How many solutions does the following system of linear equations have?

2x-3y = 4
4x - 6y = 8

Answer:

Area = 24.75 sqr units

Step-by-step explanation:

You will need these formulas:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Midpoint = [tex](\frac{x_{1} + y_{1} }{2} , \frac{x_{2} + y_{2} }{2})[/tex]

Area = b x h

Let us treat CD as the base. Find the length of the base with the distance formula. Use the coordinates for points C & D.

[tex]d = \sqrt{(-2 - (-8))^2 + (-8-(-7))^2}[/tex]

[tex]d = \sqrt{37}[/tex]

The base is [tex]\sqrt{37}[/tex].

The height is the distance between point E and the midpoint of line CD.

Midpoint of CD = [tex](\frac{-8 + (-7) }{2} , \frac{-2 + (-8) }{2})[/tex] = ([tex]-\frac{15}{2}[/tex], [tex]-5[/tex])

Use the distance formula to find the height.

[tex]d = \sqrt{(-5 - (-\frac{15}{2} ))^2 + (-2-(-5))^2}[/tex]

[tex]d = \frac{\sqrt{61} }{2}[/tex]

Find the area with the two distances that were found.

Area = [tex](\sqrt{37}) (\frac{\sqrt{61} }{2})[/tex]

Area = [tex]\frac{\sqrt{2257} }{2}[/tex]

Area = 24.75 sqr units

Answer:

(a) 100

(b) 10.27

Step-by-step explanation:

We are given  

No of elements = 15  

Σ(x-c) = 72,Σ(x-c)^2 = 499.6

,where c is a constant

and the sample mean is 104.8.

(a)  lets take into account Σ(x-c) = 72

this means that we have the sum of the 15 elements of x and each element of x is subtracted by the constant c

so the equation becomes Σxi -15c = 72, ............(1)

where xi means the sum of the elements of x from 1 to 15.

we are given the mean as 104.8

this means that Σxi/15 = 104.8

Σxi = 15*104.8 = 1572 .............(2)

substituting (2) in (1)

we get  

1572 - 15c = 72  

15c = 1500  

c = 100

(b) We will use the property that variance does not change when a constant value is added or subtracted to the elements. This we can observe in the given equation that c is a constant that has the value of 100.

so the variance is  

σ^2 = Σ(x-c)^2/15  - (Σ(x-c)/15 )^2

      = 499.6/15  - (72/15)^2

      = 33.31 - 23.04

   σ^2   = 10.27

Therefore the variance of the given problem is 10.27.

The surface area of the trumpet is [tex]\( 1256.64 \pi \)[/tex] square feet.

To find the surface area of the trumpet, we need to calculate the areas of the curved surface and the base separately, and then sum them.

The curved surface area of a truncated cone can be calculated using the formula:

[tex]\[ CSA = \pi \times (r_1 + r_2) \times l \][/tex]

Where [tex]\( r_1 \) and \( r_2 \)[/tex] are the radii of the two bases, and [tex]\( l \)[/tex] is the slant height of the truncated cone.

Given that the base diameter is [tex]40[/tex] feet, the radius of the larger base [tex](\( r_1 \))[/tex] is half of that, which is [tex]20[/tex] feet. The slant height [tex](\( l \))[/tex] can be calculated using the Pythagorean theorem:

[tex]\[ l = \sqrt{(h^2 + (r_1 - r_2)^2)} \][/tex]

The height [tex]h[/tex] of the truncated cone is [tex]30[/tex] feet, and the radius of the smaller base [tex](\( r_2 \))[/tex] can be calculated as half the diameter, which is [tex]10[/tex] feet.

Substituting the values into the equations:

[tex]\[ l = \sqrt{(30^2 + (20 - 10)^2)} = \sqrt{(900 + 100)} = \sqrt{1000} = 10\sqrt{10} \]\[ CSA = \pi \times (20 + 10) \times (10\sqrt{10}) = 30\pi\sqrt{10} \][/tex]

The base area of the truncated cone is the area of a circle with radius [tex]\( r_1 \):\[ BA = \pi \times r_1^2 = \pi \times 20^2 = 400\pi \][/tex]

Finally, we can find the total surface area by adding the curved surface area and the base area:

[tex]\[ Surface \, Area = CSA + BA = 30\pi\sqrt{10} + 400\pi \][/tex]

[tex]\[ Surface \, Area = 30\pi\sqrt{10} + 400\pi \]\[ Surface \, Area = \pi(30\sqrt{10} + 400) \]\[ Surface \, Area \approx 1256.637 \pi \]\[ Surface \, Area \approx 1256.64 \pi \][/tex]

Therefore, the simplified surface area of the trumpet is approximately [tex]\( 1256.64 \pi \)[/tex] square feet.

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To achieve this, the students must enter +31 (forward) to bring the robot back to its starting position of 0.

The robot can move forward or backward depending on the type of number entered into the control unit. For example, entering a negative number causes the robot to roll backward a specific number of inches,

while entering a positive number makes it move forward a certain number of inches. If −5 is entered, the robot moves backwards by 5 inches. As a result, the students entered the numbers −37, +22, and −16 to move the robot.

The question asks what number needs to be entered to bring the robot back to its starting position of zero. To do so, we must first calculate how far the robot has traveled in total.

When a negative number is entered into the control unit, the robot rolls backward.

As a result, when we add the negative numbers and subtract them from the positive number,

we can determine the total distance traveled by the robot.-37 (back) + 22 (forward) - 16 (back) = -31 (inches traveled)Since the robot moved a total of 31 inches,

the students must enter the opposite number to bring the robot back to its starting position of 0.

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Answer:

k²+16k+ 153

Step-by-step explanation:

k²+16k+64+89

= k²+16k+ 153

Answer:

It's 11.72

Step-by-step explanation:

Area=)1/2×15/4×25/4

Answer》11.72

Hope it helps...

Have a great day

Answer:

i have made it in above picture

To estimate Δf = f(3.5) - f(3) using the linear approximation, we'll use the formula:

Δf ≈ f'(a) * Δx

where f'(a) represents the derivative of f at the point a, and Δx represents the change in the x-values.

Given that f(x) = 41 + [tex]x^2[/tex], we can calculate the derivative as:

f'(x) = 2x

Now, let's calculate the values step by step:

Calculate Δf:

Δf ≈ f'(a) * Δx

Δf ≈ f'(3) * (3.5 - 3)

Δf ≈ 2(3) * (3.5 - 3)

Δf ≈ 6 * 0.5

Δf ≈ 3

Calculate the actual change:

To calculate the actual change, we need to evaluate f(3.5) and f(3) separately:

f(3.5) = 41 +[tex](3.5)^2[/tex]

f(3.5) = 41 + 12.25

f(3.5) = 53.25

f(3) = 41 + [tex](3)^2[/tex]

f(3) = 41 + 9

f(3) = 50

Δf = f(3.5) - f(3)

Δf = 53.25 - 50

Δf = 3.25

Calculate the error and the percentage error:

Error = |Δf - Δf_approx|

Error = |3.25 - 3|

Error = 0.25

Percentage error = (|Δf - Δf_approx| / Δf) * 100

Percentage error = (0.25 / 3.25) * 100

Percentage error ≈ 7.69%

So, the results are as follows:

Δf ≈ 3

Actual change (Δf) ≈ 3.25

Error ≈ 0.25

Percentage error ≈ 7.69%

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The length of the hypotenuse is approximately 19.8 units.

In a right-angled triangle, the hypotenuse is the longest side, and it is opposite to the right angle. To find its length, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, we have:

h^2 = 14.3^2 + 13.7^2

h^2 = 204.49 + 187.69

h^2 = 392.18

h = sqrt(392.18)

h ≈ 19.8

We can round the answer to one decimal place, as this is the nearest level of precision to the data provided. Note that for a right-angled triangle, the hypotenuse is always the longest side, so it makes sense that the hypotenuse is longer than both of the other sides in this case.

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Answer: 1/6 is its simplest form :)

Answer:

hi dear friend the answer is 6.245. hope that helps it has been a pleasure to help you can always look out for me if you have a math problem.

Answer: 1/2 of a sheet

Step-by-step explanation:

2 sheets divided by 4 people

2/4

Simplify to 1/2

Answer:

the answer is C

Step-by-step explanation:

BABYSHARK

Answer:

I think its c?

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

theres no answer

Step-by-step explanation:

The interval value at 98% confidence level for the given scenario is (73.51 ; 89.79)

From the data :

Mean(x) = (79.5+102.8+80.8+76.8+80.4+79.2+86+67.7)/8

Mean = 81.65

Sample standard deviation :

s = √[(x1 - mean)² + (x2 - mean)² + ... + (x(n) - mean)²] / n

Using a statistical calculator :

s = 9.98

The confidence interval is defined thus :

Mean ± Tcritical × s/√n

Tcritical at 98% = 2.306

Substituting values into the formula :

81.65 ± (2.306 × 9.98/√8)

81.65 ± 8.137

(73.51, 89.79)

Therefore, the confidence interval for the given scenario is (73.51 ; 89.79)

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Answer:

1).  (x - 4 = 13)

2).  (r + 17 = 51)

3). (7/9x =28)

4). (2/3x = 2)

5). { 3(x-2) = -9 }

6). (x -1.75 = 8.85)

7). Natalie buys organic almonds priced at $77 from the grocery store. How much did

she pay the cashier, if she received $23 in change?

Step-by-step explanation:

1. add 4 on both sides and it will be x=17

2. subtract 17 on both sides and it will be x= 34

3. multiply 9/7 on both sides and it will be x= 257/7 then you divide 257 by 7 then the final answer will be x= 36

4. multiply 3/2 on both sides and it will be x=6/2 then you divide 6 from 2 and the finial answer will be x= 3

5. you will distribute 3 into x and 2 and you will be 3x-6=-9 then you will add 6 on both sides so you will get 3x=3 and then divide 3 on both side so you will get x=1

6. add 1.75 on both sides so x= 10.6

7. the equation will be 23 +x = 77 so first you will subtract 23 on both sides and x will equal 54 so Natalie paid $54

Answer:

i'm taking that test rn

Step-by-step explanation:

Answer:

The second option

Step-by-step explanation:

Option D is the correct choice.

To evaluate the volume of D, the triple integral in cylindrical coordinates is required. So, let's derive the required triple integral.

Region D is bounded by two paraboloids z = 2x2 + 2y2 - 4 and z = 5 - x2 - y2 where x > 0 and y > 0.

In cylindrical coordinates,r = √(x^2 + y^2)z = zθ = tan-1(y/x)For the first paraboloid, the cylindrical equation of the paraboloid is: z = 2x2 + 2y2 - 4

By substituting the cylindrical coordinates values in this equation we get z = 2r2 sin2θ + 2r2 cos2θ - 4z = 2r2 (sin2θ + cos2θ) - 4z = 2r2 - 4 Now for the second paraboloid, the cylindrical equation of the paraboloid is: z = 5 - x2 - y2By substituting the cylindrical coordinates values in this equation we get:z = 5 - r2 The limits of r are 0 and √5; and the limits of θ are 0 and π/2.

Finally, the limits of z are obtained by equating the above two paraboloids.2r2 - 4 = 5 - r22r2 + r2 = 9r2 = 3z = 3We have got all the limits of cylindrical coordinates, we can now write the triple integral in cylindrical coordinates which evaluates the volume of D.

The triple integral is:∫(0 to π/2)∫(0 to √5)∫(2r2 - 4 to 3) r dz dr dθ

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The integral oſ sin(x - 2) dx is transformed into g(t)dt by applying an appropriate change of variable is g(t) = sin(t).

To transform the integral ∫sin(x - 2) dx into the form ∫g(t) dt using a change of variable, we can let u = x - 2.

Then, differentiating both sides with respect to x gives du = dx.

Substituting these values in the integral, we have:

∫sin(x - 2) dx = ∫sin(u) du

The integral has now been transformed into the integral of sin(u) with respect to u, denoted as g(t) dt.

Therefore, g(t) = sin(t).

So, the correct option is g(t) = sin(t).

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A. the dimension of A is 3x3. the dimension of B is 3x2.

B. the dimension of AB will be 3x2.

C. The value of AB = [[ -15 14] [ 4 -2] [ 13 -9]]

A. The dimension of a matrix is given by the number of rows and columns it has.

For matrix A, we have:

A = [[-1 -4 1], [0 2 2], [2 3 0]]

The matrix A has 3 rows and 3 columns, so the dimension of A is 3x3.

For matrix B, we have:

B = [[2 0], [3 -3], [-1 2]]

The matrix B has 3 rows and 2 columns, so the dimension of B is 3x2.

B. To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, A has 3 columns and B has 3 rows, so we can multiply them.

The dimension of AB will be the number of rows of A and the number of columns of B. Therefore, the dimension of AB will be 3x2.

C. [-1 -4 1] * [2 0]

   [0 2 2]    [3 -3]

   [2 3 0]    [-1 2]

  [-2-12-1   0+12+2]

= [0+6-2    0-6+4]

  [4+9+0   0-9+0]

  [ -15     14]

= [ 4         -2]

  [ 13       -9]

The value of AB = [[ -15 14] [ 4 -2] [ 13 -9]]

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Given question is incomplete, the complete question is below

For matrices: A =[[ -1 -4 1] [0 2 2][ 2 3 0]] B =[[2 0] [3 -3 ][-1 2] ]

A. What is the dimension of A and B?

B. What is the dimension of A*B?

C. What is A*B?

Answer:

Hey Aryabd interested to talk with me. Come in comments.

The  US Dollars for Rs 21000 would be 200 USD

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that  the rate of Rs 105 per US Dollar,

We have to calculate the US Dollars for Rs 21000.​

105 Rs = 1 USD

21000 Rs = x USD

Now the proportion can be;

105x =21000

x =21000 /105

x= 200 USD

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Answer:

52.81

Step-by-step explanat

Answer:

-6=2/3*-6

Step-by-step explanation:

y=mx+b

slope = m b=y intercept

Answer:38

Step-by-step explanation:I think it's 38 because it said right 8 and down 15 so it's kinda like a grid right mean stay positive but also means it goes up so I did 45 plus 8 which is 53 minus 15 which is 38. Hope this gets brainliest

Answer:

The equation is 157+28=185.

157+ 28= 185

I think that’s right

ok, i will help you.

For the first equation, we have points

(-1, -4)

and

(1, -1)

we also know the y-intercept is

(0, -2)

we can make systems of equations to solve for the equation of this exponiental function

y=ab^x

-1=ab

-2=a*1

a=-2

-1=-2(b)

b=1/2

The exponiental fufnction here is y=(-2)(1/2)^x

2nd equation

(0, 6)

(1, 12)

12=ab

6=a*b^0=6

a=6

12=6(b)

b=2

2nd equation is

y=6(2)^x

Answer:

25

Step-by-step explanation:

4x25=100

100-25=75 degrees

Answer:

25°

Step-by-step explanation:

(4x-25)=75

4x=100

x=25

The problem at hand involves base plates that exceed the maximum width dimension, resulting in improper fitting of the mating component. To address this issue, a sample of 50 base plates manufactured from each of the four CNC milling machines was analyzed.

Graphical analysis of the data revealed insights into the problem. Recommendations for solving the problem include identifying pertinent possible solutions through cause and effect diagrams.

The analysis of the sample data from each CNC milling machine provides valuable insights into the issue of base plates exceeding the maximum width dimension. By graphically analyzing the data, patterns or variations can be identified, helping to pinpoint the specific source of the problem. This analysis may involve creating graphs or tables to visualize the measurements and compare them across the machines.

To identify possible solutions, cause and effect diagrams, such as fishbone diagrams, can be utilized. These diagrams help to identify potential causes of the issue by categorizing them into different categories such as machine factors, material factors, human factors, and environmental factors.

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