The floor of a round hut has a diameter of 4 yards. What is the floor's area?

x = 3y perendicular to l

y = -3x parallel to l

y = 3x + 2 neither

x -3y = -6 perpendicular to l

6y = 2x + 10 perpendicular to l

A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks.

One approach for determining a line's slope from a graph is to use the formula immediately after knowing the coordinates of two points that are on the line. Let's assume that the coordinate values for the two spots are unknown. Therefore, we also have another way to determine the slope of the line. This approach entails attempting to determine the tangent of the angle formed by the line and the x-axis.

The line is

y = -3x -1

slope is -3 by slope intercept form

The line x = 3y

or y = (1/3)*x

slope is 1/3

we know for a line perpendicular to a given line slope should be -1/m so the slope will be  (1/3)

so, x = 3y  is perpendicular

y = -3x have slope -3 so it is parallel

y = 3x + 2  slope is 3 so neither

x - 3y = -6

or , y = (1/3)*x + 2 , so slope is (1/3) so perpendicular to line

And

6y = 2x + 10

here slope is 1/3 so perpendicular to line.

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number of tickets for adult = 170 and number of tickets for children = 151

What is equation with two variables?

The equation that has two unknown variables and express the equality between two or more expression is called equation with two variables.

let, x denotes the number of adults went to theater.

y denotes the number of children went to theater

price of ticket for each adult = $3.50

price of tickets for each child = $2.50

if the number of total tickets = 321

x + y = 321

total cost of tickets = $3.50x + $2.50y = 972.21 dollar

we will solve the above two equations, y = 321 - x

by putting the y value in the second equation,

3.50x + 2.50 (321- x) = 972.21

3.50x + 802.5 - 2.50x = 972.21

x = 169.71

number of adults went to theater = 170

from, y = 321 -169.71

    y = 321 - 169.71

y = 151.3, y= 151

number of children went to theater = 151

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The solution of the system of equations by using substitution method is x = 1 and y = 3

The substitution method is a method for solving systems of equations. It involves solving for one variable in one of the equations and then substituting that value into the other equation to find the value of the other variable.

We have the equations 4x + 4y = 16 and y = x+2

Substitute y = x +2 into  4x + 4y = 16:

4x + 4y = 16

4x + 4(x +2) = 16

Clear the parenthesis:

4x + 4x + 8 = 16

8x + 8 = 16

8x = 16-8

8x = 8

x = 8/8

x = 1

put x = 1 into  y = x+2:

y = x+2

y = 1 + 2

y = 3

Therefore, the solution of the system of equations is x = 1 and y = 3

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Answer:

$9 left

Step-by-step explanation:

1.50 x 2 = $3

1.50 x 2 = $3

2.50 x 2 = $5

5 + 3 + 3 = $11

$20 - $11 = $9

Answer:

Step-by-step explanation:

1.50+1.50+3

1.50+1.50+3

2.50+2.50= 5

5 + 3 + 3 = 11

20 - 11 = 9

Answer:

38[tex]\sqrt{3}[/tex]

Step-by-step explanation:

6[tex]\sqrt{5x5x3}[/tex] + 4[tex]\sqrt{2x2x3}[/tex]  We can pull out a pair of 5's and 2's

6(5) [tex]\sqrt{3}[/tex] + 4(2)[tex]\sqrt{3}[/tex]

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

38[tex]\sqrt{3}[/tex]

Verdadero. Cuando hay una potencia de una potencia, se conserva la base y los exponentes se multiplican.

Para calcular la potencia de una potencia, se puede conservar la base y multiplicar los exponentes. Esto se basa en la propiedad matemática de la potenciación que establece que (a^b)^c = a^(b*c), donde a es la base, b es el primer exponente y c es el segundo exponente.

Por ejemplo, considere (2³)⁴. La base es 2 y el primer exponente es 3 y el segundo exponente es 4. El resultado sería 2^(3*4) = 2¹². Esto significa que la expresión original (2³)⁴ es igual a 2 elevado a la potencia de 12.

En general, cuando se tiene una potencia de una potencia, el resultado se obtiene conservando la base y multiplicando los exponentes. Esto permite simplificar la expresión y encontrar el resultado de manera más fácil.

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Answer:

Option C

Step-by-step explanation:

         Factorize 768

768 = 4 * 4 * 4 * 4 * 3

For every four times of a constant or variable, take one constant or variable outside the fourth root.

[tex]\sqrt[4]{768x^8y^5}=\sqrt[4]{4*4*4*4*3 * (x^2)^4 * y^4 * y}[/tex]

                [tex]=4x^2y\sqrt[4]{3y}[/tex]

The amount that would be covered by the Insurance Plan would be and the amount that is billed to the patient is  $ 9. 75

The amount that would be covered by the insurance plan in a 85 / 15 coinsurance plan is 85 % of the bill. The amount to be covered by the insurance plan is:

= 85% x 65

= $ 55. 25

The amount billed to the patient is:

= Total bill - covered by insurance plan

= 65 - 55 .25

= $ 9. 75

In conclusion, the amount that would be covered by the insurance plan is $ 55. 25 and the amount to be billed to the patient to be paid by them is $ 9. 75.

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Answer:

(125, -312500)

C(x) = -312500

Step-by-step explanation:

use this equation into a graphing calculator and use the minimum function

the space between  [tex]3x-2\ge -5 : $x \geq-1$[/tex] the time between

[tex]2x+5\le 17 : $x \leq 6$[/tex] . When two simple inequalities are combined, the result is a compound inequality.

Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and." When a number resolves both inequalities, it also resolves the compound inequality. Compound inequality can come in two different forms. Both congruence and disjunction issues are at play.

Occasionally, these compound inequality formulas will be represented as two simple inequality formulas that have been separated by the words AND or OR. If there are multiple "and/or" compound inequalities, start by resolving each one separately. It is an inequality when two simple inequalities are combined to form it. The two expressions that make up an equation or an inequality are connected in a mathematical statement.

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Answer:

Step-by-step explanation:

To find the solutions to f(x) = g(x), we need to find the values of x that make the two sides of the equation equal.The function f(x) = −|x−4| + 4 is a piecewise function. For x≤4, f(x) = −(x−4) + 4 = 4−x and for x>4, f(x) = (x−4) + 4 = x.The function g(x) = 1/2x − 4 is a linear function.When we graph these two functions in the same coordinate plane, we can see that they intersect at the point (4, 4) this point is the only solution where f(x) = g(x)so the solution of x = 4

x = 4

Explanation:

First we solve for y.

x + 2y = -14

2y = -14 - x

2y = -x - 14

y = (-x - 14)/2

y = -x/2 - 14/2

y = (-1/2)x - 7

The equation is in slope intercept form y = mx+b

Parallel lines have equal slopes, but different y intercepts. This means the slope of any line parallel to this given one will have a slope of -1/2

For example, y = (-1/2)x + 10 is parallel to y = (-1/2)x - 7, since both have the same slope of -1/2 but different y intercepts.

Answer:

1.806 (to the nearest thousandth)

Step-by-step explanation:

1.806 (to the nearest thousandth)

The number 1.80642 would round down to 1.806

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  1.80642 to the nearest hundredth,

We can see that the 1.80642 is below 2 so it goes down, and it rounds down to 1.80642 instead of, 14.62 then that would round up to the decimal is higher than 1.

1.80642 rounded to the nearest thousandth is 1.806.

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Answer:

A = $400, B = $300, C = $240

Step-by-step explanation:

The ratio will be [tex]\frac{20}{60}:\frac{15}{60}:\frac{12}{60}[/tex], that means the total of them is (20 + 15 + 12 = 47).

Divide $940 by 47 to find the value of 1 unit [tex]\frac{940}{47}=20[/tex]

A = 20 × 20 = $400

B = 20 × 15 = $300

C = 20 × 12 = $240

The amount that Cameron is paid per hour, given the number of hours he worked, is $ 18 per hour

To find the payment that Cameron got per hour, you first need to find the number of hours that he worked.

This number of hours is:

= 4 pm  - 7 am

= 1600 hrs - 0700 hours

= 9 hours

The payment per hour is therefore:

= Amount Cameron paid / Number of hours worked

= 162 / 9

= $ 18 per hour

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The rest of the question is:

How much was Cameron paid per hour worked?

The rate of interest is given by the equation R = 3.5 %

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the rate of interest be represented as R

Now , the simple interest I = $ 175

The principal amount invested P = $ 2,500

The time period T = 2 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )

Substituting the values in the equation , we get

Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )

Rate of Interest R = 17500 / 5000

Rate of Interest R = 3.5 %

Hence , the interest rate is 3.5 %

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If a car radiator needs a 40% antifreeze solution the radiator now holds 49% of a 30% solution. The number of  liters that should be drained and replaced with 100% antifreeze to get the desired strength is 7 liters.

Let x represent the number of liters that should be drained

So, Let solve for x

x+.30(49-x)=.40× 49

x=14.7-.30x=19.6

.7x=19.6 - 14.7

.7x=4.9

x=4.9/.7

x = 7 liters need to be drained & filled with 100% antifreeze.

Therefore the number of liters is 7 liters.

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Step-by-step explanation:

the intersection of the diagonals of a parallelogram is always the middle point of either of the diagonals.

so, all we need to do is identify a diagonal and find is middle point.

a diagonal is e.g. from all the way on the left and up (-2, 5) to all the way right and down (4, 0).

the middle point between 2 points is

((x1 + x2)/2, (y1 + y2)/2)

so, here

((-2 + 4)/2, (5 + 0)/2) = (1, 2.5)

the coordinates of the intersection are (1, 2.5).

The value of n(AxB) is mathematically given as

n(A x B)  = 18

Generally, It is possible to extend the formula for calculating the magnitude of a vector to any number of dimensions. For instance, the magnitude of a four-dimensional vector denoted by

a=(a1,a2,a3,a4) may be calculated using the following formula: a=a21+a22+a23+a24.

The question "how much of a quantity" is what's meant to be answered when one asks about magnitude.

For instance, the magnitude may be used to provide an explanation for why the speeds of a vehicle and a bicycle cannot be compared directly to one another. It is also possible to use it to describe the distance traveled by an item or the quantity of an object in terms of its magnitude. Both of these applications need the usage of magnitude.

n(A x B) = |A| x |B|

= 6 x 3

n(A x B)  = 18

Where

The product of these two values is the total number of ordered pairs that can be formed from the elements of A and B, which is 18.

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Answer:First, we can simplify the equation a^2 = 3a + 1 by subtracting 3a and 1 from both sides, to get:

a^2 - 3a - 1 = 0

Now we can factor the left side:

(a-1)(a+1) = 0

This equation tells us that either a-1 = 0 or a+1 = 0. So, a = 1 or a = -1.

Next, we can substitute these values into the expression (a+1/a)^2

For a = 1, (1+1/1)^2 = 2^2 = 4

For a = -1, (-1+1/(-1))^2 = 0^2 = 0

So, the value of (a+1/a)^2 is 4 when a = 1, and 0 when a = -1

Step-by-step explanation:

Answer: (-2, 10)

Explanation:

The left endpoint is -2. The right endpoint is 10. Both endpoints are open holes, which means we don't include them as part of the green-shaded solution region. If x is a solution, then the solution can be described as [tex]-2 < x < 10[/tex] converting to interval notation [tex](-2,10)[/tex] . The curly bracket says "do not include endpoint".

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The area of the new triangle g’h’i’ is 9.

The area of a triangle is a measure of the size of the triangle, calculated as the amount of space enclosed by its three sides. It can be calculated using the following formula:

Area = (base x height) / 2

where base is the length of one side of the triangle, and height is the perpendicular distance from the base to the opposite vertex.

If a triangle is rotated 180 degrees about the origin, its coordinates will change signs. If it is then dilated by a factor of 3, its coordinates will be multiplied by 3. The new triangle g'h'i' will have the following coordinates: g' (-3,0), h' (0,3), and i' (0,-3).

The height of the new triangle will be the absolute value of the difference between its y-coordinates: h = |3 - (-3)| = 6. The base of the triangle will be the absolute value of the difference between its x-coordinates: b = |-3 - 0| = 3.

Therefore, the area of the new triangle g'h'i' is: A = (1/2)bh = (1/2)(3)(6) = 9.

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Answer:

Step-by-step explanation:

24

The balance sheet for McGuire Corporation as at December 31, 2021, is as follows:

McGuire Corporation

As at December 31, 2021

Current Assets:

Cash                                  $56,000

Accounts Receivable       $22,000

Inventory                          $50,000

Rent Prepaid                      $2,000

Total current assets                          $130,000

Long-term assets:

Office Equipment              $30,000

Accumulated Depreciation (3,000)  $27,000

Total assets                                      $157,000

Current Liabilities:

Accounts payable                            $30,000

Salaries Payable                                $5,000

Interest Payable                                $3,600

Total current liabilities                    $38,600

Long-term liabilities:

Notes Payable                                $40,000

Total liabilities                                $78,600

Common Stock      $50,000

Net income            $28,400          $78,400

Total liabilities and Equity           $157,000

The balance sheet is one of the financial statements where an entity or individual reports their financial position.

The financial position consists of assets, liabilities, and equity or net worth at a specific time.

Cash $56,000 ($410,000 - $354,000)

Accounts Receivable $22,000

Inventory $50,000

Rent Prepaid $2,000

Office Equipment $30,000

Accumulated Depreciation on Equipment $3,000

Accounts payable $30,000

Salaries Payable $5,000

Common Stock $50,000

Notes Payable $40,000

Interest Payable $3,600

Sales Revenue $342,000 ($320,000 + $22,000)

Cost of goods sold $200,000 ($220,000 + $30,000 - $50,000)

Salaries Expense $85,000 ($80,000 + $5,000)

Rent Expense $12,000 ($14,000 - $2,000)

Miscellaneous Expense $10,000

Interest Expense $3,600 ($40,000 x 12% x 9/12)

Depreciation Expense $3,000 ($30,000/10)

Account Titles                 Debit        Credit

Cash                             $56,000

Accounts Receivable    22,000

Inventory                       50,000

Rent Prepaid                   2,000

Office Equipment         30,000

Accumulated Depreciation:

  Office Equipment                        $3,000

Accounts payable                          30,000

Salaries Payable                              5,000

Common Stock                             50,000

Notes Payable                              40,000

Interest Payable                             3,600

Sales Revenue                           342,000

Cost of goods sold   200,000

Salaries Expense        85,000

Rent Expense              12,000

Miscellaneous Exp.     10,000

Interest Expense          3,600

Depreciation Expense 3,000

Totals                     $473,600  $473,600

Sales Revenue                                 $342,000

Cost of goods sold       $200,000

Salaries Expense            $85,000

Rent Expense                  $12,000

Miscellaneous Expense $10,000

Depreciation Expense     $3,000

Interest Expense              $3,600    $313,600

Net income                                        $28,400

Thus, before the balance sheet can be prepared, the general ledger must be summarized into an adjusted trial balance and an income statement that shows the net income.

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The prime polynomial in this problem is defined as follows:

D. 3x² + x - 6x + 3

A prime polynomial is a polynomial that cannot be reduced, that is, the polynomial cannot be factored.

The reduced forms of each polynomial are given as follows:

The first polynomial can be factored as follows:

x^4 - x² + 3x² - 3

x²(x² - 1) + 3(x² - 1)

(x² + 3)(x² - 1).

It can be factored, hence it is not prime.

The second polynomial is factored as follows:

x^4 - 3x² - x² + 3

x^4 - x² - 3x² + 3

x²(x² - 1) - 3(x² - 1)

(x² - 3)(x² - 1).

It can be factored, hence it is not prime.

The third polynomial is factored as follows:

3x² + x - 6x - 2

3x² - 6x + x - 2

3x(x - 2) + x - 2

(x - 2)(3x + 1)

It can be factored, hence it is not prime.

The fourth polynomial cannot be factored, hence it is prime.

3x² + x - 6x + 3

3x² + 6x + x + 3

3x(x + 2) + x + 3.

x + 2 and x + 3 cannot be factored.

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The average speed of Apolo Ohno, in the sprint in the Winter Olympics in 2006, given the time taken to complete the course, was 11. 92 m /s

A body's average speed is the mean value of its speed for a certain time period. The average speed formula is necessary because a moving body's speed vary over time instead than remaining constant. Even though the speed changes, we can still use the total time and total distance numbers, and with the help of the average speed calculation, we can determine a single value that represents the entirety of the motion.

Given the distance that Apolo Ohno had to sprint and the time he completed the course in, his average speed in the event was :

= 500 m / 41. 935 s

= 11. 92 m /s

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Answer:

a. Let x be the speed of the boat in miles per hour and y be the speed of the current in miles per hour. Since the boat traveled upstream, the speed of the current is added to the speed of the boat. Therefore, the equation for the trip upstream is:

distance = (x + y) * time

10 = (x + y) * 5

b. For the return trip, the speed of the current is subtracted from the speed of the boat. Therefore, the equation for the return trip is:

distance = (x - y) * (time/2)

10 = (x - y) * (5/2)

c. To find the speed of the boat and the speed of the current, we can use the method of elimination. From the first equation, we have:

10 = 5x + 5y

From the second equation, we have:

10 = 2.5x - 2.5y

Now we can use the elimination method by multiplying the first equation by 2 and then subtracting the second equation from it.

20 = 10x + 10y

20 = 5x - 5y

so we have

0 = 5x + 5y - 5x + 5y

0 = 10y

The equation becomes impossible to solve as we can't divide by 0.

As we know that the speed of the boat and the speed of the current are non-zero numbers, we can't find the exact speed of the boat and the current. We can conclude that the information given is not sufficient to find the exact speed of the boat and the current.

Step-by-step explanation:

The amount of the discount, in dollars and cents is $14.77

Total amount paid for the ticket = $32

Percentage discount = 30% of x

Percentage processing fee = 5%

Total amount paid = x - (30% of x) + 5% of x

32 = x - 0.3x + 0.05x

32 = 0.65x

divide both sides by 0.65

x = 32/0.65

x = 49.23076923076923

Approximately,

x = $49.23

Therefore,

Percentage discount = 30% of x

= 0.3 × $49.23

= $14.769

Approximately,

$14.77

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Answer:

y = - [tex]\frac{1}{2}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mc + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x + 6 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes , then

slope of parallel line = - [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of parallel line