Sofa co is selling sofas with a 33% discount off the original price to reduce its stock. Calculate the discounted price of a sofa originally selling for £999.00. Please show your working.

x < 3 is a solution of the inequality x - 3 < 0 and x < 3 is not the solution of the inequality x + 3 < 0.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Suppose that the inequality is x - 3 < 0.

x - 3 < 0

Adding 3 on both sides of the equation,

x - 3 + 3 < 0 + 3

x < 3

x< 3 is the solution of the expression x - 3 < 0.

Consider the inequality x + 3 < 0.

x + 3 < 0

Subtracting 3 from both sides,

x + 3 - 3 < 0 - 3

x < -3

x < 3 is not the solution of the expression x + 3 < 0

Hence the expression with x < 3 as a solution is x - 3 < 0 and not as a solution is x + 3 < 0.

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The area of triangle if sides are 9cm 12cm and 15cm is 54 square cm.

In the given question we have to find the area of triangle if sides are 9 cm 12 cm and 15 cm.

The entire area bounded by a triangle's three sides is referred to as the triangle's area. In essence, it equals half of the base times height, or A = 1/2bh. So, in order to calculate the area of a triangular polygon, we need to know its base (b) and height (h).

Area of Triangle = 1/2 bh

Area of Triangle = 1/2 9*12

Area of Triangle = 9*6

Area of Triangle = 54 square cm

Hence, the area of triangle if sides are 9cm 12cm and 15cm is 54 square cm.

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If the given ordered pair [tex](2,3) = (3x-4,3)[/tex] are equal , then on simplifying we get that the value of x is 2  .

The Ordered Pair is given as [tex](2,3) = (3x-4,3)[/tex] , and the ordered pair are equal ,

We know that the two ordered pairs [tex](a_{1} ,b_{1} )[/tex] and [tex](a_{2} ,b_{2} )[/tex] , are said to be equal if and only if the elements , [tex]a_{1} =a_{2}[/tex] and [tex]b_{1} =b_{2}[/tex]  .

So , By the above definition ,

we get that , [tex]3x-4=2[/tex] ;

adding 4 to both the sides of equation ,

we get ; [tex]3x=6[/tex]

Dividing both sides by 3 ,

we get ;

⇒ [tex]x=\frac{6}{3}[/tex] ;

On simplifying further ,

we have ;

⇒ [tex]x=2[/tex] .

Therefor , the value of x is 2 .

The given question is incomplete , the complete question is

What is the value of x if the 2 ordered pair (2 , 3) = (3x-4 , 3) are equal ?

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The combined cost of one loaf of bread and one package of cheese will be $6.5 for the equation

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1.50 more than the cost of a loaf of bread.

Let 'x' be the cost of the loaf and 'y' be the cost of cheese. Then the equations are given as,

6x + 3y = 27

2x + y = 9             ...1

y = x + 1.5            ...2

From equations 1 and 2, then we have

2x + x + 1.5 = 9

3x = 7.5

x = $2.5

Then the value of the variable 'y' is calculated as,

y = 2.5 + 1.5

y = $4

The combined cost of one loaf of bread and one package of cheese will be given as,

⇒ $4 + $2.5

⇒ $6.5

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The number of apples left with jimmy is none(zero).

Jimmy bought 50 apples and each bag had 10 apples and he gave 2 bags of apples to one of his friends and another 2 bags of apples to another friend and he ate 1 bag.

The number of apples Jimmy have left can be calculated as follows;

He has 5 bags of apples containing 10 apples each. Jimmy gave 2 bags of apples(20 apples) to his friend and gave another 2 bags of apples(20 apples) to his friend.

Finally, he ate 1 bag of apple(10 apples).

Therefore, the number of apples left is none.

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The exact value of tanθ is -4/3 that is -1.33 in the simplest radical form.

What is Tanx in terms of sinx and cosx ?

The value of Tanx can be the ratio of sinx and cosx or it can be defined by the ratio of its opposite side and adjacent side.

Given,

if theta is an angle in standard position and

it’s terminal side passes through the point (3, -4)

So, the given point is (3,-4)

By the definition we can say that ,

If the terminal side passes through the  point (a,b)

than tanθ = b/a .  

so, similarly

tanθ  = -4/ 3

Hence, The exact value of tanθ is -4/3 that is -1.33 in the simplest radical form.

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The value of all the missing angles of the triangle are;

m∠PRQ = 78°

m∠RPQ = 30°

m∠PQR = 72°

m∠PRS = 39°

m∠RPS = 15°

m∠PQS = 36°

m∠PSR = 126°

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.

Now, the sum of angles in a triangle is equal to 180 degrees. We are given;

m∠PRQ = (8x - 10)°

m∠RPQ = (4x - 14)°

m∠PQR = (7x - 5)°

Thus;

(8x - 10) + (4x - 14) + (7x - 5) = 180

19x - 29 = 180

19x = 209

x = 209/19

x = 11

Thus;

m∠PRQ = (8(11) - 10)° = 78°

m∠RPQ = (4(11) - 14)° = 30°

m∠PQR = (7(11) - 5)° = 72°

By the definition of incenter of a triangle, we can say that;

m∠PRS = 78°/2 = 39°

m∠RPS =  30°/2 = 15°

m∠PQS = 72°/2 = 36°

Similarly;

m∠PSR = 180 - (m∠RPS + m∠PRS)

m∠PSR = 180 - 54

m∠PSR = 126°

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Answer:

1/3

Step-by-step explanation:

7/3 = 6/3 + 1/3 = 2 + 1/3 = 2 1/3

The fractional part is 1/3.

Answer:

Step-by-step explanation:

We can solve this by either identifying the equation or by graphing.  We'll try both.

Find the Equation

The slope of the line can be determined from the Rise/Run of the 2 given points:

Going from ((3,-3.8) to (5,-3):

 Rise = (-3 - (-3.8) = 0.8

Run = (5 - 3) = 2

Slope = 0.8/2 or 0.4

The equation for this line is y = 0.4x + b, where b is the y-intercept.

Enter either point to find b:  

y = 0.4x + b

-3 = 0.4*(5) + b  for point (5,-3)

-3 = 2+b

b = -5

The equation is y = 0.4x - 5

The y=intercept is -5 (the value of b)

Graphing

See the attached graph.  Mark the two points and then draw a straight line between them.  The point at which the line crosses the y axis is the y-intercept (0,

The required relationship formed as of the given information is a linear function.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Justin opens a savings account with $8. He saves $4 each week.
Let the x be the number of weeks and y be the number of money saved after x weeks.
According to the question,
y = 8 + 4x

Since the above function is a linear function, so table representing the data followed the above expression shows the linear function

Thus, the required relationship formed as of the given information is a linear function.

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The number of tacos that the taco truck made in all for the year were 22, 280 tacos

First, we know that the taco truck made 11, 380 chicken tacos. We also know that the beef tacos were 3, 780 less than chicken which means they were :

= 11, 380 - 3, 780

= 7, 600 beef tacos

The number of fish tacos made were 4, 300 fewer than beef tacos which means it was :

= 7, 600 - 4, 300

= 3, 300 tacos

The total tacos made is:

= 11, 380 + 7, 600 + 3, 300

= 22, 280 tacos

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Abby can make 26 tie-dyed T-shirts.

We can start by setting up a linear equation to represent the total cost of making the tie-dyed T-shirts.

What is a linear equation?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable).

Multiple variables may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.

Let x be the number of T-shirts Abby makes

The cost for each T-shirt is $3.95 + $0.50 = $4.45

The cost of the two boxes of salt is $4.50 * 2 = $9

So the total cost for x T-shirts is $4.45x + $9

We know that the total cost is 124.70 and we want to find the value of x, so we can set up the equation as:

$4.45x + $9 = 124.70

Solving for x:

$4.45x = 115.70

x = 115.70 / 4.45

x = 26

Therefore, Abby can make 26 tie-dyed T-shirts.

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The value of x is 1/2, and JT = 1/2(TK), TK = 2JT.

What is the centroid of a triangle?

A centroid of a triangle is a point that is the arithmetic mean position of all the points of a triangle, which is the point where the three medians of the triangle intersect. The medians of a triangle divide the triangle into 6 equal areas.

We know that:

JT = x(TK),

\where J is the centroid and x is a constant.

Since J is the centroid, it divides the median TK into a ratio of 2:1, which means that TK = 2*JT.

Substituting this into the original equation gives:

JT = x(2*JT)

Solving for JT gives:

JT/JT = 2x

x = 1/2

JT = 1/2(TK),

TK = 2JT

Hence, the value of x is 1/2, and JT = 1/2(TK), TK = 2JT.

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Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.

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The 5 is the numerical coefficient in the expression 5x. 5x denotes a 5x multiplication of the variable x.

x ax2+bx+c=0, a quadratic polynomial in a single variable, is a quadratic equation. a 0. Since this polynomial is of second order, the Fundamental Theorem of Algebra guarantees that there is at least one solution. There are both straightforward and complex solutions. A quadratic equation is a quadratic equation. This suggests that it contains at least one word that has to be squared. One of the commonly used answers to quadratic equations is "ax2 + bx + c = 0." where the unknown variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

X is the coefficient term, while an is the variable.

Together, x and a2 are multiplied.

A mathematical problem is solved using an algebraic expression, which combines words and numbers.

For illustration

The 5 is the numerical coefficient in the expression 5x. 5x denotes a 5x multiplication of the variable x.

The variable is therefore a, and the coefficient term is x.

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Therefore the solution to the given question equation will shift the graph of the original equation up 2 units in  y=2x + 9

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.

Here,

It follows a linear function. y=mx + b

If A is the location where the y-axis intersects, then x = 0 and y = b are the coordinates of A.

In order to move the graph up by 2 units, you must add 2 units to b.

In our case, b was originally equal to 7, so shifting it up makes b become 7+2=9, and the new function is y=2x + 9.

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In order to have the correct expression of -24x + 12/12, the student erred by expressing the product of two negative signs as a negative sign rather than a positive sign.

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x.

given

Given that a pupil stretched the statement to become 6 (4x 2/ 13),

Using the distributive theorem to expand;

= −6 ( 4x − 2/ 13 )

= -6(4x) -6(-2/13)

= -24x + 6(2/13)

= -24x + 12/12

In order to have the correct expression of -24x + 12/12, the student erred by expressing the product of two negative signs as a negative sign rather than a positive sign.

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The expression for x fewer than 62 can be written as 62 - x

An expression can be evaluated to a single value by substituting specific values for the variables and performing the operations in the correct order. Mathematical expressions can be used to model real-world phenomena, make predictions, and solve problems. Expressions are used in various branches of mathematics such as Algebra, Calculus and Geometry.

Fewer than tells us that x is less than 62, the solution is to tell us by what number that it is less than.

Hence 62 - x is the expression for x fewer than 62

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The solution to the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55).

A system of linear equations is a set of two or more equations which includes common variables. The solution to a system of equations, is the value of the unknown variables used in the equations that satisfies both equations.

Given two linear equations in x and y,

y = -3x - 2     (equation 1)

5x + 2y = 15     (equation 2)

Use substitution method to find its solution. Since the first equation is already expressed as y in terms of x, substitute the first equation to the second equation.

5x + 2y = 15     (equation 2)

5x + 2(-3x - 2) = 15

5x - 6x - 4 = 15

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.

5x - 6x - 4 = 15

-x = 15 + 4

x = -19

Substitute the value of x in the first equation and solve for y.

y = -3x - 2     (equation 1)

y = -3(-19) - 2

y = 55

Hence, the solution of the given system of equations is (-19, 55).

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A quadratic equation with real or complex coefficients has two roots.

A quadratic equation with real or complex coefficients has two roots. A quadratic equation is any algebraic equation that can be expressed in standard form as where x is an unknown value and a, b, and c are known values, with a 0. A second-degree equation is a quadratic equation.This signifies that it has at least one (1) squared phrase. 'ax2 + bx + c = 0' is a typical formula for solving quadratic equations, where a, b, and c are constants or numerical coefficients.

Here,

A quadratic equation with real or complex coefficients has two solutions, known as roots.

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The answer is:

Work/explanation:

You would classify a polynomial with a degree of 2 based on the number of terms. The degree is second.

So you would say "this is a second-degree polynomial".

An example of a second-degree polynomial would be [tex]\bf{y^2+7}[/tex].

The coordinate of the circumcenter of the triangle is A'(9,9) , B' ( 4,4) and C' ( -2,7)

Circumcenter of triangle is the point where three perpendicular bisectors from the sides of a triangle intersect or meet. The circumcenter of a triangle is also known as the point of concurrency of a triangle.

Also the circumcenter is the intersection point of the perpendicular bisectors of sides of a triangle. It is the centre of a triangle's circumcircle.

Since circumcenter Is the point of perpendicular bisector

the bisect of line AB (A') is (14+4)/2 , (12+6)/2 = (9,9)

the bisect of line BC (B') is (14-6)/2 , (6+2)/2 = (4,4)

The bisect of line AC (C') is( 4-6)/2 , (12+2)/2 = ( -2,7)

Therefore the the coordinates of the circumcenter of the A'(9,9) , B' ( 4,4) and C' ( -2,7)

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(B) 2.25 is three-fourths of the way between -3 and 4 on the number line.

A number line is basically a straight line that illustrates real numbers.

It has all the integers marked out evenly and each point corresponds to a certain real number.

We can usually see numbers from -3 up to 3, but it includes all real numbers and even the ones in between the integers.

It's a great tool to help teach basic addition and subtraction, especially when you're dealing with negative numbers.

So, according to the number line, we have to count from -3 to 4.

If we count as 3/4 from -3 to 4.

Then, we will land on 2.25 on the number line.

Therefore, (B) 2.25 is three-fourths of the way between -3 and 4 on the number line.

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Complete question:

What point on the number line is three-fourths of the way from point −3 to point 4?

(A) 5.25

(B) 2.25

(C) −1.25

(D) −2.25

Answer:

2.25

Step-by-step explanation:

No, S is not a basis for P³. In order for a set of vectors to be a basis for a vector space, the vectors must be linearly independent and span the space.

In this case, the set of vectors does not span P³ because the highest order of the polynomials in S is t³, which does not span all of P³ which contains polynomials of order up to and including t³.

Additionally, the set of vectors is not linearly independent. For instance, 4t−t²= 5+3t−2t³, which means that the two vectors are linearly dependent. Therefore, S is not a basis for P³.

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So on solving the provided question, we can say that here in the quadrilateral; angle MJL = angle JLK = 60

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here in the quadrilateral

angle MJL = 60

angle MJL = angle JLK = 60

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The graph of y = 3 - 4x is given above.

The coordinates on the graph are:

(-2, 11) and (7, -25).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = 3 - 4t

Where -2 ≤ t ≤ 7

Now,

Find the coordinates on the graph.

y = 3 - 4t

For t = -2

y = 3 - 4 x (-2) = 3 + 8 = 11

i.e

(-2, 11)

For t = 7

y = 3 - 4 x 7 = 3 - 28 = -25

i.e

(7, -25)

Thus,

The coordinates on the graph are:

(-2, 11) and (7, -25).

The graph is given below.

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The probability of number of 1-2 Children in car and 3 plus children in car is 0.203.

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

The probability of P(1-2 children| car). P (3 plus children| car) is given by:

P = 63/88 × 25/88

P=0.203

The probability of P(Bus| 1-2 children). P (Bus | 3 plus children) is given by:

P = 38/101 × 49/74

P=0.249

The probability of P(Car |1-2 Children) is given by:

P= 63/101

P=0.624

The probability of P(3 plus children | Bus)is given by:

P=49/87

P=0.563

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Answer: The picture below

Step-by-step explanation: Correct on Edmentum, if you give me a low rating than you are mean :(

Answer:

[tex] y = -\dfrac{7}{36} [/tex]

Step-by-step explanation:

[tex] 2 \dfrac{1}{4} - 6y = 3 \dfrac{5}{12} [/tex]

[tex] \dfrac{9}{4} - 6y = \dfrac{41}{12} [/tex]

[tex] -6y = \dfrac{41}{12} - \dfrac{27}{12} [/tex]

[tex] -6y = \dfrac{14}{12} [/tex]

[tex] -6y = \dfrac{7}{6} [/tex]

[tex] y = -\dfrac{7}{36} [/tex]

Answer:Greatest to Smallest > 7.44, 7.404, 7.2041, 7.2   and Smallest To Largest > 7.2, 7.2041, 7.404, 7.44

Step-by-step explanation:

The equation of g(x), after the translation of [tex]f(x) = \sqrt{x}[/tex] 4 units to the right is given as follows:

[tex]g(x) = \sqrt{x - 4}[/tex]

Among the many transformations that a function or a figure can undergo is a translation, along with reflections, rotations and dilation.

In a translation, only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are defined as follows:

The parent function for this problem is given as follows:

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

After the translation 4 units right, the function g(x) is defined as follows:

[tex]g(x) = f(x - 4) = \sqrt{x - 4}[/tex]

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