Linear equation that passes through the points of (1,4) and (6,-1)

Answer:

27.87

Step-by-step explanation:

In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the sum of the squares of the two shorter sides is equal to the square of the length of the hypotenuse.

Using the given sides, we can write the equation:

AB^2 + BC^2 = AC^2

Substituting the given values, we have:

17^2 + 22^2 = AC^2

Simplifying the left side, we get:

289 + 484 = AC^2

773 = AC^2

Taking the square root of both sides, we find:

AC = √773 = 27.87

Rounding to two decimal places, the length of side AC is approximately 27.87.

Answer:

The $30,000 in revenue should be entered as a credit in the journal entry.

Step-by-step explanation:

In accounting, revenues are recorded as credits, which means that they increase the credit side of the accounting equation (revenues increase equity, which is a credit account). Debits, on the other hand, are used to record expenses and decreases in assets.Therefore, the journal entry to record $30,000 in revenue for the business on October 1 would be:Date

Account Account Number Debit Credit

1 - Oct Revenue 4050 30,000Since revenue is being credited, there is no debit amount entered in this entry. The credit amount of $30,000 is entered in the credit column, as shown above.

Answer:

Salary with $3300 raise per year:

t (years)     Salary

1            $69300

5            $82600

10            $95900

15            $1092000

20            $1225000

Salary with 4% raise per year:

t (years)      Salary

1             $68640

5             $83833

10             $102219

15             $124869

20             $152947

Note: The calculations for the 4% raise are done as follows:

Year 1: 66000 * 1.04 = $68640

Year 5: 66000 * 1.04^5 = $83833

Year 10: 66000 * 1.04^10 = $102219

Year 15: 66000 * 1.04^15 = $124869

Year 20: 66000 * 1.04^20 = $152947

Step-by-step explanation:

The coordinates after the rotation of 90° will be (-2, -3), (3, 4), and (4, -5) respectively.

Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

Precession, nutation, and intrinsic rotation are the names of these rotations.

Shapes can be rotated by being moved around a fixed point (clockwise or anticlockwise, and by a certain number of degrees).

Although the shape will remain precisely the same, its location within the room will shift.

So, we have:

(-3,2),(4,-3) and (-5,-4)

Now, the graph then as follows.

Now, rotate them to 90°.

(Refer to the graph attached below)

Then, the coordinates after 90° rotation will be:

(-3,2) = (-2, -3)

(4,-3) = (3, 4)

(-5,-4) = (4, -5)

Therefore, the coordinates after the rotation of 90° will be (-2, -3), (3, 4), and (4, -5) respectively.

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Showing this information in a ledger is given below":

Ordinary Share Capital:

28 February 2021: 1,000,000 authorized shares * 500 cents per share (for the shares issued on 31 August 2020) = R500,000

28 February 2020: 600,000 issued shares * R35 (2,100,000 / 60) = R21,000

Retained Income:

28 February 2021: R500,000 (Ordinary Share Capital) - R21,000 (Ordinary Share Capital) + R120,000 (repurchased shares at 620 cents per share) = R599,000

28 February 2020: R737,100 (Retained Income)

Note: The R35 per share in 28 February 2020 was calculated by dividing the total ordinary share capital of R2,100,000 by the number of shares in issue (600,000).

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Answer:

a. 1996

Step-by-step explanation:

Let Paul's age in 2000 be P

Let Bilko's age in 2000 be B

Statement: Paul was twice as old as his brother Biko in 2000 means
P = 2B          (1)

In 2008 Paul was only four years older than his brother.

Since 2008 is 8 years from 2000, both Paul and Bilko have aged 8 years

Paul's age in 2008 = P + 8

Bilko's age in 2008 = B + 8

Statement: In 2008 Paul was only four years older than his brother means

P + 8 = B + 8 - 4

P = B + 4           (2)

Given these two equations (1) and (2)

Substitute P = 2B from (1) in (2):
2B = B + 4

==> 2B - B = 4

==> B = 4

Therefore in 2000, Paul was 8 years old and Bilko was 4 years old

Bilko's year of birth = 2000 - 4 = 1996

Answer:

(3x-2)(10x+3)

Step-by-step explanation:

The change in temperature between 11.00am and 11.00pm would be = 43°F. That is option D.

Temperature is defined as the scalar quantity that shows or measure the degree of hotness or coldness of a medium.

The temperature of a medium at 11.00am = 37°F

The temperature of a medium at 11.00 pm = -6°F

The difference between the both given temperature = 37-(-6) = 37+6 = 43°F.

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Units are a natural number, a natural number that are negative, or zero. The number zero and any number generated by adding one to it repeatedly. A single integer or the product of two integers (division by zero excluded).

What exactly are integers?

In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.

The number zero and any number generated by adding one to it repeatedly. A single integer or the product of two integers (division by zero excluded).A natural number, a negative of a natural number, or zero is a unit of an abstract mathematical system according to the principles of arithmetic. 

e.g. 1,2,0, 0+1, 0+2+3, 8, 8/2=4, -8/2=-4 etc. all are units of  an abstract mathematical system subject to the laws of arithmetic.

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Answer: 9 - 36n

Step-by-step explanation: So, first you multiply 9 by 1 and 9 by 4n, which gives you 9 - 36n.

Answer:

n=1/4

Step-by-step explanation:

9(1-4n)

Distribute the 9 to create the equation 9-36n.

Now set it equal to zero.

9-36n = 0

Add 36n to both sides to get 9 = 36n

Now divide by sides by 36 to get 9/36 = n

Now simplify your fraction 9/36 = 1/4 so 1/4=n

Answer:

Step-by-step explanation:

You want the area of the composite figure consisting of a rectangle and a triangle.

The area of the rectangle is ...

  A = LW

  A = (5 ft)(6 ft) = 30 ft² . . . . rectangle area

The base of the triangle is the difference in length of the horizontal segments:

  b = 9 ft -5 ft = 4 ft

The area is given by the formula ...

  A = 1/2bh

  A = 1/2(4 ft)(6 ft) = 12 ft² . . . . triangle area

The area of the figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 30 ft² +12 ft²

  total area = 42 ft²

__

Additional comment

The area of this trapezoid can also be found using the trapezoid formula:

  A = 1/2(b1 +b2)h

  A = 1/2(9 ft +5 ft)(6 ft) = 42 ft²

The rectangle is shown in the figure as 5 ft wide and 6 ft tall. It does not matter which of these dimensions you call the length and which you call the width. Their product is the same either way.

Answer:

Any odd number multiplied by an even number will make an even number.

The column vectors of this matrix are linearly independent, meaning they are not dependent upon one another, and the determinant is not equal to 0.

The given matrix is:

| 1 0 5 |

| -2 1 -6 |

| 0 2 8 |

We must compute the matrix's determinant in order to determine if the matrix's column vectors are linearly independent or linearly dependent.

A scalar value that can be used to assess linear dependency or independence is the determinant of a matrix.

The determinant of the matrix is:

det(A) = 1(-68) - 0(18) + 5(-2*2) = -6 + 0 - 20 = -26

Since The column vectors of this matrix are linearly independent, meaning they are not dependent upon one another, and the determinant is not equal to 0.

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Answer:

[tex]\displaystyle \int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x}-\frac{1}{25}e^{5x}+C[/tex]

Step-by-step explanation:

Given Problem

[tex]\displaystyle \int {xe^{5x}} \, dx[/tex]

Make substitutions for IBP

Let [tex]u=x,\,du=dx[/tex] and [tex]v=\frac{1}{5}e^{5x},\,dv=e^{5x}dx[/tex]

Perform IBP

[tex]\displaystyle \int {u} \,dv=uv-\int {v} \, du\\\\\int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x} -\int {\frac{1}{5}e^{5x}} \, dx\\\\\displaystyle \int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x}-\frac{1}{25}e^{5x}+C[/tex]

Answer: (-1.25, 0.41)

Step-by-step explanation:

For given function f(x) = √x + 9, the inverse function and domain are respectively, f⁻¹(x) = (y - 9)², x ≥ 0 & x ∈ (∞, ∞)

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Given that,

A function,

⇒ f(x) = √x + 9

f⁻¹(x) = ?

the given function is defined for all the values of x,

So domain of the function is real number,

x ∈ (∞, ∞)

Now for f⁻¹(x),

Suppose, f(x) = y

y = √x + 9

y - 9 = √x

squaring both the sides,

(y - 9)² = (√x)²

x  = (y - 9)²

And value of x should be greater than zero

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The entire length of the trip is 9/12 miles.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

After biking 5/12 miles,

Jada has traveled 2/3 of the length of her trip.

Let x be the entire length of the trip.

The equation is,

x = 1/3 + 2/3

x = 1/3 + 5/12

x = 9/12

Therefore, the distance is 9/12 miles.

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Answer:

Option A: 4/5

Step-by-step explanation:

If y varies directly as x written as y ∝ x, this can be written as an equation:
y = kx  where k is a constant

Since y = 6 when x = 15:
6 =k · 15

6 = 15k

15k  = 6

k = 6/15  = 2/5

The equation beocmes
y = (2/5) x

Therefore when x = 2,

y = (2/5) x 2 = 4/5

Option A: 4/5

Answer:

[tex] \frac{14}{16} \: and \: \frac{13}{16} [/tex]

Step-by-step explanation:

So we have these two fractions

[tex] \frac{7}{8} \: and \: \frac{13}{16} [/tex]

Does 8 go into 16? Yes. It goes in twice because 8 times 2 is 16. That means 16 is our common denominator.

Because of that, since we multiplied 8 by 2, we will do the same to the 7. 7 times 2 is 14.

Because of that we have 14/16 and 13/16 as our answers.

Equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are

x² + (y - 3)² = 36 and x² + (y + 8)² = 36

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

Given equations

⇒ x² + (y - 3)² = 36

comparing with general equation of circle

( x - h )² + ( y - k )² = r²

Center (h , k) = (0 , 3)

Center is on y - axis

Radius r = √36 = 6units

Diameter = 2r = 2×6 = 12units

⇒ x² + (y - 5)² = 6

comparing with general equation of circle

( x - h )² + ( y - k )² = r²

Center (h , k) = (0 , 5)

Center is on y-axis

Radius r = √6 units

Diameter = 2r = 2√6 units

⇒ (x – 4)² + y² = 36

comparing with general equation of circle

( x - h )² + ( y - k )² = r²

Center (h , k) = (4 , 0)

Center is on x-axis

Radius r = √36 = 6units

Diameter = 2r = 2×6 = 12units

⇒ (x + 6)² + y² = 144

comparing with general equation of circle

( x - h )² + ( y - k )² = r²

Center (h , k) = (-6 , 0)

center is on x-axis

Radius r = √144 = 16units

Diameter = 2r = 2×16 = 32units

⇒ x² + (y + 8)² = 36

comparing with general equation of circle

( x - h )² + ( y - k )² = r²

Center (h , k) = (0 , -8)

Center is on y-axis.

Radius r = √36 = 6units

Diameter = 2r = 2×6 = 12units

Hence, equation x² + (y - 3)² = 36 and x² + (y + 8)² = 36 represents the circle with diameter 12 units and a center that lies on y-axis.

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It is a translation of 3 units up and one unit to the left,  then the correct option is D.

For any function y = f(x), we can define:

A vertical translation of N units as:

g(x) =f(x) + N

if N > 0, the translation is up

if N < 0, the translation is down.

A horizontal translation of N units as:

g(x) =f(x + N)

if N > 0, the translation is left

if N < 0, the translation is to the right.

Here we have:

g(x) = f(x + 1) + 3

So we have a translation of 1 unit to the left and 3 units up.

The correct option is d.

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a. there are three vectors in {a₁, a₂, a₃}.

b. There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. we have that a₁ is in the W.

A matrix is a set of integers arranged in rows and columns. The rows and columns of integers are arranged in a rectangular matrix. The matrix A, for instance, contains two rows and three columns. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.

a. The vector b is not in {a₁ ,a₂, a₃} since b is not equal to any of the column vectors of A. Clearly, there are three vectors in {a₁, a₂, a₃}.

b. Vector b is in W if the augmented matrix [a₁, a₂, a₃ b] is consistent.

The augmented matrix is:

[tex]\left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\-2&6&3&-4\end{array}\right] \sim \left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\0&6&-5&4\end{array}\right] \sim \left[\begin{array}{cccc}1&0&-4&4\\0&3&-2&1\\0&6&-1&2\end{array}\right][/tex]

Thus, since the system is consistent we have that b must be in W.

There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. since   [tex]\left[\begin{array}{c}1\\0\\-2\end{array}\right] = 1. \left[\begin{array}{c}1\\0\\-2\end{array}\right] + 0. \left[\begin{array}{c}1\\0\\-2\end{array}\right] + 0. \left[\begin{array}{c}1\\0\\-2\end{array}\right][/tex] we have that a₁ is in the W.

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a. there are three vectors in {a₁, a₂, a₃}.

b. There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. we have that a₁ is in the W.

A matrix is a set of integers arranged in rows and columns. The rows and columns of integers are arranged in a rectangular matrix. The matrix A, for instance, contains two rows and three columns. The elements of the matrix, also known as the entries, are the integers. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.

a. The vector b is not in {a₁ ,a₂, a₃} since b is not equal to any of the column vectors of A. Clearly, there are three vectors in {a₁, a₂, a₃}.

b. Vector b is in W if the augmented matrix [a₁, a₂, a₃ b] is consistent.

No, b is not in {a1, a2, a3}.

There are 3 vectors in {a1, a2, a3}.

Yes, b is in W.

There are infinitely many vectors in W.

Yes, a1 is in W because it can be expressed as a linear combination of the vectors in W. This is shown by the equation a1 = 1(a1) + 0(a2) + 0(a3).  The coefficients of the vectors in the linear combination are all integers and this equation shows that a1 is in the span of the vectors in W.

Thus, since the system is consistent we have that b must be in W.

There are infinitely many vectors in W = span {a₁, a₂, a₃} by definition.

c. since we have that a₁ is in the W.

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Answer:

(1/x)+31

Step-by-step explanation:

To simplify the expression

5/(1/6) + 1/X + 1,

we need to first simplify the fraction 5/(1/6):

5/(1/6) = 5 * 6/1 = 30

Now we can substitute this value back into the expression:

30 + 1/X + 1

To combine the last two terms, we need to find a common denominator, which is X:

30X/X + 1/X + X/X

Simplifying the numerator:

30X + 1 + X

Combining like terms:31X + 1

so the simplified rational expression is (1/x)+31

Answer:

Step-by-step explanation:

If you work 55 hours in one week and earn $15 per hour, your gross pay before taking into account any overtime can be calculated as follows:

Gross pay = 55 hours x $15/hour = $825

If you work overtime, which is time and a half, the additional pay can be calculated as follows:

Overtime pay = ($15/hour x 1.5) x (55 hours - 40 hours) = ($22.50/hour x 15 hours) = $337.50

So, the total gross pay including the overtime pay is:

Gross pay = $825 + $337.50 = $1,162.50

Therefore, the total gross pay for working 55 hours in one week at $15 per hour, with overtime pay calculated as time and a half, is $1,162.50.

The first step is to rewrite the equations in standard form by subtracting the constant from each side.

Standard form is a type of numerical notation used to express large numbers in a concise form. It is based on powers of 10, which means each place value of a number is multiplied by a power of 10. Standard form is typically used in scientific and mathematical applications, and it is also known as scientific notation. To write a number in standard form, the number is written as a coefficient, followed by the base of 10, raised to an exponent.

3x - 2y = 10  becomes  3x - 2y - 10 = 0

3x - y = 17 becomes 3x - y - 17 = 0

Let's multiply the first equation by 2 and the second equation by 3.

2(3x - 2y - 10) = 0

3(3x - y - 17) = 0

6x - 4y - 20 = 0

9x - 3y - 51 = 0

The next step is to add the two equations together.

6x - 4y - 20 + 9x - 3y - 51 = 0

15x - 7y - 71 = 0

The last step is to solve for the variable.

15x - 7y = 71

15x = 71 + 7y

x = (71 + 7y)/15

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Hi there, here's your answer:

Highest temperature = 18 degrees

Least temperature = -5 degrees

The difference between the two is 18 - (-5) = 18 + 5 = 23 degrees

Hope it helps!

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The probability of buying 3 tires is 0.05 and the cumulative probability distribution table is created.

What is meant by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,

     Percentage of people who buys 4 tires = 50%

      Percentage of people who buys 2 tires = 32%

      Percentage of people who buys less than 2 tires = 13%

    Percentage of people who buys none = 6%

a) Prob(X=0) = 0.06

    Prob(X=2)  = 0.32

   Prob(X=4)  = 0.50

 Prob(X < 2) = Prob(X=0) + prob(X=1) = 0.06+ prob(X=1)

   prob(X=1) =   Prob(X < 2) - 0.06  = 0.13 - 0.06 = 0.07

Therefore prob(X = 3) = 1 - ( 0.5+0.32+0.07+0.06) = 1 - 0.95 = 0.05 = 5%

b) Cumulative probability distribution is as given in the figure.

Therefore the probability of buying 3 tires is 0.05 and the cumulative probability distribution table is created.

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