gross income £12000 tax free allowance £6475 what is taxable amount @20%, tax payable,net income and weekly net amount how to work out?

The algebraic expressions for the given verbal expression are 4x+y, 4x, y-4, x/4

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given are some verbal expression, we need to translate it into algebraic expressions,

The variables will be x and y,

1) The sum of four and some number =

x+x+x+x + y = 4x+y

2) The product of some number and four =

4×x = 4x

3) The difference of four and some number =

y-4

4) The quotient of some number and four =

x/4

Hence, the algebraic expressions for the given verbal expression are 4x+y, 4x, y-4, x/4

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Final answer:

The algebraic expression with a variable 'x' in the numerator and '4' in the denominator translates to the verbal expression 'The quotient of some number and four', indicating a division of 'x' by 4.

Explanation:

The algebraic expression given is a fraction with variable x in the numerator and 4 in the denominator. This expression can be translated into a verbal expression as "The quotient of some number and four". It's important to understand each term used in this expression:

Quotient refers to the result of division.

Some number refers to an unspecified or unknown quantity, which is represented by x in this context.

The number 4 is the divisor in this expression.

Therefore, when we talk about the quotient of some number and four, we are referring to dividing an unknown quantity (x) by four (4).

Scale factors greater than 1 will produce an image larger than the original.

The scale factor that will produce an image larger than the original is any scale factor greater than 1.

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Answer:

Square, and Rectangle

Step-by-step explanation:

the others don't have a 90 degree angle

Given:

Complex number: i − 2?

To add, expressing a number in the form a + bi, whereas the real numbers are b an a, while i is the imaginary unit (which satisfies the equation i2 = −1) is called a complex number. a is called the real part of the complex number, and b is called the imaginary part In the given expression.

The value is 24 1/3

First, we need to know that division is an arithmetic operation that is the result of a divisor and a dividend

We have other arithmetic operations, such as;

From the information given, we have that;

74 divided by 3

This is represented as;

74/3

Divide the values

24 1/3

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The answer is A or 14.1!

The main difference between tangent and chord is that the tangent touches the curve at only one point whereas the chord touches the curve at two points.

Chord:

Tangent:

From above definitions of Chord and Tangent , we say that chord touches the curve at two points where as Tangent touches the curve at only one point .

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A tangent is a line that touches a circle at only one point and is perpendicular to the radius at the point of contact, while a chord is a line segment with both endpoints on the circle.

A tangent and a chord are lines that relate to the curve of a circle, but they have distinct differences. A tangent is a line that touches a circle at exactly one point, and at this point of contact, it is perpendicular to the radius of the circle, which is called the axis in this context. In sharp contrast, a chord is a line segment whose endpoints both lie on the circle. When constructing the perpendicular from the midpoint of a chord, you are drawing an axis. For tangents, the perpendicular erected from the point of contact with the circle is also an axis.

This shows that the tangent is unique in that it has a "no-cut" property; it is the only line that will touch the circle at that single point without cutting through it. When looking at the slope of curves, the slope of the tangent line at the point of contact represents the exact slope of the curve at that point. The differentiation process in mathematics is used to find this slope of the tangent, which is important for understanding the rate of change at a specific point on a curve.

The values of x and y are 80 and 70 respectively which make k parallel to j and m parallel to n.

Geometrically, parallel means two or more lines, line segments, or rays that never intersect or cross each other, it doesn't matter how far they are extended. Parallel lines always maintain the same distance between them and remain equidistant at every point.

The sum of two adjacent angles is [tex]180^o[/tex],

therefore,

[tex](x-30)^o+(x+50)^o= 180^o[/tex]

2x +20 = 180

2x = 180 - 20

2x = 160

[tex]\frac{2x}{2} = \frac{160}{2}[/tex]

x = 80.

Again, as the sum of two adjacent angles is [tex]180^o[/tex],

[tex](x-30)^o+y^o= 180^o[/tex]

x + y = 180 + 30

Substitute value of x,

80 + y = 150

y = 150 - 80

y = 70.

Thus, x = 80 and y = 70 are the values for which k is parallel to j and m is parallel to n.

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Answer:

for ever 1 hour the price goes up by ten

Step-by-step explanation:

Which graph represents the function r(x) = |x – 2| – 1

we have

[tex] r(x) = |x- 2|- 1 [/tex]

using a graph tool

see the attached figure

So

1) the domain of the function is all real numbers-----> interval (-∞,∞)

2) the range of the function is the interval [-1, ∞)

3) the function decrease on the interval (-∞,2)

4) the function increase on the interval (2,∞)

5) the function has two x-intercepts-----> (1,0) and (3,0)

6) the function has one y-intercept-----> (0,1)

therefore

the graph in the attached figure

Answer:

solve the equation.  

4n−18=52

n= 17.5

There are 7 numbers between 1 and 100 that are multiples of both 2 and 7.

To find the numbers between 1 and 100 that are multiples of both 2 and 7, we need to find the common multiples of these two numbers. The multiples of 2 are 2, 4, 6, 8, 10, and so on. The multiples of 7 are 7, 14, 21, 28, and so on.

We can see that the common multiples of 2 and 7 are 14, 28, 42, 56, 70, 84, and 98. There are a total of 7 numbers between 1 and 100 that are multiples of both 2 and 7.

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The function for the length of a row of bookshelves is [tex]\( f(x) = \frac{4}{5} \sqrt{x} \)[/tex]. graph below.

To find the length of a row of bookshelves, you can use the given relationship that the total length of each row of bookshelves will be [tex]\( \frac{4}{5} \)[/tex] of the length of the storage space. Let's denote the area of the space Isabel rents as [tex]\( x \).[/tex] Then, the length of the side of the square storage space is [tex]\( \sqrt{x} \).[/tex]

So, the length of a row of bookshelves,[tex]\( f(x) \)[/tex], would be:

[tex]\[ f(x) = \frac{4}{5} \times \sqrt{x} \][/tex]

For the function expressing [tex]\( f(x) \)[/tex], it would be:

[tex]\[ f(x) = \frac{4}{5} \sqrt{x} \][/tex]

Now, let's graph this function.

Attached below:

Complete Question:

User

When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square. The total length of each row of bookshelves will be 4/5 of the length of the storage space.1)

Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves?

F(x)= 4/5 √ x 100 ≤ x ≤ 8100 8 ≤ y ≤ 722)

Write a function that expresses f(x). (I wrote) F(x)= 4/5 √ x3)

Graph the function.

The values of the coefficients and constant are 1, -8 and -5

The standard quadratic expression is given as:

y = ax^2 + bx + c

where a, b and c are the constant

Given the quadratic function f(p) = p2 – 8p – 5, on comparing:

a = 1

b = -8

c = -5

Hence the values of the coefficients and constant are 1, -8 and -5

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Answer:

The new price of the guitar would be $464.00

Step-by-step explanation:

The original price of the guitar = $320

The music store increased the price of guitar by = 45%

First we calculate 45% of the 320 and then add it to the original price.

The new price of the guitar = 320 + ( 45% × 320 )

                                              = 320 + ( 0.45 × 320 )

                                              = 320 + 144

                                              = $464

The new price of the guitar would be $464.00

If you exchange $522 for euros, the number of euros you would have is equal to 412.38 euros (€).

In Mathematics and Geometry, a direct proportion is a mathematical equation which is typically used to represent the equality of two (2) ratios.

Based on the information provided, we have the following exchange rate:

1 US dollar = 0.79 euro (€).

522 US dollar = X euro (€).

By cross-multiplying, we have the following:

X = 0.79 euro (€) × 522 US dollar

X = 412.38 euros (€).

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