What is an equation in point slope form for the line perpendicular to..

We cannot determine the exact area of triangle ABC or the values of a, b, and c.

To draw a diagram, we need to determine the values of a, b, and c. We can do this by using the properties of a parallelogram.

In a parallelogram, opposite sides are parallel, and their corresponding vectors are equal. Therefore, we can find the vectors corresponding to the sides of the parallelogram and equate them.

Let's find the vectors for sides AB and AD:

Vector AB = (4 - a, b + 6, -9 - 2) = (4 - a, b + 6, -11)

Vector AD = (-2 - a, -5 + 6, 11 - 2) = (-2 - a, 1, 9)

Since AB and AD are opposite sides, their corresponding vectors are equal:

(4 - a, b + 6, -11) = (-2 - a, 1, 9)

Equating the corresponding components, we get the following system of equations:

4 - a = -2 - a (1)

b + 6 = 1 (2)

-11 = 9 (3)

From equation (3), we can see that -11 is not equal to 9, which means there is no solution for the system of equations. Therefore, the given points A, B, C, and D do not form a parallelogram.

Without a parallelogram, we cannot determine the exact area of triangle ABC or the values of a, b, and c.

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Answer:

925 full marks

Step-by-step explanation:

350 + 20 = 370 marks required to pass

370 / 0.40 = 925 full marks

Using Green's Theorem to evaluate ∫ C → F ⋅ d → r , where → F = 〈 √ x + 6 y , 2 x + √ y 〉 and C consists of the arc of the curve y = 3 x − x 2 from (0,0) to (3,0) and the line segment from (3,0) to (0,0).The orientation of C is counterclockwise, so the integral evaluates to:

              ∫ C → F ⋅ d → r = ∫ 0 3 ∫ 0 3 x − 2 y dx dy = −2/3.

Let's understand this in detail:

1. Parametrize the curve C

Let x = t and y = 3t - t2

2. Calculate the area enclosed by the curve

A = ∫ 0 3 (3t - t2) dt

       = 9 x 3/2 - x2/3 + 10

3. Check the orientation of the curve

Since the curve and the line segment are traced in the counterclockwise direction, the orientation of the curve will be counterclockwise.

4. Use Green's Theorem

∫ C → F ⋅ d → r  = ∇ x F(x,y) dA

            = 9 x 3/2 - x2/3 + 10

5. Simplify the Integral

∫ C → F ⋅ d → r = [ √ (3t - t2) + 6 (3t - t2) ] [6t - 2t2] dt

                 = [ 3 (3t - t2) + 6 (3t - t2) ] (36t2 - 12t3 + 2t4)

                 = −2/3.

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To check which point satisfies the inequality 2x + y > 10, we substitute each value of x and y in the equation.

A. 2(2) + 3 > 10

    7 > 10

  This is incorrect. So the point does not satisfy the expression.

B. 2(3) + 2 > 10

    8 > 10

    This is also incorrect.

C. 2(4) + 3 >10

     11 > 10

     This is correct since 11 is greater than 10. So point (4,3) satisfies the inequality.

D. 2(3) + 4 > 10

    10 > 10

 This is also incorrect.

What is inequality?

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Hey there! I'm happy to help!

To find the volume of a cone, we multiply the base by the height and then divide by three.

First, we find the area of the base, which is a circle. To find a circle, you square the radius and then multiply by pi (or 3.14 in our case).

Radius is half of the diameter.

3/2=1.5

We square this.

1.5²=2.25

We multiply by 3.14

2.25×3.14=7.065

Now, we multiply this base area by the height.

7.065×7=49.455

We divide by 3.

49.455/3=16.485

Therefore, if we round this, our answer is 16.49 in³.

Now you can find the volume of a cone! Have a wonderful day! :D

Answer:

16.49

Step-by-step explanation:

The array's valid indexes are 0 through 24. Integers array int myArray[25] constitutes a 25-piece array of the type integer. As a result, choice B is the right one.

An index (as well as indexes) in mathematics is the power and exponent applied to a number and variable. For instance, with the number 24, the ranking of 2 is 4. The plural of the term is indexes. Algebraic ideas include constants and variables. A constant is an unchangeable number. Integers array int myArray[25] represents a 25-piece array of the type integer. At index =0 through index =size-1=25-1=24, the array begins.

Therefore, the correct option is option B.

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Answer:

6

Step-by-step explanation:

add 2 each time

Answer:

4 cans

Step-by-step explanation:

2.5 + 2.5 = 5 servings

5 servings = 2 cans

If you need 10 servings, double 2 which is 4 cans.

Answer:aint no way

Step-by-step explanation:

Answer:

Ok, this question seems incomplete, so i will answer it in a general way.

Suppose that regularly, Ken eats A calories during the day. (A is a positive number)

Now, Ken wants to reduce this number, but his nutritionist tells him to reduce no more than 7% (So the max reduction possible is a reduction of the 7%).

So after the reduction, Ken eats C calories per day.

First, the maximum reduction that Ken can do is when he reduces exactly 7% of the calories.

So if he regularly consumes A calories, the reduction will be of

(7%/100%)*A = 0.07*A

So after the reduction, the amount of calories that he consumes per day is:

C = A - 0.07*A = A*(1 - 0.07) = A*0.93

But this is the minimum amount of calories that he can consume, the actual range of possible options will be:

A < C ≤ A*0.97.

C is strictly smaller than A because we must have a reduction in the number of calories.

Those values of C is all the posible amounts of calories that Ken eats per day after the initial reduction in the number of calories per day.

the speed of the car was 5.33 meters per second. Speed = 10 / 2.32 = 4.31 meters per second (rounded to two decimal places) .

a. To find the speed of the car, we use the formula

Speed = Distance / Time

If the car raced 8 meters in 1.5 seconds, we can substitute these values in the formula to get:

Speed = 8 / 1.5 = 5.33 meters per second (rounded to two decimal places)

Therefore, the speed of the car was 5.33 meters per second.

b. The record time of 10 meters in 2.32 seconds gives us a speed of:

Speed = 10 / 2.32 = 4.31 meters per second (rounded to two decimal places)

Comparing this to the speed of the car that raced 8 meters in 1.5 seconds, we see that the car that raced 8 meters was faster, with a speed of 5.33 meters per second compared to the record time of 4.31 meters per second. This suggests that the car that raced 8 meters was well-designed and well-built, and was able to travel a greater distance in a shorter amount of time.            

It is important to note, however, that one data point is not enough to draw a firm conclusion about the superiority of one car over another. It is possible that the car that raced 8 meters had a lucky run, or that the car that set the record had a mechanical issue or was not driven to its full potential. To truly compare the performance of different cars, we would need to collect data from multiple trials and multiple cars, and analyze the data using statistical methods to determine which cars consistently perform better.

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Answer:

Step-by-step explanation:

Angles (7x + 3)° and (8x + 1)° are corresponding angles

Therefore:

m║n      ⇒      (7x + 3)° = (8x + 1)°

(7x)° + 3° = (8x)° + 1°     {subtract (7x)° from both sides}

3° = x° + 1°                   {subtract 1° from both sides}

2° = x°                          

x = 2

Answer: In order to describe a translation using arrow notation, we need to specify the direction and distance of the translation. In the case of the given translation, point P is translated to point P' by moving 6 units to the left and 2 units down. This can be represented using arrow notation as follows:

P' = P ← 6 ↓ 2

Here, the symbol ← represents a leftward movement, and the symbol ↓ represents a downward movement. The numbers 6 and 2 indicate the distance of the movement in the respective directions. This means that point P is translated to point P' by moving 6 units to the left and 2 units down from its original position.

Answer:did you get the answer tho

Step-by-step explanation:

Answer:

\( 4x}^{6} {y}^{10} \)

Step-by-step explanation:

The reason it is 4x^2 for the first part is because the entirety of -2x^3 is being squared, so we need to do -2×-2 which will give us the 4 and 3×2 which will give us the 6.

It's y^10 because we have y×y^9, so we ADD the powers, giving us the power of 10.

The total area of the room and the sitting area is 286.93 ft².

We have,

The area of the rectangle.

= Length x Width

= 15 x 14

= 210 ft²

Semicircle.

r = 14/2 = 7 ft

= 1/2 x πr²

Area = 1/2 x 3.14 x 7²

= 1/2 x 3.14 x 49

= 76.93 ft²

Now,

The total area of the room and the sitting area.

= 210 + 76.93

= 286.93 ft²

Thus,

The total area of the room and the sitting area is 286.93 ft².

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Answer:

The first three terms is 64, 32, 16

Step-by-step explanation:

Given

Number of participants = 64

Decrement = 1/2

Required

Find the first three terms

To calculate the first three terms, we make use of the following formula;

Current Term = Previous Term - 1/2 * Previous Term

The first term = Initial number of participants

First Term = 64

Second Term = First Term - 1/2 * First Term

Second Term = 64 - 1/2 * 64

Second Term = 64 - 32

Second Term = 32

Third Term = Second Term - 1/2 * Second Term

Third Term = 32 - 1/2 * 32

Third Term = 32 - 16

Third Term = 16

Hence, the first three terms is 64, 32, 16

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

A=30

Step-by-step explanation:

Answer: Please cheak

Step-by-step explanation: is there supposed to be a picture cause I see none?

Answer:

I see no picture

Step-by-step explanation:

However, here's a quick guide to classifying triangles!

Look for a line/notch on the side of the triangle which will the sides are of equal length

Equilateral Triangle: all 3 sides are of equal length

Isosceles Triangle: 2 sides are of equal length

Scalene Triangle: No sides are of equal length

Right Triangle: One of the angles is 90 degrees

Using the Counting the faces of two dice,

the atleast 17 number of faces are possible on the combination of two dice.

First, we have to count the favorable cases,

We know both dice have atleast 6 faces.

It gives 6 favorable cases for a sum of 7.

If we can count them if mean even if dice had more than 6 faces, will matter of for sum of 7.

Now, the mean, we need 6× 4/3=8 (favorable cases for the sum of 10)

If we count 3 favorable cases for each having 6 faces.

For more than 9 faces on a dice matter give the denominator (sample space) are the same for both sum of 7 and the sum of 10, and the probability of one is in proportion to the other.

It mean, additional 5 cases must be ( 7,2), (2,7), (8,2), (2,8) ,(9,1)

So , one of the dice has 8 faces and the other has atleast 9 faces.

Now, we must have atleast 17 combined faces of two dice for probability . So, we get if 12 with configration of 8 faces on one dice.

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Answer:

Distribute

5x - 20 + 7x + 7

either add like terms or take away

12x -13 or -20 2x + 7

Step-by-step explanation:

Answer:

12x-13

Step-by-step explanation:

i simplified it  cause you didnt put what it equaled

Answer:

The answer would be D

Step-by-step explanation:

In order for a problem to be infinite, it must be 0=0. But since this is equal, and can equal 0=0, it would be d

Answer:

-42

Step-by-step explanation:

Answer:

£2175

Step-by-step explanation:

14.5%×£15000=£2175

Emily runs at the fastest speed of 15 ft per second, Liz runs at 13.03 ft per second, and Zack runs at 12.8 ft per second.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that Emily runs 15 ft per second no one runs 358 ft and 36 seconds Liz runs 1 mi in 405 seconds Zack runs 768 feet in 1 minute.

Emily's speed = 15 ft/sec

Liz's speed = 1 mile per 405 sec = 5280/405 = 13.03 ft /sec

Zack's speed = 768 / 60 = 12.8 ft /sec

Therefore, Emily runs at the fastest speed of 15 ft per second, Liz runs at 13.03 ft per second, and Zack runs at 12.8 ft per second.

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Answer:

13/20 written as a decimal is 0.65 and as a percent is 65%

1) Make the denominator 100 (20 x 5)

2) Multiply by five from the numerator too (13 x 5 = 65)

A researcher wished to estimate the difference between the proportion of users of two shampoos who are satisfied with the product at a 90% confidence level,

the true difference between the proportion of users satisfied with shampoo A and shampoo B is estimated to be between -0.0262 and 0.0482.

To construct a 90% confidence interval for the true difference between the two population proportions, we can use the formula for the confidence interval for the difference between two proportions.

Let's denote the proportion of users satisfied with shampoo A as p1 and the proportion of users satisfied with shampoo B as p2.

The sample proportion for shampoo A, denoted as 1, is calculated by dividing the number of users satisfied in the sample of 400 (78) by the sample size (400):

1 = 78/400 = 0.195

The sample proportion for shampoo B, denoted as 2, is calculated by dividing the number of users satisfied in the sample of 500 (92) by the sample size (500):

2 = 92/500 = 0.184

Next, we calculate the standard error, which measures the variability of the difference between the two proportions:

SE = sqrt[(1 * (1 - 1) / n1) + (2 * (1 - 2) / n2)]

where n1 is the sample size for shampoo A (400) and n2 is the sample size for shampoo B (500).

SE = sqrt[(0.195 * (1 - 0.195) / 400) + (0.184 * (1 - 0.184) / 500)]

SE = sqrt[(0.152025 / 400) + (0.151856 / 500)]

SE ≈ 0.0226

Now, we can calculate the margin of error by multiplying the standard error by the critical value corresponding to a 90% confidence level. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = 1.645 * 0.0226 ≈ 0.0372

Finally, we construct the confidence interval by subtracting and adding the margin of error from the difference in sample proportions:

Confidence Interval = (1 - 2) ± Margin of Error

Confidence Interval = (0.195 - 0.184) ± 0.0372

Confidence Interval = 0.011 ± 0.0372

Confidence Interval ≈ (-0.0262, 0.0482)

Therefore, at a 90% confidence level, the true difference between the proportion of users satisfied with shampoo A and shampoo B is estimated to be between -0.0262 and 0.0482.

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The sequence's numbers are all multiples of 30. Every number can be divided by 30.

If two integers are divided equally, leaving no remainder, then we say that one integer divides the other (we sometimes say, "with no remainder," but that is not technically correct). Mathematicians express this more explicitly as follows: If a and b are integers (with a not zero), then a divides b if c is an integer such that b = ac. Sequence: 1 51, 2 52,....., n 5n,....n 5n=n(n 4 1)=n(n1)(n1)(n+1)(n 2 +1)

At n=1, n 5, n=0, n=1, 2, 3, etc. Not attainable

Atn=2,n 5 −n=30 ∴ The sequence's numbers are all multiples of 30. Every number can be divided by 30.

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