What are the domain and range of the function graphed below?

The solution to the division problem 2x³-4x²-3x-9/ x-3 is 2x² + 6x + 15

Synthetic division is a method of polynomial division used to divide a polynomial by a linear expression of the form x - a, where a is a constant. It is a shorthand way of performing long division for polynomials and is particularly useful when the divisor is of the form x - a, as it eliminates the need for writing out the full divisor in each step of the division process.

The advantage of synthetic division is that it is quicker and easier than long division, especially for dividing polynomials by linear expressions. It can also be used to evaluate a polynomial at a specific value of x, by setting the divisor to x - a and using the result in the final row of the synthetic division as the value of the polynomial at x = a.

We can use long division to solve this problem:

        2x² + 6x + 15

   ---------------------

x - 3 | 2x³ - 4x² - 3x - 9

       - (2x³ - 6x²)

       ---------------

              2x² - 3x

              - (2x² - 6x)

              ------------

                     3x - 9

                     - (3x - 9)

                     --------

                            0

So the solution to the division problem is:

2x² + 6x + 15

Therefore, the answer is (none of the above).

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Answer:

Solving a word problem is similar to specific tasks we do in various areas of our lives, such as school, home, or job, in that it requires critical thinking, attention to detail, and logical reasoning. In school, we solve math problems to understand different concepts, and in our job, we solve various problems related to our work to improve efficiency and productivity. Similarly, in our personal lives, we encounter problems and challenges that require problem-solving skills.

Addition problems are crucial in almost every job. For example, in accounting, addition is necessary when calculating profit and loss or taxes. In the retail sector, addition is necessary when calculating inventory or the total amount of sales. Even in fields such as medicine, addition is necessary when calculating dosages and other related calculations.

Knowing how to problem solve in this way can be incredibly helpful in the real world. Being able to identify the problem, analyze it, and find a suitable solution can make us more effective and efficient in our personal and professional lives. The ability to solve problems can also help us develop critical thinking skills, which can be useful in various situations.

In conclusion, solving word problems is an essential skill that can be applied to various areas of our lives. Being proficient in addition problems is essential for success in most jobs. Developing problem-solving skills can make us more effective and efficient in our personal and professional lives, and critical thinking skills can help us analyze problems and identify the best solutions.

The total amount of money collected is $180.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, person collected $12 each from 15 family members.

Total money = Amount of money collected from each × Number of people

= 12×15

= $180

Therefore, the total amount of money collected is $180.

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Answer: This is a binomial probability problem. Let X be the number of properties sold during a week, then X has a binomial distribution with parameters n=19 and p=0.3.

The probability of selling at least 5 properties is:

P(X ≥ 5) = 1 - P(X < 5)

To calculate P(X < 5), we can use the binomial cumulative distribution function or the normal approximation to the binomial distribution.

Using the binomial cumulative distribution function, we have:

P(X < 5) = Σ P(X = k) for k = 0 to 4

Using the formula for the binomial probability mass function, we get:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (0.7)^19 + 19(0.3)(0.7)^18 + 171(0.3)^2(0.7)^17 + 969(0.3)^3(0.7)^16 + 3876(0.3)^4(0.7)^15

Using a calculator or statistical software, we get:

P(X < 5) = 0.95044

Therefore, the probability of selling at least 5 properties in one week is:

P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.95044 = 0.0496 (rounded to four decimal places).

So the probability of selling at least 5 properties in one week is approximately 0.0496 or 4.96%.

Step-by-step explanation:

Therefore, unitary method solution is in order to have enough turf to cover the amphitheatre, the city must purchase at least 6 pallets of it.

Take the lengths of this minute subsection and split the sum by two to complete a task using a variable unitary technique. The unit technique, in a nutshell, removes a wanted item both from the specific sets and color subsets. For instance, 40 pencils will cost Rs/kg ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality.

Here,

A is equal to (70)2/4, which is 15,386.78 square feet.

We split the area by the area covered by each roll of turf to determine the quantity of rolls necessary to cover this area:

Rolls Equals A / Rolls' surface area

Given that the size per roll is 30 square feet, we have:

15,386.78 rolls divided by 30 equals 512.89 rolls.

Ceil(number of rolls / 100) = minimal number of pallets

the smallest number larger than or equal to x, ceil(x), is. If we replace the value we discovered with the quantity of rolls, we get:

Ceil (512.89 / 100) = Ceil (5.1289) = Minimum number of boxes = 6

Therefore, in order to have enough turf to cover the amphitheatre, the city must purchase at least 6 pallets of it.

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The value of x for the given cone will be 4. The correct option is C.

The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.

Given that the volume of the cone is V = 128π and the height of the cone is h = 24 units.

The value of the radius x will be calculated as,

V = ( 1 / 3 )πr²h

128π = ( 1 / 3) π x r² x 24

r² = 16

r = 4 units

Therefore, the value of x will be 4 units.

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The price after the reduction is 0.72x

From the question, we have the following parameters that can be used in our computation:

Original price = x

Reduction = 28%

Using the above as a guide, we have the following:

Reduced price = Original price * (1 - Reduction)

Substitute the known values in the above equation, so, we have the following representation

Reduced price = x * (1 - 28%)

Evaluate

Reduced price = 0.72x

Hence, the reduced price is 0.72x

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The solution to equation 1, 2, 3, 4, 5 and 6 are y = (-3/2) + 6, y = (-5/3) + 3,  y = (-1/5)x + 9/5, y = (1/4)x + 3/2, y = (-7/3)x + 3 and y = 6x + 3 respectively.

Given the linear equations in the question;

To make y the subject of the formula, we need to isolate y on one side of the equation by moving all other terms to the other side.

1) 3x + 2y = 12

Subtract 3x from both sides:

3x - 3x + 2y = -3x + 12

2y = -3x + 12

Divide each term by 2

2y/2 = -3x/2 + 12/2

y = (-3/2) + 6

2) 5x + 3y = 9

Subtract 5x from both sides:

5x - 5x + 3y = -5x + 9

3y = -5x + 9

Divide each term by 3

3y/3 = -5x/3 + 9/3

y = (-5/3) + 3

3) x + 5y = 9

Subtract x from both sides:

x - x + 5y = -x + 9

5y = -x + 9

y = (-1/5)x + 9/5

4) -2x + 8y = 12

8y = 2x + 12

y = (2/8)x + 12/8

y = (1/4)x + 3/2

5) -7x - 3y = -9

-3y = 7x - 9

y = (-7/3)x + 3

6) 6x - y = -3

-y = -6x - 3

y = 6x + 3

Therefore, the formula in terms of x is: y = 6x + 3.

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In the given situation, one snack bar has 14 carbohydrates.

Let's denote the number of carbs in one snack bar as "x".

From the given information, we can set up a system of two equations:

2x + 3y = 73 (where y is the number of carbs in one glass of milk)

4x + 2y = 86

We can then solve for x by using elimination or substitution.

Using elimination, we can multiply the first equation by 2 and subtract it from the second equation:

4x + 2y = 86

(4x + 6y = 146) (2 times the first equation)

-4y = -60

Dividing both sides by -4, we get:

y = 15

Substituting this value of y into the first equation, we can solve for x:

2x + 3y = 73

2x + 3(15) = 73

2x + 45 = 73

2x = 28

x = 14

Therefore, there are 14 carbs in one snack bar.

Step-by-step explanation:

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of carbohydrates in one snack bar.

Now, we can use the given information to set up a system of equations:

2x + 3y = 73 (where y is the number of carbohydrates in one glass of milk)

2y + 4x = 86

We have two equations and two unknowns, so we can solve for x and y using any method we prefer. Here, we will use the substitution method:

Rearrange the first equation to solve for y: y = (73 - 2x)/3

Substitute this expression for y in the second equation: 2((73 - 2x)/3) + 4x = 86

Simplify: (146 - 4x)/3 + 4x = 86

Multiply both sides by 3 to eliminate the fraction: 146 - 4x + 12x = 258

Simplify: 8x = 112

Solve for x: x = 14

Therefore, one snack bar has 14 carbohydrates.

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In the given situation, one snack bar has 14 carbohydrates.

Let's denote the number of carbs in one snack bar as "x".

From the given information, we can set up a system of two equations:

2x + 3y = 73 (where y is the number of carbs in one glass of milk)

4x + 2y = 86

We can then solve for x by using elimination or substitution.

Using elimination, we can multiply the first equation by 2 and subtract it from the second equation:

4x + 2y = 86

(4x + 6y = 146) (2 times the first equation)

-4y = -60

Dividing both sides by -4, we get:

y = 15

Substituting this value of y into the first equation, we can solve for x:

2x + 3y = 73

2x + 3(15) = 73

2x + 45 = 73

2x = 28

x = 14

Therefore, there are 14 carbs in one snack bar.

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of carbohydrates in one snack bar.

Now, we can use the given information to set up a system of equations:

2x + 3y = 73 (where y is the number of carbohydrates in one glass of milk)

2y + 4x = 86

We have two equations and two unknowns, so we can solve for x and y using any method we prefer. Here, we will use the substitution method:

Rearrange the first equation to solve for y: y = (73 - 2x)/3

Substitute this expression for y in the second equation: 2((73 - 2x)/3) + 4x = 86

Simplify: (146 - 4x)/3 + 4x = 86

Multiply both sides by 3 to eliminate the fraction: 146 - 4x + 12x = 258

Simplify: 8x = 112

Solve for x: x = 14

Therefore, one snack bar has 14 carbohydrates.

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Answer:

Step-by-step explanation:

1 gallon= 4 liters

2gallons=8liters

8liters answered

But exactly: 7.57082 liters

The key features of the parabola include the following:

A) opens down

C) directrix at y = 1/8

D) vertex at (-1/2, 0).

Mathematically, the standard equation of the directrix lines for any parabola is given by this mathematical expression:

y = a(x - h)² + k.

Where:

Based on the information provided about the parabola, we have:

4x^2 + 4x + 2y + 1 = 0

2(y + 1/2) = -4(x + 1/2)^2 + 1

(y + 1/2) = -2(x + 1/2)^2 + 1/2

By comparing to the standard form, we have:

Vertex, (h, k) = (-1/2, 0).

Additionally, the distance between the vertex and the directrix is given by:

y = |1/(4a)|

y = |1/(4 × -2)|

y = |-1/8|

y = 1/8.

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Answer:

Sophia's paint is lighter.

Step-by-step explanation:

percent = part/whole × 100%

Sophia:

3 cups black, 4 cups white

total: 7 cups

white percent = 4/7 × 100% = 57%

Jeriel:

9 cups black, 10 cups white

total: 19 cups

white percent = 10/19 × 100% = 53%

Sophia's paint is lighter.

Answer:

Step-by-step explanation:

yes this relationship is pporportianal

Answer:

c

Step-by-step explanation:

So what you need to do is split who is part of each:

1/2:

Wife:$?

1/2:

Daughter:$40,000

Butler:$?

Charity:$6,000

This makes it much easier to see as you know the charity and Butler received the same amount. You take your total (x) and do a simple equation of x=$40,000+6,000+6,000 as you know the butler must have also received the $6,000 the charity did. You will get x=$52,000 and you know that is half of the estate as he gave the other half to his wife. This is the same as knowing the butler and charity received the same amount as halves are equal to each other. SO now all you have to do is add $52,000+$52,000=$104,000 getting your answer.  

Figure B is the correct option which represents the the contrapositive of the statement "If it is a square, then it is a quadrilateral".

What is a contrapositive statement ?

A contrapositive statement is a statement formed by negating both the hypothesis and the conclusion of the original statement, and then switching them and negating the entire statement.

In other words, if the original statement is of the form "If A, then B", then the contrapositive statement is of the form "If not B, then not A". The contrapositive statement is logically equivalent to the original statement, which means that if the original statement is true, then the contrapositive statement is also true, and if the original statement is false, then the contrapositive statement is also false.

Finding the contrapositive statement -

We are given "if it is a square,then it is a quadrilateral ".

To determine the contrapositive of a conditional statement, we must switch the hypothesis and the conclusion and negate both.

The original statement is "If it is a square, then it is a quadrilateral." The hypothesis is "it is a square," and the conclusion is "it is a quadrilateral."

Contrapositive of our given statement is -

"if it is not a square,then it is not a quadrilateral "

Therefore, figure B is correct option.

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Angle AXC is congruent to both angle CAX (78 degrees) and angle CDX (102 degrees), its measurement is also 102 degrees.

To find the measurement of angle AXC, we need to consider that it is an inscribed angle subtended by the same arc CX as arc CA and arc DB.

Inscribed angles that subtend the same arc are congruent. Therefore, we can conclude that angle AXC is congruent to both angle CAX and angle CDX.

Since angle CAX and angle CDX are supplementary angles (they add up to 180 degrees) and we know the measurement of angle CAX, we can find the measurement of angle CDX.

angle CAX + angle CDX = 180 degrees

78 degrees + angle CDX = 180 degrees

angle CDX = 180 degrees - 78 degrees

angle CDX = 102 degrees

Since angle AXC is congruent to both angle CAX (78 degrees) and angle CDX (102 degrees), its measurement is also 102 degrees.

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Answer:

10.3

Step-by-step explanation:

Let's say

a leg = 9

b leg = 5

The formula to find the hypotenuse is [tex]\sqrt{a^{2}+b^{2} } = \sqrt{9^{2} +5^{2} } = \sqrt{81+25} = \sqrt{106} = 10.246\\[/tex]

Round [tex]10.246[/tex] to get [tex]10.3[/tex]

The answer is 6

but specifically, it can land on green 6.8181%

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

[tex]4x^2+5xy+y^4=370[/tex]

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

[tex]\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370[/tex]

Differentiate the terms in x only (and constant terms):

[tex]\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0[/tex]

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

[tex]\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]

Use the product rule to differentiate terms in both x and y.

[tex]\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}[/tex]

[tex]\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]

[tex]\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0[/tex]

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

[tex]\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}[/tex]

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}[/tex]

Therefore, slope of the tangent line to the curve at the given point is -11/7.

In the equation, the ordered pair for x = 5 is (5, 5.5), the ordered pair for x = 10 is (10, 8), the ordered pair for x = 20 is (20, 13).

A linear equation has the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. The line's rate of change, or how steeply it rises or descends as we go down the x-axis, is indicated by the slope. The line's intersection with the y-axis, or the value of y when x is equal to 0, is represented by the y-intercept.

The given equation is:

y=0.50x + 3

Substituting the different values of x we find the required ordered pair as follows:

When x = 5:

y = 0.50(5) + 3 = 5/2 + 6/2 = 11/2 = 5.5

When x = 10:

y = 0.50(10) + 3 = 5 + 3 = 8

When x = 20:

y = 0.50(20) + 3 = 10 + 3 = 13

Therefore, the ordered pair for x = 5 is (5, 5.5), the ordered pair for x = 10 is (10, 8), the ordered pair for x = 20 is (20, 13).

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Answer:

See below.

Step-by-step explanation:

Hello!

The topic we should review for this problem is Order of Operations.

Order of Operations is a rule that identifies which part of an equation should be simplified first.

You might've heard of PEMDAS, where;

P for Parentheses, always first unless there's an exponent inside.

E for Exponent, simplified after the Parentheses.

M or D - Multiplication or Division after the Exponent(s).

A or S - Addition or Subtraction after Multiplication or Division.

[tex](5+3^2)+18[/tex]

First we know that there's an Exponent inside the Parentheses, so we must evaluate that number first.

[tex](5+9)+18[/tex]

Next, evaluate what's in the Parentheses.

[tex]14+18\\32[/tex]

Our correct answer is 32.

We are asked what mistake did Raquel make, and what's the correct simplified version of the expression.

1a.) Raquel's mistake is combining unlike terms. It's impossible to combine together a natural number (5) and an exponential number. (3²)

1b.) The correct simplified version of the expression is represented here;

[tex](5+9)+18\\(First \ Step)[/tex]

π - This is an irrational number. 22/7 - The number is rational but not an integer. 3.3 - The number is an integer but not a whole number.

The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it may be expressed as p/q.

Irrational numbers are those that are not logical in nature. Let's explain; irrational numbers may be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.

π - This is an irrational number.

22/7 - The number is rational but not an integer.

3.3 - The number is an integer but not a whole number.

The number is a whole number but not a natural number.

9 -This number can be written as a natural number.

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Answer:

Step-by-step explanation:

To solve the equation graphically, we need to first rearrange it into the form of y = f(x). So, let's simplify the given equation:

(x - 3)² - 2 = x + 1

Expanding the left side:

x² - 6x + 9 - 2 = x + 1

Simplifying:

x² - 7x + 6 = 0

Now we can graph the function y = f(x) = x² - 7x + 6 and the line y = x + 1 on the same coordinate axes and find their intersection points.

Here's a graph of the function and the line:

Graph of y=x^2-7x+6 and y=x+1

We can see that the two curves intersect at two points, which have x-coordinates of approximately 1.2 and 5.8. So, the solutions to the equation are x ≈ 1.2 and x ≈ 5.8.

9% percent of Team B’s mean absolute deviation is the difference in the mean of the individual times of members.

The result of dividing the sum of a set of values by the total number of values in the set is mean.

The average distance between each observation and the mean is shown via a measure of variability known as the mean absolute deviation (MAD).

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

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Answer: 390

Step-by-step explanation:

m

Isabel is in a hot air balloon that has just taken off and is now floating 140 meters above

its launching point. Debbie is standing on the ground, 147 meters away from the

launching point. How many meters apart are Isabel and Debb

Answer:

Isabel and Debbie are 203m apart.

Step-by-step explanation:

Since Isabel went straight up in the balloon and Debbie is straight over presumably on flat ground, they make a right triangle with the third point being the launching spot.

It is a right triangle. See image. Use the Pythagorean Theorem.

140^2 + 147^2 = d^2

Where d is the distance between Isabel and Debbie.

see image for work shown.

The probability that at least 5 of the callers received a busy signal is given as follows:

0.3712 = 37.12%.

The mass probability formula, giving the probability of x successes on n trials, is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

n = 1000, p = 0.004.

The probability of less than 5 busy signals is:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X < 5) = 0.6288.

Hence the probability of at least 5 busy signals is of:

P(X >= 5) = 1 - P(X < 5)

P(X >= 5) = 1 - 0.6288

P(X >= 5) = 0.3712.

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The point after 30, 000 km will they first have to change the oil, rotate the tires and replace the wiper blades all at once.

Arithmetic Progression (AP) is a numerical series in which the difference between any two consecutive numbers is a constant value. Arithmetic Sequence is another name for it.

The First term is an "oil change" with a step d = 3000 km;

and, the second term is tire rotation = 10, 000 Km

and, the third term is replacement of wiper blades = 15, 000 Km

Now, we know from the formula of Arithmetic Progression is

= + d(n-1)

So, 15,000 = 10,000 + 10,000 (n-1)

15, 000 = 10,000 + 10, 000n- 10,000

150000 = 10000n

n = 1.5

This means that at the point 15 000 km and all three progressions will not intersect.

Now, We take the second term of the progression as  = 30,000 km

So, 30,000 = 10,000 + 10,000 (n-1)

20,000 = 10,000n - 10,000

30, 000 = 10,000n

n= 3

Similarly, check this intersection point for the first progression with a step of d = 3 000 km we get n =9.

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The complete question is :-

Peter's parents follow a regular schedule for taking care of the car. They change the plugs every 30 000km, rotate the tyres every 10 000km and replace the brake pads blades every 15 000km. After how many kilometers will they have to change the plugs, rotate the tyres and replace the brake pads all at once for the first time?

The total cost of the tablet is $684.48

The first step is to write out the parameters given in the question

The cost of the tablet computer is $713

The tablet computer is on sale at 11%

Next is to multiply the total cost by the sales percent

11/100 × 713

= 0.11 × 713

= 78.43

= 713 - 78.43

= 634.57

The local sales tax rate is 7%

= 7/100 × 713

= 0.07 × 713

= 49.91

The total cost can be calculated as follows

= 49.91 + 634.57

= 684.48

Hence the total cost of the tablet is $684.48

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Answer: less then

Step-by-step explanation: Less than means subtraction, whereas more than means addition. · Saying twice a number means that you are multiplying that number by 2.

Tom's total annual tax for the following year, assuming the tax table remains the same, is R325,287.17.

To calculate Tom's tax for the following year, we need to first calculate his current monthly PAYE (Pay As You Earn) deduction. We can use the current tax table to do this.

Tom's gross salary is R25,780.25 per month, and he is 45 years old, so according to the 2021/2022 tax table for individuals under 65 years old, his monthly PAYE deduction is:

= R1,458.75 + 25% of the amount over R14,958

= R4,569.96

Tom argues that his PAYE will increase by R593.09 for the following year. This means that his expected monthly PAYE deduction for the following year is:

= R4,569.96 + R593.09

= R5,163.05

Tom's salary for the following year will increase by 8.5%, so his new gross salary will be:

= R25,780.25 + (8.5% x R25,780.25)

= R27,959.83

Tom's pension fund contribution remains the same at 7.5% of his gross salary:

= R27,959.83 x 7.5%

= R2,097.49

His charity organization contribution increases by R50.00 per month:

= R50.00 x 12

= R600.00

Assuming the tax table remains the same as the previous year, Tom's new monthly PAYE deduction is:

= R1,577.98 + 26% of the amount over R17,708

= R5,502.86

To calculate Tom's total annual tax, we need to subtract his annual PAYE deduction from his gross salary and then add back his pension and charity contributions:

Total annual tax = (R27,959.83 x 12) - (R5,502.86 x 12) + R2,097.49 + R600.00

Total annual tax = R325,287.17.

Full question "Tom is 45 years old. He earns a gross salary of R25,780.25 per month.. Tom argues that his PAYE for the following year will increase by R593.09. The following year Tom's salary increases by 8.5%. How much tax will Tom pay per year, if he still contributes only 7.5% of his gross salary to a pension fund but increases his contribution to the charity organization by further R50.00 a month? Calculate as if the tax table for the following year remains the same."​

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