Choose the correct way to complete the sentence to explain how to correctly use the Fillet command in the given situation.

When using the Fillet command, if you specify the radius as __________ you can create lines that connect as a sharp edge.

The solution of the equations is x = -5/6 and y = 7/6.

We are given that;

18x + 12y = 13

30x + 24y= 23

Now,

To find X, we multiply both sides of the equation by A^(-1):

To multiply two matrices, we multiply each element in a row of the first matrix by each element in a column of the second matrix, and add them up. For example, to find the first element of X, we multiply the first row of A^(-1) by the first column of B:

We repeat this process for each element of X and simplify:

Therefore, by the given equations the answer will be x = -5/6 and y = 7/6.

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Answer:

The mean is 3.5 whales

Step-by-step explanation:

The mean is the average.

So add up the numbers, and the divide by the count of the numbers.

3 + 3 + 5 + 3 = 14

We have 4 numbers in this data set. So divide by 4.

14/4 = 3.5

The mean is 3.5.

The person that has the longer piece of string is Kayla.

To determine the person with the longer piece of string, we need to convert the figures to one unit. So, let us convert 200 millimeters to centimeters as follows:

1 centimeter = 10 millimeters

So, x             = 200 millimeters

200 = 10 x

x = 200/10

x = 20 cm.

So, while Norman has a 15 centimeters long string, Kayla has a 20 cm long string. The person with the longer piece is Kayla.

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The vector w in trigonometric form is B. w = 29(cos 223.603°i + sin 223.603°j). Therefore,  option B: w = 29(cos 223.603°i + sin 223.603°j) is correct.

To represent a vector in trigonometric form, we need to find the magnitude and angle of the vector. Given the vector w = <-21,-20>, the magnitude can be found using the Pythagorean theorem as:

[tex]|w| = \sqrt{((-21)^2 + (-20)^2) } = 29[/tex]

Next, we need to find the angle of the vector. Since the vector has negative components, the angle will be in the third or fourth quadrant. We can find the angle using the arctangent function as:

theta = arctan(-20/-21) = 46.603 degrees

Since the angle is in the fourth quadrant, we need to add 180 degrees to get the angle in trigonometric form:

theta = 46.603 + 180 = 223.603 degrees

Therefore, the vector w in trigonometric form is:

w = 29(cos 223.603°i + sin 223.603°j)

Hence, the correct answer is option B: w = 29(cos 223.603°i + sin 223.603°j).

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The second additional Polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

We have a point in polar coordinates (3,-π/6) and we have to find two additional polar representations of this point. Let's recall the formula for converting from Cartesian to polar coordinates :x = rcosθy = rsinθAnd

the formula for converting from polar to Cartesian coordinates :r = √(x²+y²)θ = arctan(y/x)So, we can use the second formula to convert (3,-π/6) to Cartesian coordinates:$$x=3\cos(-\frac{\pi}{6})=3\cdot \frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{2}$$$$y=3\sin(-\frac{\pi}{6})=3\cdot \frac{-1}{2}=-\frac{3}{2}$$

Now we can use the first formula to convert back to polar coordinates:$$r=\sqrt{(\frac{3\sqrt{3}}{2})^2+(-\frac{3}{2})^2}=\frac{3\sqrt{6}}{2}$$$$\theta=\arctan(-\frac{3}{3\sqrt{3}})=-\frac{\pi}{3}$$

So, the first additional polar representation of the point (3,-π/6) is ($\frac{3\sqrt{6}}{2}$, $-\frac{\pi}{3}$).To find the second polar representation,

we need to add or subtract multiples of π to the angle until it is in the range [-2π, 2π].$$-\frac{\pi}{3}+2\pi=\frac{5\pi}{3}$$$$-\frac{\pi}{3}-2\pi=-\frac{7\pi}{3}$$

So, the second additional polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

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Answer: p < 5 1/2

Step-by-step explanation:your using inequality signs and since it’s less  than 5 1/2 you use the < sign and add the variable (I’m using p as the variable) to get p < 5  1/2

The requried simplified expression is 135.

To simplify the expression, we follow the order of operations: parentheses first, then exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Using this order of operations, we get:

64 ÷ 4(3 5-14 ÷ 2) + 7 = 64 ÷ 4(15 - 7) + 7 [Performing the division inside the parentheses first]

= 64 ÷ 4(8) + 7 [Simplifying inside the parentheses]

= 16(8) + 7 [Performing the multiplication]

= 128 + 7 [Adding the two terms]

= 135

Therefore, the simplified expression is 135.

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The required box plot has been shown.

To make a box plot of the coat prices, we need the following statistical measures:

With these five measures, we can construct a box plot that shows the distribution of the coat prices, including the median, quartiles, and any outliers.

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Yes, I agree with Benito's approach to finding the quotient of 45 ÷ 9.

We have,

When we divide 45 by 9, we are essentially asking, "How many times does 9 go into 45?"

This can also be rephrased as "What is the result of multiplying 9 by some number to get 45?"

Now,

To find the quotient of 45 ÷ 9, we can recall the related multiplication fact that 9 times 5 is equal to 45.

Then, we can use the Commutative Property of Multiplication, which states that the order of multiplication can be changed without changing the result, to recall the other related multiplication fact that 5 times 9 is equal to 45.

Therefore,

The quotient of 45 ÷ 9 is 5, which we can obtain by recalling either the multiplication fact 9 times 5 equals 45 or 5 times 9 equals 45.

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The length of each bracelet is  6.375 inches, and the remaining length of string after making the necklace is 51 inches.

Total length of string = 67 inches

Length of string used for the necklace = 16 inches

To find the remaining length of string, we subtract the length used for the necklace from the total length of string:

Remaining length of string = Total length of string - Length used for necklace

Remaining length of string = 67 inches - 16 inches

Remaining length of string = 51 inches

Since the remaining length of string is used to make 8 bracelets, we can divide the remaining length by the number of bracelets to find the length of each bracelet:

Length of each bracelet = Remaining length of string / Number of bracelets

Length of each bracelet = 51 inches / 8 bracelets

Simplifying the fraction:

Length of each bracelet = 6.375 inches

Therefore, the length of each bracelet is 6.375 inches.

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To determine which angle in a given shape is obtuse, we need to understand that an obtuse angle measures more than 90 degrees but less than 180 degrees.

1. Identify the vertices of the polygon: Determine the points where the sides of the polygon intersect.

2. Measure the angles: Use a protractor or angle measuring tool to measure each angle formed by the sides of the polygon.

3. Compare angle measurements: Look for an angle that measures more than 90 degrees but less than 180 degrees. This angle will be the obtuse angle in the shape.

It is important to note that the location of the obtuse angle will depend on the specific shape and its angles.

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$63,490 must be paid back at the end of that period.

To determine how much must be paid back, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal, $28,000

r = the interest rate, 6.5% = 0.065

n = the number of times the interest is compounded per year, in this case annually (n = 1)

t = the time period in years, 13

Substituting the values :

A = 28,000(1 + 0.065/1)¹ˣ¹³

A = 28,000(1 + 0.065)¹³

A = 28,000(1.065)¹³

A = $63,490

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There are 7 cups of 2/3 cups are there in 4 1/3.

We have to find that;

Number of 2/3 cups are there in 4 1/3.

Now, We can simplify the expression as;

Number of 2/3 cups are there in 4 1/3 is,

⇒ (4 1/3) / (2/3)

⇒ (13/3) / (2/3)

⇒ 13/2

⇒ 6.5

⇒ 7

Thus, There are 7 cups of 2/3 cups are there in 4 1/3.

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Answer: 40/3 or 13.33

Step-by-step explanation:

16/1 times 5/6

16•5=80

1•6=6

80/6 can be simplified to 40/3 by dividing 80 and 6 by 2 (Which is the GFC)

Answer: 183

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf x = 140\°}[/tex]

Step-by-step explanation:

According to the statement,

x = 72 + 68

[tex]\rule[225]{225}{2}[/tex]

Part A: the amount of taxes owed on a taxable income of $31,000 is $3,514.50. Part B: the effective tax rate on a taxable income of $31,000 is 11.33%.

Part A: From the tax bracket chart, we can see that $31,000 falls into the tax bracket $10,276 - $41,175, which has a marginal tax rate of 12%.

Using the piecewise function, we can substitute $31,000 into the equation for this tax bracket:

f(x) = 0.12x - 205.50

f(31,000) = 0.12(31,000) - 205.50

         = 3,720 - 205.50

         = $3,514.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,514.50.

Part B: The effective tax rate is calculated by dividing the total taxes owed by the taxable income. In this case, we can calculate the effective tax rate using the taxes owed from Part A and the taxable income of $31,000:

Effective tax rate = (Taxes owed / Taxable income) * 100

Effective tax rate = (3,514.50 / 31,000) * 100

                  = 11.33%

Therefore, the effective tax rate on a taxable income of $31,000 is 11.33%.

Part C: The marginal tax rate chart is represented in the piecewise function through a series of intervals and corresponding equations. Each interval represents a specific range of taxable income, and the corresponding equation within that interval represents the tax owed in that range.

For example, the marginal tax rate chart shows the tax brackets and their respective marginal tax rates. The piecewise function represents these tax brackets using the intervals and equations:

Therefore, the piecewise function captures the different tax brackets and their respective equations, representing the marginal tax rates for different ranges of taxable income.

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Answer: 204

Step-by-step explanation:

This is a funny question.

35 mph, there are 5280 feet per mile.

(35*5280) feet per hour

There are 60 minutes in a hour and 60 seconds in a minute

(35*5280/3600) feet per second

We calculate 5280/3600 first (exchangeable)

528/360

264/180

132/90

66/45

22/15

(22*35)/15

51.33333333333333 (etc)

Multiply 51 by 4

204

Using the concept of change of subject of formula, V = D/R

When changing the subject of formula, we rearrange the formula's components to create the new subject. Remember: Change side, change operation when doing this. In other words, alter the operation to do the reverse if you transfer a term from one side of the equals sign to the other.

In the given problem;

Let's make v the subject of formula in terms of D and R;

Dividing both sides of the equation by R, we have:

D/R = V

Therefore, V can be represented in terms of D and R as V = D/R.

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To transform the equation [tex]Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F = 0[/tex]  B≠0 into one in x' and y' without an x'y'-term, rotate the axes through an acute angle θ that satisfies the equation B' = 0.

The steps involved in transforming the equation are as follows:

Step 1: Determine the angle of rotation

The angle of rotation, θ, is determined using the following equation: tan2θ = B / A - C Where A > C, which implies that the angle of rotation θ lies between -45° and 45° (i.e., it is an acute angle).

Step 2: Compute the transformed equation

The transformed equation is given by: [tex]A'x'^{2} + C'y'^{2} + Dx' + Ey' + F = 0[/tex]where A' = A cos²θ + B sin θ cos θ + C sin²θ, C' = A sin²θ - B sin θ cos θ + C cos²θ,D' = D cos θ + E sin θ, E' = -D sin θ + E cos θ.

To eliminate the x'y'-term from the transformed equation, we need to find an angle of rotation θ such that B' = 0.

If B' is not equal to 0, we need to repeat the process with a different value of θ until we get B' = 0.

Once we have found the angle of rotation θ that gives B' = 0, we can then use the transformed equation to solve the original equation.

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Answer:

Not sure what you mean, but x = -6

Step-by-step explanation:

3x - 5 = 5x + 7

Start by crossing off the 3x and subtracting 3x from 5x.

-5 = 2x + 7

Subtract 7.

2x = -12

-12 divided by 2 = -6

x = -6

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Answer: D

Step-by-step explanation:

The graph isn't fully labeled, but I'm assuming that the bottom ticks are pi/2, pi, 3pi/2, and so on.

So: the equation is 2/(pi/2)

Using fraction division, we know that a/(b/c)=(ac)/b

4 over pi

The value of domain of the equation is [3, ∞) and the range of the equation is [2, ∞).

The given equation is,

⇒ y= 4√(x-3) + 2.

Now, To find the domain of the equation, we need to consider the values of x for which the expression under the square root is greater than or equal to zero.

So, we have

x-3 ≥ 0,

which gives,

x ≥ 3.

Therefore, the domain of the equation is [3, ∞).

And, the range of the equation, we need to consider the values of y that the equation can take.

Since the square root of any non-negative number is always non-negative,

we know that 4√(x-3) is always greater than or equal to zero.

And adding 2 to that gives us a range of [2, ∞).

So, the domain of the equation is [3, ∞) and the range of the equation is [2, ∞).

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The simplified expression is cos²x - sin²x, which is equivalent to cos(2x).

option A.

To simplify the expression cosx (cosx - tanx sinx), we can use the trigonometric identity.

cosx (cosx - tanx sinx)

Using the identity tanx = sinx/cosx, we will have;

= cosx (cosx - sinx/cosx(sinx) )

= cosx (cos²x - sin²x)/cosx

= cos²x - sin²x

Using the identity cos(2x) = cos²x - sin²x

= cos(2x)

Therefore, the simplified expression is cos²x - sin²x, which is equivalent to cos(2x) .

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The width of the tent with a length of 7.5 ft and a height of 6 ft will be 4 ft.

Given that:

Volume, V = 180 cubic ft

Length, L = 7.5 ft

Height, H = 6 ft

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

The width of the tent is calculated as,

180 = L x 7.5 x 6

L = 4 feet

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The number of hot dogs sold was 48 and the number of sodas sold was 3 times that, which is 144.

Let x be the number of hot dogs sold.

Then, the number of sodas sold is 3x.

So, the total number of sodas and hot dogs sold is 192, so we have the equation:

x + 3x = 192

4x = 192

x = 48

Thus, the number of hot dogs sold was 48 and the number of sodas sold was 3 times that, which is 144.

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The measure of the centre that best describes salaries at the company is the median because people who earn a lot make the mean too large.

In contrast to the mean, the median reflects the midway value in a collection of data and is unaffected by extreme values. The median annual wage in this situation is $35,000, meaning that half of the employees make less than this amount and the other half make more. Because it offers a typical value unaffected by the excessive incomes of a few high earners, this is a helpful measure of the middle.

On the other hand, the high values or outliers have an effect on the mean, and in this case, the mean yearly salary is $62,000. This demonstrates how a small group of people with high salaries may have pushed the numbers towards the top end. As a result, the median is a better way to express the range of incomes in the organisation.

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