the endpoints of segment mn have coordinates (0, 0) and (5, 1). the endpoints of segment ab have coordinates (1 1 2 , 2 1 4 ) and (−2 1 4 , k ). for what value of k are these segments parallel?

The equation will be,

→ 5/10 = 12/24

Is 5/10 equivalent to 12/24?

→ 5/10 = 12/24

→ 24 × 5 = 12 × 10

→ 120 = 120

→ [ LHS = RHS ]

Hence, they are equivalent.

Answer:

Step-by-step explanation:

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4}

Finite And Infinite Sets: Union Of Sets

Power Set: Complement Of A Set

Equivalent Sets: Universal Set

Types Of Sets: Set Theory

Answer:

a). 16, 25, 36, 49, 64

b). ???

Step-by-step explanation:

16 + 9 = 25

25 + 11 = 36

36 + 13 = 49

49 + 15 = 64

I don't think b is possible

At this point, the canoe will be under a net force of 51.52 N.

The total mass of a canoe and a paddler is 100.0 kg. A river that runs from east to west is where the canoe is thrown in. The power of the water current on the canoe is 18.0 N. The paddler exerts a force of 36.0 N [E 37.0° N].

The Free Body Diagram is then displayed below.

The canoe's net force would then be indicated as follows:

F = (18 + 36 cos 37°) i + (36 sin 37°) j

F = 46.75 i + 21.67 j

Therefore the force's strength will be

|F| = √(46.75² + 21.67²)

|F| = √2655.15

|F| = 51.52 N

Thus, at this point, the canoe will be under a net force of 51.52 N.

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Considering the concepts of parallel lines and alternate interior angles, it is found that Mitch created diagram C.

Parallel lines are lines that never intersect. For this problem, lines l and k are parallel, that is, they are the horizontal lines.

When two parallel lines are crossed by a transversal, the alternate interior angles are between the two parallel lines, one in each side.

Since 1 and 2 are alternate interior angles, Mitch created diagram C.

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Step-by-step explanation:

[tex] 3\sqrt{8} + \sqrt{114} [/tex]

Answer:

c. Fence posts with a cost of $10 would sell for how much?

Step-by-step explanation:

Answer:6.986

Step-by-step explanation:

To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.

Answer: Standard deviation is 6.986.

Step-by-step explanation:

Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation

To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.

Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.

In this case standard deviation is 6.986.

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Answer:

10%

Step-by-step explanation:

firstly express as a fraction then multiply the fraction by 100% , that is

[tex]\frac{2}{20}[/tex] × 100% = 2 × 5 = 10% of the flowers are roses

The compound inequalities for all the balls that are sports regulated are  { (x,y) : 2(1/2) ≤ x ≤ 2(5/8) and 2 ≤y≤ 2(1/6) } for Tennis ball.

{ (x,y) : 2(7/8) ≤ x≤ 3 and 5≤ y ≤ 5(1/4) } for Baseball.

{ (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 } for women's Basket ball.

{ (x,y) : 21.64 ≤x ≤ 22.28 and 14.46 ≤ y ≤ 15.87 } for Scoccer Ball.

Suppose we are given { (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 } this reads as The set of all x comma y such that x is between this range and y is between in this range.

Sports regulations have some rules that the diameters and weights of sports pieces of equipment must lie between the regulations that have been set.

We are denoting the Diameters of the balls as x in inches and the weights of the balls as y in ounces.

Now for a Tennis ball the range for x and y can be written in roaster form of set is { (x,y) : 2(1/2) ≤ x ≤ 2(5/8) and 2 ≤y≤ 2(1/6) }.

For Baseball it is { (x,y) : 2(7/8) ≤ x≤ 3 and 5≤ y ≤ 5(1/4) }.

For women's Basketball it is { (x,y) : 9.07 ≤ x ≤ 9.23 and 20 ≤ y ≤ 22 }.

For Soccer ball the set in roaster form can be written as

{ (x,y) : 21.64 ≤x ≤ 22.28 and 14.46 ≤ y ≤ 15.87 }.

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Answer: 85 in

Step-by-step explanation:

A=Area of rectangle. L=length of rectangle. W=width of rectangle

A=L*W

1445=L*17

1445/17=L*17/17

L=85 in

The rate of margin used is 37.5% . The cost price of the batch of plywood is $312.5. Fence post sell for $16. The selling price was $133.33

Margin is the difference between the Selling price and the cost price. The price at which a item is sold is called the selling price and the price at which an item is bought is called the cost price.

The given markup is 60%.

We know that margin=markup÷(1+markup)

markup=60%

Substituting the values we get the rate of margin:

[tex]=\frac{\frac{60}{100} }{1+\frac{60}{100} } \\=\frac{60}{160}\\ =37.5[/tex]

Hence the rate of margin is 37.5 %.

Selling price for the plywood=$500

We know that selling price=cost price ÷(1-margin)

Let the cost price be x

[tex]x=500(1-\frac{37.5}{100} )\\x=312.50[/tex]

The cost price is $ 312.50 .

Now cost of fence = $10

Selling price of fence=cost price÷(1-margin)

substituting the values we get:

Selling price =10÷0.625

or, selling price= $16

Therefore the selling price is $16 .

Now we know that Markup percentage= profit÷ cost price

Substituting the values we get:

[tex]60\% = \frac{50}{CP}\\or,\frac{60}{10}=\frac{50}{CP}\\or,CP=83.33[/tex]

Therefore sell price=cost price+ profit

or, sell price=83.33+50

or, sell price =133.33

The sell price is $133.33

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Using proportions, the financial measures for the home purchase are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates, which along with operations such as multiplication or division are used to find the equivalent measures.

For this problem, the beginning balance is the purchase value of the home, hence:

Beginning Balance: $220,000.

15% of that goes towards the down payment, hence:

0.15 x 220,000 = $33,000.

Payment toward principal: $33,000.

The number of monthly payments is given by:

20 x 12 = 360 monthly payments.

Considering the monthly payment, the ending balance is given as follows:

33,000 + 360 x 1,152.99 = $448,076.4.

Hence the interest owed is:

448,076.4 - 220,000 = $228,076.4.

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Answer:

x = 4 and x = 7

Step-by-step explanation:

→ Find the sum of both the angles

3x + x + 74 = 4x + 74

6x + x + 13 = 7x + 13

→ Equate both equations to 90

4x + 74 = 90

7x + 13 = 90

→ Minus 74 and 13

4x = 16

7x = 77

→ Divide by 4 and 7 respectively

x = 4 and x = 7

The value of the f(x) = (x + 4) / x at x = 4 is equal to - 1 / 4.

In this problem we have the following rational equation, which is equivalent to the following sum of functions:

f(x) = (x + 4) / x = 1 + 4 / x = g(x) + h(x)

Then, we must find both the derivatives of the functions g(x) and h(x) by using the definition of derivative:

g(x):

g'(x) = [1 - 1] / h

g'(x) = 0 / h

g'(x) = 0

h(x):

h'(x) = [4 / (x + h) - 4 / x] / h

h'(x) = [4 · x - 4 · (x + h)] / [h · (x + h) · x]

h'(x) = - 4 · h / [h · (x + h) · x]

h'(x) = - 4 /[(x + h) · x]

If h = 0, then:

h'(x) = - 4 / x²

Then, the first derivative of the function is f(x) = - 4 / x². Now we evaluate the function at x = 4:

f(4) = - 4 / 4²

f(4) = - 1 / 4

The value of the f(x) = (x + 4) / x at x = 4 is equal to - 1 / 4.

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The given function is greater than or equal to 0 for the interval given as follows:

{x | x ≤ -3 or -1 ≤ x ≤ 0 or x ≥ 2}.

For this problem, with a closed interval, we have that the function is above for:

x ≤ -3, -1 ≤ x ≤ 0, x ≥ 2.

Hence the interval notation is:

{x | x ≤ -3 or -1 ≤ x ≤ 0 or x ≥ 2}.

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Answer: 7

Step-by-step explanation: A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals

Answer:

7

Step-by-step explanation:

:D

The profit function is P(x) = ( - x² / 5000 ) + 13.9x - 75000.

50,000 baseball game tickets were sold at $4 per ticket.

When the price is raised to $5, then 45,000 tickets were sold.

The variable and fixed costs for the ballpark owners are $0.10 and $75,000 respectively.

Let's say x is the number of tickets sold, and P is the profit.

Then,

P = ax + b

At P = 4,

4 = (50000)a + b                                                                                  ---------(1)

At P = 5,

5 = (45000)a + b                                                                                  --------(2)

Subtracting (2) from (1),

4 - 5 = (50000)a + b - (45000)a - b

- 1 = 5000(a)

a = ( - 1/5000)

So if a = ( - 1/5000),

Then,

4 = (50000)a + b

4 = (50000)( - 1 / 5000 ) + b

4 = -10 + b

b = 14

Therefore,

p(x) = ( - x /5000) + 14

Now, the profit function is:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Now, R(x) =  xp(x)

R(x) = x[ ( - x/5000) + 14]

R(x) = ( - x² / 5000 ) + 14x

The fixed cost is F(x) = $75000

Hence, the costs will be:

C(x) = 75000 + (0.10)x

Therefore the profit function is:

P(x) = R(x) - C(x)

P(x) = ( - x² / 5000 ) + 14x - 75000 - (0.10)x

P(x) = ( - x² / 5000 ) + 13.9x - 75000

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The complete question is mentioned below:

When the admission price for a baseball game was $4 per ticket, 50,000 tickets were sold. When the price was raised to $5, only 45,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ballpark owners are $0.10 and $75,000 respectively.

Find the profit P as a function of x, the number of tickets sold

Answer:3

Step-by-step explanation:easy 2 cups of pj plus cranberry juice is 3, get 6 by adding 3 again

Answer:

Step-by-step explanation:

What is an angle that is adjacent to BEC?

two angles that have the same vertex and a side in common

so

angle BEA

Answer: 46.5 by 19.5

Step-by-step explanation:

P=perimeter of panel. L=length. W=width

L=3W-12

P=2L+2W

132=2(3W-12)+2W

132=6W-24+2W

132=6W+2W-24

132=8W-24

156=8W

W=19.5

P=2L+2W

132=2L+2(19.5)

132=2L+39

2L=93

L=46.5

46.5 by 19.5

Answer:

7)B

8)B

9)A

10)C

Step-by-step explanation:

LET ME KNOW IF THIS HELPS.

Answer:

Step-by-step explanation:

8.2% of what amount is $2.87

2.87 : 8.2 * 100 =

35

Answer:

  45

Step-by-step explanation:

You want the product of 6+3i and its conjugate.

The conjugate of a complex number is created by reversing the sign of the imaginary part.

  (6 +3i)* = 6 -3i

The product of a complex number and its conjugate is recognizable as the factored form of the difference of squares:

  (6 +3i)(6 -3i) = (6)² -(3i)²

Of course, i² = -1, so this becomes ...

  6² -(3i)² = 36 -(-9) = 36 +9 = 45

The product of 6+3i and its conjugate is 45.

__

Additional comment

The product of a complex number and its conjugate is the sum of the squares of the magnitudes of the real and imaginary parts. It is always a real number. This fact is used to simplify expressions involving complex numbers.

Answer:

70 in^2

Step-by-step explanation:

Make a line through the middle separating the 5 by 5 square and the rectangle. Then you find the individual areas of each. The bottom shape is a 5 by 5 square, so 5*5 is 25. The top shape's length is 5+2+2 because the bottom shape is a square, so each side=5. Then the blank space between both of the length 2's is 5. As a result, the rectangle's dimensions is 9 by 5. 9*5=45. When we add both areas, we get 45+25=70

Answer: 30%

Step-by-step explanation: just add the 20% and 10% and you get 30%