factorise completely
\(4 - 8x\)
​

Answer:

  67.5 ft

Step-by-step explanation:

You want the length of x=MB in triangle MAB similar to triangle MNP with MN=71.5 ft, AN=22 ft, MP=97.5 ft, and AB║NP with A on MN and B on MP.

Corresponding sides of similar triangles  are proportional, so we can write the proportion ...

  MB/MA = MP/MN

  x/(71.5 -22) = 97.5/71.5

  x = 49.5×97.5/71.5 . . . . . . multiply by 49.5

  x = 67.5 . . . . . . feet

Answer:

BCDA

Step-by-step explanation:

There are few homes in a typical home

there are about 20 cookies in a bag of cookies

there are several thousand in a used car

there are tens of thousands of miles from the earth to the sun.

Answer:

B

C

D

A

Step-by-step explanation:

MILES FROM EARTH TO SUN IS MORE

COMPARED TO

VALUE OF A USED CAR IS MORE

COMPARED TO

NUMBER OF DOORS IN A TYPICAL HOME ARE MORE

COMPARED TO

NUMBER OF COOKIES IN A TYPICAL BAG OF OREOS

I HOPE YOU GOT YOUR ANSWER

The convolution integral y(t) = x(t) * h(t) for the given pair of signals x(t) and h(t) can be computed as follows:

y(t) = ∫[x(τ) * h(t - τ)] dτ

1) x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1)

The convolution integral becomes:

y(t) = ∫[δ(τ) * δ(t - τ - 2) * (τ - 1)] dτ

To evaluate this integral, we consider the properties of the Dirac delta function. When the argument of the Dirac delta function is not zero, the integral evaluates to zero. Therefore, the integral simplifies to:

y(t) = δ(t - 2) * (t - 1)

The convolution result y(t) is equal to the shifted impulse response h(t - 2) scaled by the factor of (t - 1). This means that the output y(t) will be a shifted and scaled version of the impulse response h(t) at t = 2, delayed by 1 unit.

In summary, for x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1), the convolution integral y(t) = x(t) * h(t) simplifies to y(t) = δ(t - 2) * (t - 1).

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Answer:

12.2

Step-by-step explanation:

First add all numbers.

Then divide it by the amount of numbers you added.

Then you have the average.

Hope this helped.

Answer: D and F

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

59 - 44 + 1 = 16.

16/59

Please mark as brainliest!

Answer:

D

Step-by-step explanation:

count 44,45,46... , then count how many numbers you counted

Answer:

x should equal 27/23 or 1 4/23 or 1.17

Step-by-step explanation:

Hope this Helped

a) The standard matrix of the linear transformation T is

|cos(3°) -sin(3°)|

|sin(3°) cos(3°)|

(b) The standard matrix of the linear transformation T

| 0 1 |

|-1 0 |

(c) The standard matrix of the linear transformation T

| 1 0 0 |

| 0 0 0 |

| 0 0 1 |

d) the standard matrix of T is:

|-5x² + 4x³   0           |

| 0               x²  - 6x³ |

(a) The standard matrix of the linear transformation T in this case is:

cos(3°) -sin(3°) 0

sin(3°) cos(3°) 0

Thus, the standard matrix of T is:

|cos(3°) -sin(3°)|

|sin(3°) cos(3°)|

(b) The standard matrix of the linear transformation T in this case will be

1 0

0 -1

Multiplying by the reflection across the line y = x:

| 0 1 |

| 1 0 |

Thus, the standard matrix of T is:

| 0 1 |

|-1 0 |

(c) The standard matrix of the linear transformation T in this case is:

1 0 0

0 0 0

0 0 1

Thus, the standard matrix of T is:

| 1 0 0 |

| 0 0 0 |

| 0 0 1 |

(d)

The standard matrix of the linear transformation T in this case is:

|-5x² + 4x³   0           |

| 0               x²  - 6x³ |

Thus, the standard matrix of T is:

|-5x² + 4x³   0           |

| 0               x²  - 6x³ |

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Answer: ✨4(2+1)✨

Step-by-step explanation: ✨3+6−2+53x+6−2+5x3+4+53✨

Answer:

4(2x + 1)

---->

Step-by-step explanation:

1:    3x + 6 - 2 + 5x = 4(2x + 1)

2:    Orignal Cost=80

Discounted Cost=60

Discount=80-60=20

Discount%=(20/80)*100=25%

A student can select the questions in 420 different ways implies that the student can select any number of questions from the set, without any restrictions or limitations, the number of ways to select questions would be determined by the power set of the question set.

To calculate the number of ways a student can select the questions, we need to consider the combinations of selecting questions from Part I and Part II, while ensuring that at least 3 questions are selected from each part.

Number of questions in Part I: 5

Number of questions in Part II: 7

Total number of questions to be attempted: 8

We can consider different combinations of selecting questions from each part to meet the requirements. Let's break it down into cases:

Case 1: Selecting 3 questions from Part I and 5 questions from Part II

Number of ways to select 3 questions from Part I: C(5,3) = 10

Number of ways to select 5 questions from Part II: C(7,5) = 21

Total ways for Case 1: 10 * 21 = 210

Case 2: Selecting 4 questions from Part I and 4 questions from Part II

Number of ways to select 4 questions from Part I: C(5,4) = 5

Number of ways to select 4 questions from Part II: C(7,4) = 35

Total ways for Case 2: 5 * 35 = 175

Case 3: Selecting 5 questions from Part I and 3 questions from Part II

Number of ways to select 5 questions from Part I: C(5,5) = 1

Number of ways to select 3 questions from Part II: C(7,3) = 35

Total ways for Case 3: 1 * 35 = 35

Therefore, the total number of ways a student can select the questions, while meeting the given criteria, is:

Total ways = Total ways for Case 1 + Total ways for Case 2 + Total ways for Case 3

= 210 + 175 + 35

= 420

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A student can select the questions in 14,400 different ways.

To find the number of ways a student can select the questions, we can break down the problem into two parts: selecting questions from Part I and selecting questions from Part II.

In Part I, there are 5 questions, and the student needs to select at least 3. So, there are 3 possible choices for the first question, 4 for the second, and 5 for the third. However, the remaining 2 questions can be selected in any way. So, the number of ways to select questions from Part I is 3 * 4 * 5 * 2 * 1 = 120.

In Part II, there are 7 questions, and the student needs to select at least 3. So, there are 3 possible choices for the first question, 4 for the second, and 5 for the third, just like in Part I. The remaining 4 questions can be selected in any way.

So, the number of ways to select questions from Part II is also 120.

To find the total number of ways a student can select the questions, we multiply the number of ways from Part I and

Part II together: 120 * 120 = 14,400.

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Elements in set A is 7.

Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.

RECALL: The number of proper subsets of a set with nn elements is 2^n-12

N

−1.

Let n = number of elements of the set.$

Then,Then, 2^n-1 = 127

2^n = 127+1

2^n=128

2^n = 2^7

N=7

$The set has 7 elements.

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According to the given information in the question the element in set A is  7.

Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.

RECALL: The number of proper subsets of a set with nn elements is 2^n-12

N

−1.

Let n = number of elements of the set.$

Then, Then, 2^n-1 = 127

2^n = 127+1

2^n=128

2^n = 2^7

N=7

$The set has 7 elements.

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Answer:  

42,893 + 2,432,743 = 2,475,636

, Hope this helps :)

Have a great day!!

Answer:

\(\sf 42893+2432743\)

\(\sf =2475636\)

Eigenvalues of A: We begin by calculating the eigenvalues of A by solving the characteristic equation det(A - λI) = 0. Where I is the identity matrix of the same size as A.

1. First, we calculate A - λI :A - λI = 1 - λ -2 1 -2 1 1 1 -2 - λ

2. Next, we calculate det(A - λI): det(A - λI) = (1 - λ)[(-2)(-2 - λ) - 1] - 1[(-2)(1) - (-2)(1)] + 1[1(-2) - 1(1 - λ)] = (1 - λ)[4 + λ] + 2 + 1 + λ = λ³ - 6λ² - 7λ = λ(λ - 7)(λ + 1)

Therefore, the eigenvalues of A are λ₁ = 0, λ₂ = 3, λ₃ = -3.

Eigenvectors of A: Once we have obtained the eigenvalues, we can proceed to find the eigenvectors of A. An eigenvector v of A corresponding to an eigenvalue λ satisfies the equation Av = λv. We will solve this equation for each eigenvalue of A.1. For λ₁ = 0, we have A - 0I = A, and we must solve the equation Av = 0.

We can do this by row reducing A to get its row-echelon form [A|0]:1 -2 1 0 -2 1 1 1 -2 0 0 0

The solutions of this system (up to scaling) are given by: x₁ = 2x₃ - x₂ and x₃ = x₃, where x₁, x₂, x₃ are the components of the eigenvector v₁ corresponding to λ₁ = 0.

Therefore, the eigenvector corresponding to λ₁ is v₁ = (2, -1, 1).2. For λ₂ = 3, we have A - 3I: A - 3I = -2 -2 1 -2 -2 1 1 1 -5

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Answer:9 /12 -4/12 = 5/12

Step-by-step explanation: First you need to find the same demointaor  which can be 12 .You take  3/4 and times on boths side by 3 which gives you 9/12 .You take 1/3 and times on both sides by 4 which gives you 4/12. Now put 9 /12 and then put  4/12 and then subtract both which gives you 5/12.

Look at pic below.

A circle can be defined as a geometric shape consisting of all points in a plane that are equidistant from a given point, which is known as the center. The distance between the center of the circle and any point on the circle is referred to as the radius.

In order to find the center and radius of a circle, we need to have three points on the circle's circumference, and then we can use algebraic formulas to solve for the center and radius. Let's look at the given problem to find the center and radius of the circle that passes through the points (-1,5), (5,-3), and (6,4).

Center of the circle can be determined using the formula:

(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)

Let's plug in the values of the given points and simplify:

(x,y)=(−(−1)−5−6/3,−5+3+4/3)=(2,2/3)

Next, we need to find the radius of the circle. We can use the distance formula to find the distance between any of the three given points and the center of the circle:

Distance between (-1,5) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(2+1)2+(2/3−5)2=√10.111

Distance between (5,-3) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(5−2)2+(−3−2/3)2=√42.222

Distance between (6,4) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(6−2)2+(4−2/3)2=√33.361

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Step-by-step explanation:

shape BCD is an isosceles triangle meaning the base angles will be the same.

CA is a straight line meaning that it is 180

the sum of angles in a triangle always is 180

so

180-36= 144

to find x you need to half 144 as it is the sum of the base angles of the isosceles triangle.

144/2= 72

x=72

the angle just below y is also 72.

as CA is a straight line,

180-72= 108 giving you the answer for y

y= 108

so to make the answer clear

x= 72

y= 108

hope that helped! :)

if you would like to give me a brainliest feel free as im nearly to the end of my goal.

a. The party that won the highest percentage of votes and seats in 1982 is democrat.

b. A change between the percentage of seats won by republicans in 1982 and 2012 is 4%

c. The difference between votes percentage and seats percentage for democrat is 4% and 26% respectively. The difference between votes percentage and seats percentage for republican is 3% and 26% respectively.

The pie chart is given below:

a. We have to identify the party that won the highest percentage of votes and seats in 1982.

We can see that in diagram that gray part of circle shows the vote percentage of democrat and white part of circle shows the vote percentage of republican.

Republican gain votes in 1982 = 52%

Democrat gain votes in 1982 = 49%

So the democrats get the maximum votes in 1982.

b. We have to describe a change between the percentage of seats won by republicans in 1982 and 2012.

In 2012 republican get votes percentage = 48%

In 1982 republican get votes percentage = 52%

So the change between 1982 and 2012 = (52 - 48)% = 4%

c. We have to draw a conclusion about the difference in percentage of votes won and seats.

In 2012 republican get votes percentage = 48%

In 1982 republican get votes percentage = 52%

So, the difference between vote percentage is 4%.

In 2012 republican get seats percentage = 25%

In 1982 republican get seats percentage = 51%

So, the difference between seats percentage is 26%.

In 1982 democrat get votes percentage = 49%

In 2012 democrat get votes percentage = 52%

So, the difference between vote percentage is 3%.

In 2012 democrat get seats percentage = 75%

In 1982 democrat get seats percentage = 49%

So, the difference between seats percentage is 26%.

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The unit tangent vector to the level curve at the point (4, -4) that has a positive x-component is (0.999)i + (0.005)j.

For the function f(x,y) = (− 1 – x² – y²)/1

to find a unit tangent vector to the level curve at the point (-5, -4) that has a positive x-component, the steps are as follows:

Step 1: Find the gradient of the function ∇f(x, y)f(x, y) = (-1-x²-y²)/1∇f(x, y) = (∂f/∂x)i + (∂f/∂y)j∂f/∂x = -2x and ∂f/∂y = -2ySo, ∇f(x, y) = -2xi -2yj

Step 2: Evaluate the gradient at the given point(x, y) = (-5, -4)∇f(-5, -4) = 10i + 8j

Step 3: To find the unit tangent vector, divide the gradient by its magnitude.

                               v = ∇f(x, y) / |∇f(x, y)|v = (10i + 8j) / √(10²+8²)

                                        v = (10/14)i + (8/14)j

                                          v = (5/7)i + (4/7)j

Therefore, the unit tangent vector to the level curve at the point (-5, -4) that has a positive x-component is (5/7)i + (4/7)j.

For the function f(x, y) = 5e^(3x)sin(y) to find a unit tangent vector to the level curve at the point (4, -4) that has a positive x-component, the steps are as follows:

Step 1: Find the gradient of the function

                                                  ∇f(x, y)f(x, y) = 5e^(3x)sin(y)

                                                  ∇f(x, y) = (∂f/∂x)i + (∂f/∂y)j∂f/∂x = 15e^(3x)sin(y) and ∂f/∂y = 5e^(3x)cos(y)

So, ∇f(x, y) = 15e^(3x)sin(y)i + 5e^(3x)cos(y)j

Step 2: Evaluate the gradient at the given point

                                  (x, y) = (4, -4)∇f(4, -4) = -105sin(-4)i + 5cos(-4)j

                                  ∇f(4, -4) = 105sin(4)i + 5cos(4)j

Step 3: To find the unit tangent vector, divide the gradient by its magnitude.

                                                  v = ∇f(x, y) / |∇f(x, y)|

                                                 v = (105sin(4)i + 5cos(4)j) / √(105²sin²(4)+5²cos²(4)).

                                                 v = (105sin(4)/105.002)i + (5cos(4)/105.002)j

Therefore, the unit tangent vector to the level curve at the point (4, -4) that has a positive x-component is (0.999)i + (0.005)j.

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Answer:

2.5

Step-by-step explanation:

Answer:

2 1/2

Step-by-step explanation:

5/8 ÷ 1/4

Copy dot flip

5/8 * 4/1

Rewriting

5/1 * 4/8

5/1 * 1/2

5/2

Writing as a mixed number

2 1/2

Answer:

Step-by-step explanation:

The approximate value of the fifteenth term is 244.141 or it can also be written as 244 1/8.

The seventh term of a geometric sequence is 5 and the tenth term is 16.875. The given information shows that a=5 and a10=16.875.

We have to find a15. Since the sequence is geometric, therefore the common ratio (r) can be determined from this information as below; a10 = ar9 16.875 = 5r9 r = (16.875)/5r9 r = 1.25On substituting the values of a, r and n in the nth term formula of a geometric sequence,

we can determine the value of a15 as below; an = arn-1 a15 = 5 × (1.25)14 a15 = 244.140625So, the fifteenth term of the sequence is 244.140625 (approximately).

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Answer:

I hope the image helps!

Answer:

6.5%

Step-by-step explanation:

M.P= ₹6,000

Amount excluding VAT= 5,610

discount= x/100

discount= 6000*x/100=60x

equating

6000-60x= 5610

6000-5610=60x

390=60x

390/60=x

6.5=x

therefore, there is a discount of  6.5%

Answer:6.25 laps

Step-by-step explanation:

24/3=8

1 lap is 8 min

50/8=6.25

The required answers are:

a) The focal length of the mirror is -2.4 m.

b) The mirror is concave.

c) The magnification of the mirror is 6.00.

d) The image is real, upright, and magnified.

a. To find the focal length of the mirror, we can use the mirror equation:

1/f = 1/s + 1/s'

Where:

f is the focal length of the mirror,

s is the object distance (distance of the shopper from the mirror), and

s' is the image distance (distance of the image from the mirror).

Given:

s = 2.00 m

s' = -12.0 m (negative sign indicates the image is behind the mirror)

Plugging in the values:

1/f = 1/2.00 + 1/(-12.0)

Simplifying the equation:

1/f = -5/12

Taking the reciprocal of both sides:

f = -12/5 = -2.4 m

Therefore, the focal length of the mirror is -2.4 m.

b. The mirror is concave. We know this because the image distance (s') is negative, which indicates that the image is formed on the same side as the object (in this case, behind the mirror). In concave mirrors, the focal length is negative.

c. The magnification of the mirror can be determined using the magnification formula:

m = -s'/s

Given:

s = 2.00 m

s' = -12.0 m

Plugging in the values:

m = -(-12.0) / 2.00 = 6.00

Therefore, the magnification of the mirror is 6.00.

d. Based on the information given, we can describe the image of the shopper as follows:

- The image is real because it is formed by the actual convergence of light rays.

- The image is upright because the magnification is positive.

- The image is enlarged because the magnification is greater than 1 (magnification = 6.00).

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(a) To sketch a graph of the speed over a 3-second time span, we need to know the equation that describes the relationship between speed and time. Without this information, we cannot create an accurate graph.

(b) To find the volume of blood that passes along the artery in one second, we need to use the formula Q = A * v, where Q is the flow rate, A is the cross-sectional area of the artery, and v is the speed of blood flow. The cross-sectional area of the artery is given by A = pi * r^2, where r is the radius of the artery.

Thus, substituting the given values, we get:

A = pi * (5mm)^2 = 78.54 mm^2

v = 0.2 + 0.1 sin(2pit/0.8) (using the given information)

Q = A * v = 78.54 * (0.2 + 0.1 sin(2pit/0.8))

To find the volume of blood that passes along the artery in one second, we need to evaluate Q at t = 1 second, so we get:

Q = 78.54 * (0.2 + 0.1 sin(2pi1/0.8)) = 31.39 mm^3/s

Therefore, the volume of blood that passes along the artery in one second is approximately 31.39 cubic millimeters.

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To solve this problem, let's assume the speed of the current is "x" mph. When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the current. Therefore, the speed of the boat relative to the water is 11 - x mph.

When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. Therefore, the speed of the boat relative to the water is 11 + x mph.

Now, let's calculate the time taken for each leg of the journey:

Time taken to go 40 miles upstream = Distance / Speed
Time taken to go 40 miles upstream = 40 / (11 - x) hours

Time taken to go 70 miles downstream = Distance / Speed
Time taken to go 70 miles downstream = 70 / (11 + x) hours

According to the problem, these times are equal. So, we can set up the equation:

40 / (11 - x) = 70 / (11 + x)

To solve this equation, we can cross-multiply:

40 * (11 + x) = 70 * (11 - x)

440 + 40x = 770 - 70x

Now, let's solve for x:

110x = 330

x = 3

Therefore, the speed of the current is 3 mph.

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Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network.

Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network. This technique allows a user to take advantage of the computing power of multiple computers to render a scene. To do this, the user would divide the scene into several parts, assigning each part to a different computer. The computers would then render each part of the scene independently, and then the results are combined into a single image. This process can significantly reduce the time required to render a scene, as the workload is distributed over multiple computers. For example, if it would normally take a single computer 10 minutes to render a scene, net rendering could reduce that time to 2 minutes.

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The slope of the tangent line to the polar curve at

`r = sin(4θ)` is:

`dy/dx = (dy/dθ)/(dx/dθ)`

at `r = sin(4θ)`= `(4cos(4θ)sin(θ) + sin(4θ)cos(θ)) / (4cos(4θ)cos(θ) - sin(4θ)sin(θ))`

To find the slope of the tangent line to the polar curve at

`r = sin(4θ)`,

we can use the polar differentiation formula, which is:

`dy/dx = (dy/dθ)/(dx/dθ)`

For a polar curve given by

`r = f(θ)`,

we can find

`(dy/dθ)` and `(dx/dθ)`

using the following formulas:

`(dy/dθ) = f'(θ)sin(θ) + f(θ)cos(θ)` and `(dx/dθ) = f'(θ)cos(θ) - f(θ)sin(θ)`

where `f'(θ)` represents the derivative of `f(θ)` with respect to `θ`.

For the given curve,

`r = sin(4θ)`,

we have

`f(θ) = sin(4θ)`.

So, we first need to find `f'(θ)` as follows:

`f'(θ) = d/dθ(sin(4θ)) = 4cos(4θ)`

Now, we can substitute

`f(θ)` and `f'(θ)` in the above formulas to get

`(dy/dθ)` and `(dx/dθ)`

:

`(dy/dθ) = f'(θ)sin(θ) + f(θ)cos(θ)``  = 4cos(4θ)sin(θ) + sin(4θ)cos(θ)`

and

`(dx/dθ) = f'(θ)cos(θ) - f(θ)sin(θ)``  = 4cos(4θ)cos(θ) - sin(4θ)sin(θ)

Now, we can find the slope of the tangent line using the polar differentiation formula:

`dy/dx = (dy/dθ)/(dx/dθ)`

at

`r = sin(4θ)`

So, the slope of the tangent line to the polar curve at

`r = sin(4θ)` is:

`dy/dx = (dy/dθ)/(dx/dθ)`

at `r = sin(4θ)`= `(4cos(4θ)sin(θ) + sin(4θ)cos(θ)) / (4cos(4θ)cos(θ) - sin(4θ)sin(θ))`

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\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

Here we go ~

\(\qquad \sf  \dashrightarrow \: (f + g)(x)\)

\(\qquad \sf  \dashrightarrow \: f(x) + g(x)\)

\(\qquad \sf  \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)\)

\(\qquad \sf  \dashrightarrow \: 7 {x}^{2} + x - 4\)