movie is $1.50 while a video game's is $5.50.

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To solve this question we will use the formula for the volume of a cone and solve for h.

Recall that the volume of a cone is given by the following formula:

where h is the height, and r is its radius.

Solving the above equation for h we get:

Substituting r=3.5 cm and V=63 cu cm we get:

Answer: 4.9 cm.

Answer:

Robot will take  hour to complete each task.

The robot can complete  tasks in one hour.

Step-by-step explanation

We have been given that a robot can complete 8 tasks in 3/10 hour. Each task takes the same amount of time.

To find the time taken by robot to complete each task we will divide total time taken to complete 8 tasks by 8 as:

Now we will convert division problem into multiplication problem by flipping the 2nd fraction.

Therefore, robot will take  hour to complete each task.

To find tasks completed by robot in one hour we will use proportions.

Therefore, the robot can complete  tasks in one hour.

The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

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The best estimate we can give for the number of orange balls in the tub is 7, and the number of white balls in the tub is 43.

To calculate this, we take the number of orange balls picked (7) and divide it by the total number of balls picked (25) to get the proportion of orange balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of orange balls in the tub.

7 / 25 = 0.28

0.28 x 50 = 14

Similarly, we take the number of white balls picked (18) and divide it by the total number of balls picked (25) to get the proportion of white balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of white balls in the tub.

18 / 25 = 0.72

0.72 x 50 = 36

This method of calculation makes sense because it uses the data we have (the number of orange and white balls picked) to estimate the overall makeup of the tub. By using the proportion of orange and white balls picked, we can make an educated guess about how many of each color ball are in the tub without seeing it.

However, it's important to note that this best estimate is not necessarily accurate. The real number of orange and white balls in the tub could be different. The method used here is a probability method, it's best estimate based on the sample data. The sample data is based on a random selection of 25 balls, and the number of orange or white balls that would be picked could vary depending on the random draw. The more samples we take, the more accurate our estimate would be.

Answer:

$21.40 for each ticket

Step-by-step explanation:

Answer:

$21.1

Step-by-step explanation:

Answer:

A. x=32

B. x=55

C. y=-18

D. m=-70

E. p=3

F. t=7

G= x=-11

H. n=-25

I. u=16

J. v=27

Answer:

A) x = 32

B) x=55

C) y = -18

D) m = -70

E) p = 3

F) t = 7

G) x = -11

Step-by-step explanation:

\(A) \ \dfrac18x=4\implies x=4\times8\implies x=32\)

\(B) \ \dfrac15x=11\implies x=11\times5\implies x=55\)

\(C) \ \dfrac19y=-2\implies y=-2\times9\implies y=-18\)

\(D) \ \dfrac12m=-35\implies m=-35\times2\implies m=-70\)

\(E) \ 6p=18\implies p=\dfrac{18}6\implies p=3\)

\(F) \ 12t=84\implies t=\dfrac{84}{12}\implies t=7\)

\(G) \ 3x=-33\implies x=\dfrac{-33}3\implies x=-11\)

Given:

The relation S is:

\(S=\{(4,9),(-9,4),(0,-9),(6,6)\}\)

To find:

The domain and range of S.

Solution:

If a relation is defined by the set of ordered pairs (x,y), then the domain is the set of x-values and range is the set of y-values.

Let R be a relation defined as \(R=\{(x,y):x\in R,y\in R\}\), then \(Domain=\{x:x\in R\}\) and \(Range=\{y:y\in R\}\).

The given relation is:

\(S=\{(4,9),(-9,4),(0,-9),(6,6)\}\)

Here, x-values are 4,-9,0,6 and the y-values are 9,4,-9,6.

So, the domain and range of the given relation S are

\(Domain=\{-9,0,4,6\}\)

\(Range=\{-9,4,6,9\}\)

Therefore, \(Domain=\{-9,0,4,6\}\) and \(Range=\{-9,4,6,9\}\).