6. Find the components of the vector V with initial point P(-4,5) and terminal point
Q(-2,7).
(i) < -2,-2>
(iv) <-6, 12>
(ii) < 8,35 >
(iii) <2, 5/7>
(v) <2,2>
(vi) not listed

Answer:

  $9.34 per square foot

Step-by-step explanation:

You want the cost per square foot of a 36 foot square building that costs $12,099.

The cost per square foot is found by dividing the cost by the number of square feet. That area is found as the square of the side length:

  A = s²

  A = (36 ft)² = 1296 ft²

Then the cost is ...

  cost per square foot = ($12099)/(1296 ft²) ≈ $9.34/ft²

The cost of the building is about $9.34 per square foot.

<95141404393>

The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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The value of 'x' is 1 and value of y is '0'.

An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

We have the equations are:

-3x + 5y = -3 ___eq.1

and, y = -7 + 7 ___eq.2

We have to find the value of 'x' and 'y'

Now, Firstly find the value of y

We know that :

Opposite sign with same digit is cancel to each other it is always zero.

y = -7 + 7

So, y = 0

Now, We have to put the value of y in eq. 1

-3x + 5(0) = -3

-3x + 0 = -3

x = -3/-3

x = 1

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The experimental probability that an arrangement will contain at least one red balloon and at least one blue balloon is 0.53. Therefore, option B is the correct answer.

The given sample space is {ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr}

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favorable outcomes =16

Probability of an event 16/30

= 0.53

Therefore, option B is the correct answer.

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The horizontal distance the ball travelled is 2.73 m.

A projectile is any object that is moving in space under the influence of gravity and its momentum. The horizontal distance covered by a projectile from its point of projection is called range. It can be determined by;

R = U[tex]\sqrt{\frac{2H}{g} }[/tex]

where u is the initial speed of the object, H is the height of projection and g is the gravitational constant.

So that in the information given, we can determine the range as;

R = U[tex]\sqrt{\frac{2H}{g} }[/tex]

  = 35[tex]\sqrt{\frac{2*0.39}{10} }[/tex]

  = 35*0.078

  = 2.73

R = 2.73 m

The horizontal distance the ball has travelled is 2.73 m.

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Answer:

Set your calculator to degree mode.

Please sketch the figure to confirm my answer.

cos(49.4°) = d/16.2

d = 16.2cos(49.4°) = 10.5 feet

Answer:

The circumference of a circle is given by the formula "C = pi x d" where "d" is the diameter and "pi" is the mathematical constant with an approximate value of 3.14.

In this problem, the diameter of the bicycle wheel is 60 centimeters, so its circumference is:

C = pi x d = 3.14 x 60 = 188.4 centimeters

When the wheel makes one revolution, it travels one circumference distance. Therefore, when the wheel makes 35 revolutions, it will travel:

distance = 35 x circumference = 35 x 188.4 = 6584 centimeters

We can convert centimeters to meters by dividing the distance by 100:

distance = 6584 ÷ 100 = 65.84 meters

Therefore, the wheel travels 65.84 meters when it makes 35 revolutions.

Answer:131290

Step-by-step explanation:13129*100/10=131290

Answer: The answer is 171.2 Miles

Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.

Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.

To find the domain of a function, we need to determine all values of the independent variable (usually denoted as x) for which the function is defined and has a real output.

For example, if we have the function:

f(x) = 1/(x-3)

We need to exclude any values of x that would make the denominator zero, since division by zero is undefined. Therefore, the domain of this function would be all real numbers except x = 3. We could write this as:

Domain: x ∈ ℝ, x ≠ 3

If we have a more complex function, we need to consider any other restrictions on the independent variable that may be imposed by the function.

For instance, if we have the function:

g(x) = sqrt(x-2)/(x+3)

Here, the square root function is defined only for nonnegative values of its argument. Therefore, we need to ensure that x-2 ≥ 0, or equivalently, x ≥ 2. Additionally, the denominator of the fraction cannot be zero, so we need to exclude x = -3. Combining these two conditions, we get:

Domain: x ∈ [2, ∞), x ≠ -3

This means that the function g(x) is defined and has a real output for all values of x greater than or equal to 2, except x = -3.

In general, to find the domain of a function, we need to consider any restrictions on the independent variable imposed by the function itself (such as division by zero, taking the square root of a negative number, etc.), as well as any restrictions that may be imposed by the context in which the function is used (such as physical or mathematical constraints). We then express the domain as a set of values of x that satisfy all the relevant conditions.

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In a case whreby the electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r the simpification of the expression is 1/r(1-r).

Looking at the expression we can see that it is adion of two expression which implies that we will need to perform an addition operation then later simplified the result, this is been done below

We can find the LCM as r(1-r)

(1-r +r)/ r(1-r)

=1/r(1-r)

Therfore, after performing the addition operation as well as the simplification, then the the simpification of the expression is 1/r(1-r).

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complete question;

The electrical potential between two electrons is given by a formula has the form 1/r + 1/ 1-r simplify the expression.

Answer:

The points selected on the graph are:

(0, 0), (2, 4), (3, 6), (4, 8), (6, 12), (4, 8), (8, 16), (5, 10)

Here is a table showing the coordinates of the selected points:

x      y

0      0

2      4

3      6

4      8

6      12

4      8

8      16

5      10

Christo's monthly repayments for a loan of R5,100,000 for 10 years at 9,5% interest compounded monthly is R65,992.75.

The monthly repayments can be determined using an online finance calculator as follows:

The monthly repayments show the periodic payments to settle the loan.

Wine Farm Price = R8,500,000

Down Payment = R3,400,000

Loan Term = 10 years

Interest Rate = 9.5%

Start Date = Apr. 2023

Monthly Pay:   R65,992.75

Loan Amount = R5,100,000.00

Total of 120 Mortgage Payments = R7,919,130.52

Total Interest = R2,819,130.52

Mortgage Payoff Date = Apr. 2033

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Answer:

True

Explanation:

Bridget Riley was one of the most prominent artists associated with the 1960s 'Op Art' movement, which was an art movement that explored optical illusions and effects to create abstract art that played with the viewer's perception. However, there were many other artists associated with this movement, including Victor Vasarely, Richard Anuszkiewicz, and Yaacov Agam, among others.

Answer:

Thousand

Step-by-step explanation:

Solve:

58,391

Knowing that:

When rounding to:

Because the digit to the right in the hundreds place is 3 which is less than 5- Thus, it goes down to 58,000.

RevyBreeze

Answer:

I think it's Thousand

Answer: The Correct answer is E (2,pie/6)

Step-by-step explanation:

To find the polar coordinates of a point given its Cartesian coordinates (x, y), we can use the following formulas:

r = √(x^2 + y^2)

θ = atan2(y, x)

where r is the radial distance from the origin to the point, and θ is the angle measured counterclockwise from the positive x-axis to the line connecting the origin and the point.

Given the Cartesian coordinates (x, y) = (√3, 1), we can plug these values into the formulas to find the polar coordinates:

r = √(√3^2 + 1^2) = √(3 + 1) = 2

θ = atan2(1, √3)

Using a calculator, we can find that θ is approximately 0.5236 radians.

So, the polar coordinates of the point (√3, 1) are (r, θ) = (2, 0.5236 radians).

The second job offer is better by $21,840.

We have :

An employee is considering two job offers.

First offer: $57,000 yearly salary with an 8% matching 401k

Second offer: $63,000 yearly salary with a 4% matching 401k

Let's calculate the total value of the second offer after 4 years:

Yearly salary is : $63,000

Total gross income after 4 years: $63,000 x 4 = $252,000

The company matches 5% of the employee's salary.

So, the employee contributes 5% of $63,000 = $3,150 per year

After 4 years,

Company matches: $3,150 x 4 = $12,600

Employee contributions: $3,150 x 4 = $12,600

Total 401k contributions: $12,600 + $12,600 = $25,200

The total value of the second offer after 4 years is:

Total value: $252,000 + $25,200 = $277,200

Now, let's compare this to the total value of the first offer, which is : $255,360.

Therefore, the second job offer is better by:

$277,200 - $255,360 = $21,840

Hence, The second job offer is better by $21,840.

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2 3/4 cups is equivalent to 1 3/8 pints as a mixed number.

There are 2 cups in a pint. To convert 2 3/4 cups into pints, we can follow these steps:

Convert the whole number part of the mixed number to pints by dividing by 2.

Convert the fractional part of the mixed number to cups, then divide by 2 to get the corresponding pints.

Add the two results together to get the total in pints as a mixed number.

So, let's apply these steps to 2 3/4 cups:

The whole number part is 2, so 2 cups = 1 pint.

The fractional part is 3/4 cups, which is equivalent to 3/4 ÷ 2 = 3/8 pints.

Adding the two results, we get:

1 pint (from the whole number part) + 3/8 pint (from the fractional part) = 1 3/8 pints.

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Answer:

[tex]100000( {.70}^{3} ) = 34300[/tex]

The most reasonable unit of measurement for 3) is option (C): [tex]m^2[/tex], 4) is option (B): [tex]km^2[/tex], 5) is [tex]in^2[/tex].

3) The most reasonable unit for the measurement of the baseball field is [tex]m^2[/tex] because the baseball field covers a large distance which is not accurately measured by small units  [tex]cm^2[/tex] or [tex]mm^2[/tex]  where it is not that big to be measured in large units like [tex]km^2[/tex]. So option C is the correct option.

4) The most reasonable unit for the measurement of a lake is [tex]km^2[/tex] because lakes are generally very large water bodies that cover a large distance and are not accurately measured by small units like [tex]cm^2[/tex] , [tex]mm^2[/tex] , and [tex]m^2[/tex]. So option B is the correct option.

5) The most reasonable unit for the measurement of the area of a door is [tex]in^2[/tex] because doors are relatively small compared to the other options and are often measured in square inches or square feet. So option B is the correct option.

Therefore the correct answers question-wise are:

3) [tex]m^2[/tex]

4) [tex]km^2[/tex]

5) [tex]in^2[/tex]

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The Galois group of f over R is isomorphic to the symmetric group S4. The given statement "Each intermediate field of F/Q is a Galois extension of Q." is true because f is separable.

The roots of f are given by

x = ±(√(5) + √(2)), ±(√(5) - √(2))

Let φ be the automorphism defined by

φ(√(5) + √(2)) = √(5) + i√(2)

φ(√(5) - √(2)) = √(5) - i√(2)

φ(-√(5) + √(2)) = -√(5) - i√(2)

φ(-√(5) - √(2)) = -√(5) + i√(2)

where i is the imaginary unit. Then φ has order four since φ⁴ is the identity automorphism. Let σ be the automorphism defined by

σ(√(5) + √(2)) = -√(5) + √(2)

σ(√(5) - √(2)) = √(5) - √(2)

σ(-√(5) + √(2)) = -√(5) - √(2)

σ(-√(5) - √(2)) = √(5) + √(2)

Then σ has order two since σ² is the identity automorphism. It can be shown that the Galois group of f over Q is generated by φ and σ. Since φ has order four and σ has order two, the Galois group is a non-abelian group of order eight.

To prove or disprove that each intermediate field of F/Q is a Galois extension of Q, we need to show that each intermediate field is a splitting field of a separable polynomial over Q. Since F is the splitting field of f over Q, any intermediate field of F/Q is also a splitting field of f over Q. Since f is separable (its roots are distinct), every intermediate field of F/Q is a Galois extension of Q, and hence a splitting field of a separable polynomial over Q. Therefore, the statement is true.

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Answer:

Here's how to graph the piecewise function:

First, we graph the function for the first interval, which is f(x) = 3x - 5 when x ≤ -1. This is a straight line with a slope of 3 and a y-intercept of -5. Since this interval includes -1, we draw a closed circle at x = -1 to indicate that it is included in the interval. The line is decreasing as x increases.

Next, we graph the function for the second interval, which is f(x) = -2x + 3 when -1 < x < 4. This is also a straight line, but with a slope of -2 and a y-intercept of 3. Since this interval does not include -1, we draw an open circle at x = -1 to indicate that it is not included in the interval. We also draw an open circle at x = 4 to indicate that it is not included in the interval. The line is increasing as x increases.

Finally, we graph the function for the third interval, which is f(x) = 2 when x ≥ 4. This is a horizontal line at y = 2. Since this interval includes 4, we draw a closed circle at x = 4 to indicate that it is included in the interval.

When we put all three intervals together, we get a graph that looks like this:

```

         |         /

  2      |        /

         |       /

         |      /

         |     /

         |    /

         |   /

         |  /

         | /

         |/

  _______|_____________

         -1   4

```

The graph consists of a downward-sloping line from (-∞, -1], an upward-sloping line from (-1, 4), and a horizontal line from [4, ∞).

The width of each poster cannot be greater than 11/4 feet or 2.75 feet.

For given expression w represents the width, 4w represents the total width of four posters, 5 represents space between posters and edges of wall, and 16 represents width of the wall.

The boundary value satisfies the inequality.

In the given problem, Marie-Renee wants to hang 4 identical posters on her wall, and she needs to leave at least 5 feet of space total between the posters and between the edges of the wall. Let's assume that the width of each poster is w feet.

The inequality 4w + 5 ≤ 16 represents the maximum space the posters can take on the wall. In this inequality,

w represents the width of each poster,

4w represents the total width of four identical posters,

5 represents the total space between the posters and between the edges of the wall, and

16 represents the total width of the wall.

To find the acceptable width of each poster, we need to solve 4w + 5 = 16.

4w + 5 = 16

4w = 16 - 5

4w = 11

w = 11/4

So, the width of each poster cannot be greater than 11/4 feet or 2.75 feet.

Now, we need to check if the boundary value of w satisfies the original inequality or not.

4w + 5 ≤ 16

4(11/4) + 5 ≤ 16

11 + 5 ≤ 16

16 ≤ 16

Since the boundary value satisfies the inequality, the solution to Marie-Renee's inequality is w ≤ 11/4 or w ≤ 2.75 feet.

Therefore, the width of each poster cannot exceed 2.75 feet, and all four posters can be hung on the 16 feet wide wall with at least 5 feet of space total between them and the edges of the wall.

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Answer:

The tip of the minute hand on a clock travels 15π inches in 45 minutes if the distance from the center to the tip is 10 inches.

Answer: The market demand is x = 750.

Step-by-step explanation:

Answer: The market demand is x = 750.

Explanation:

To find the market demand, we need to set the demand function equal to the supply function and solve for x:

d(x) = s(x)

600 − 0.8x = 0.4x

Combining like terms, we get:

600 = 1.2x

Dividing both sides by 1.2, we get:

x = 500

However, we need to find the positive value of x. Since x represents the quantity demanded, it cannot be negative.

Substituting x = 500 into both the demand and supply functions, we find that:

d(500) = 600 - 0.8(500) = 200

s(500) = 0.4(500) = 200

Since d(500) = s(500), x = 500 is not the market demand.

Substituting x = 750 into both the demand and supply functions, we find that:

d(750) = 600 - 0.8(750) = 0

s(750) = 0.4(750) = 300

Since d(750) = s(750), x = 750 is the market demand.

Therefore, the market demand is x = 750.

Answer:

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's check if the triangle with sides of 30, 64, and 90 is a right triangle:

30^2 + 64^2 = 900 + 4096 = 4996

90^2 = 8100

Since 4996 is less than 8100, the triangle is not a right triangle.

In an acute triangle, all angles are less than 90 degrees. In an obtuse triangle, one angle is greater than 90 degrees.

To determine if the triangle is acute or obtuse, we need to find the largest side. The largest side is 90. Let's find the sum of the squares of the other two sides:

30^2 + 64^2 = 900 + 4096 = 4996

Since 4996 is less than 90^2, the triangle is acute.

Therefore, the triangle with sides of 30, 64, and 90 is an acute triangle.

the triangle is obtuse

Step-by-step explanation:

[tex] {90}^{2} = 8100[/tex]

[tex] {30}^{2} + {64}^{2} = 4996[/tex]

[tex] {30}^{2} + {60}^{2} < {90}^{2} [/tex]

triangle is obtuse because the square of the largest is greater than the sum of the square of the other 2 sides

The equivalent equation of  r sinθ = 10 in rectangular coordinates is y²  +   y⁴/x² - 100 = 0.

The rectangular coordinates is calculated from the polar equation as follows;

r sinθ = 10

the conversion from polar to rectangular coordinates;

r² = x² + y²

r = √(x² + y²) ----- (1)

y/x = tanθ  ------ (2)

r sinθ = 10

√(x² + y²)(y/x) = 10

(x² + y²)(y²/x²) = 100

y²  +   y⁴/x² = 100

y²  +   y⁴/x² - 100 = 0

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Answer:

Step-by-step explanation:

Answer: 108

Step-by-step explanation:

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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