21. The marks obtained by the students of class VII in the class test of Mathematics are given in the table below. Find the average marks. Marks obtained No. of students 10 3 20 6 30 10 40 7 50 4​

Using the distributive property we will find the equivalent expression:

8*(a + 4) = 8a + 32

Remember that the distributive property for the multiplication says that:

A*(B + C) = A*B + A*C

So we distributed the product along the addition.

Here we want to rewrite the expression:

8*(a + 4)

Using the distrubitive property, we can rewrite this as:

8*(a + 4) = 8*a + 8*4

              = 8a + 32

That is the equivalent expression.

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The square root of negative x undefined is undefined for the set of Real numbers.

We know that the square root of a number is nothing but the factor/value that we can multiply by itself to get that number.

Finding a square root of number is an inverse method of squaring a number.

A radical symbol '√' used to represent the square root of number.

If m is the square root of n, then it is represented as m = [tex]\sqrt{n}[/tex],

We can write above relation as, m² = n

We know that square of any real number is positive.

For example, 3² = (3 × 3) = 9

(-3)² = (-3) × (-3) = 9

i.e., the square root of 9 is 3 and -3

Thus the square root of number is not defined for negative real number.

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The complete question is:

Why is the square root of negative x undefined?.

The value of cos 5pi/12 is found to be 0.2588.

The given trigonometric ratio is-

= cos (5π/12)

The value of π in degrees is 180, substitute it.

= cos (5*180/12)

= cos (900/12)

= cos (75)

Using calculator

≈ 0.2588

Thus, the value of cos 5pi/12 is found to be 0.2588.

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Answer:

A to B:  Scale of 3, and (10,6)

B to A:  Scale of (1/3) and (10,6)

Step-by-step explanation:

See attached worksheet.

Yes, the given points  (3 ,2) , ( -2 ,- 3 ),  and ( 2, 3 ) forms a triangle.

As given in the question,

Given points to form a triangle is given be :

(3 ,2) , ( -2 ,- 3 ),  and ( 2, 3 )

Let the triangle name be ABC.

Coordinates of vertex A(x₁ ,y₁ ) = ( 3, 2 )

Coordinates of vertex B(x₂ ,y₂ )  = ( -2, -3 )

Coordinates of vertex C(x₃, y₃) = ( 2, 3 )

General distance formula is :

= √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Distance between :

AB = √( -3-2)² + (-2 -3)²

     = 5√2

BC = √(3+ 3)² + (2 + 2)²

     = 2√13

CA = √( 3-2)² + (2 -3)²

     = √2

Using Pythagoras theorem we have:

( Hypotenuse )² = ( Side1 )² + ( Side 2)²

Right hand side

= (5√2)² + (√2 )²

= 50 + 2

= 52

= ( 2√13)²

= Left hand side

This implies the triangle formed by the points is right angled triangle.

Therefore, yes the given points forms a right angled triangle.

The above question is incomplete , the complete question is:

Do the points (3 ,2) , ( -2 , -3 ),  and ( 2, 3 ) form a triangle?.

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The size of QRS in the given figure 15 cm.

A fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean theorem, also referred to as Pythagoras' theorem. According to this definition, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

step1

We know

PS=8cm

PQ=12cm

QR=4cm

because we know that both of these parts have to do with right triangles, we know that we can use the Pythagorean theorem.

a²  + b²  = 4²  (add in values)

8²  + 12² +4²   

64 + 144 +16=224

find the square root of 224= 15

Size of QRZ =15 cm

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60° triangle can be calculated in radians as π/3 radians.

60 degree angle is an acute angle in geometry and is expressed as π/3 in radians. Each angle in an equilateral triangle is equal to 60 degrees.

A 60-degree angle is an acute angle since angles less than 90 degrees are considered acute. In the case of a geometric angle, the arc is confined by the sides and is centered at the vertex. When rotated, the arc is centered in the center of rotation and is limited to any other point and its image.

Thus, 60° triangle can be calculated in radians as π/3 radians.

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By using the fact that the triangles are similar, we can see that u = 8, then the length of side PR is:

PR = 68

We know that R is the midpoint of QS and P is the midpoint of QT, this means that tiangles QRP and QST are similar triangles, and that the scale factor between them is 2.

Then we know that:

ST = 2*RP

We know that:

RP = 4u + 2

ST = u + 60

Then we can write the linear equation:

u + 60 = 2*(4u + 2)

u + 60 = 8u + 4

60 - 4 = 8u - u

56 = 7u

56/7 = u

8 = u

Now we can find the length of side PR.

PR = u + 60

PR = 8 + 60

PR = 68

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Under Trigonometric ratios, the values of sin, cos, and tan are defined by the ratio of sides of a right-angled triangle.

 One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.

The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

To determine a right triangle's unknown angle or sides, utilize the sine function. The sine function for any right triangle with an angle, let's say ABC, will be:

Opposite/hypotenuse = Sin

According to the trigonometric table, the value of Sin 45=[tex]\sqrt[/tex]2/2 which can be simplified as [tex]\sqrt{2} /2[/tex]×[tex]\sqrt{2} /\sqrt{2} =2/\sqrt[]{2}[/tex][tex]=1/\sqrt{2}[/tex]

Simplified value of Sin 45=1/[tex]\sqrt{2}[/tex]

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a) To find the company's revenue and costs if it sells 2000 shirts, we can substitute 2000 for x in the given revenue and cost functions:

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Revenue: r(x) = 10x, so r(2000) = 10(2000) = $20,000

Costs: c(x) = 3x + 9000, so c(2000) = 3(2000) + 9000 = $15,000

b) The profit function, p(x), is the difference between the revenue function and the cost function. So, the profit function for this company is:

p(x) = r(x) - c(x) = 10x - (3x + 9000) = 7x - 9000

c) To find the company's profit in 2012, when it sold 5000 shirts, we substitute 5000 for x in the profit function:

p(5000) = 7(5000) - 9000 = $20,000

So, the company had a profit of $20,000 in 2012 when it sold 5000 shirts.

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The correct answer is option A (4, 3), 35 units squared.

The coordinates of the three vertices of a rectangle are :

A(-3,3) ,  b(-3,-2)  and   c(4,-2)

The easy way to find the fourth vertex by the graphing the given points

See the attached figure

the given points are in blue color

and by using the symmetry of the rectangle

So, the coordinates of the fourth point D is (4,3) which are in red color

The base of the rectangle is the distance BC

From the graph ⇒⇒ BC = 7

The height of the rectangle is the distance AB

From the graph ⇒⇒ AB = 5

The area of the rectangle = base * height = 7 * 5 = 35

So, the correct answer is option A(4, 3), 35 units squared.

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Answer:

1 d.p to c 7m

Step-by-step explanation:

you should use phythagoras theorem to caculate the leght of BF ang that is my answer

The percentage of getting grey is 78.5%. Amy's spinner is fair.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Amy flicks the spinner 200 times and it comes up grey 157 times.

The percentage of the grey comes up 157 times will be calculated as:-

P = 157 / 200

P = 0.785 x 100

P = 78.5%

Amy's spinner is fair.

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By trigonometric formulas and algebra properties, the trigonometric equation [cos² (90° + β) · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · cos (180° - β)] is equivalent to - 2.

In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be simplified by trigonometric formulas and algebra properties. First, write the entire trigonometric formulas:

[cos² (90° + β) · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · cos (180° - β)]

Second, eliminate the cosine squared of the equation by trigonometric formula:

[[1 + cos (180° + 2 · β)] · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · sin (180° - β)]

[sin (90° - β) + cos (180° + 2 · β) · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · sin (180° - β)]

Third, simplify the trigonometric functions for angle additions and subtractions:

[sin (90° - β) + cos (180° + 2 · β) · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · cos (180° - β)]

[cos β - cos 2β · cos β] / [cos β · sin (- β) · sin β]

- (cos β - cos 2β · cos β) / (cos β · sin β · sin β)

Fourth, simplify the expression by algebra properties:

- (1 - cos 2β) / sin² β

(cos 2β - 1) / sin² β

Fifth, eliminate the double angle by trigonometric formulas:

(cos² β - sin² β - sin² β - cos² β) / sin² β

Sixth, simplify the expression by algebra properties:

- 2 · sin² β / sin ² β

- 2 · 1

- 2

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x²= 4 and 3x=9 is not an empty set because there is no element we can say that is an empty set but there is an element, so it is not an empty set.

In arithmetic, the empty set is a completely unique set having no elements; its size or cardinality (depending on elements in a fixed) is 0. some axiomatic set theories make certain that the empty set exists by including an axiom of the empty set, whilst in different theories, its lifestyles may be deduced. Many feasible properties of sets are vacuously genuine for the empty set.

Any set aside from the empty set is known as non-empty. In a few textbooks and popularizations, the empty set is known as the "null set". but, a null set is a distinct belief inside the context of the measure concept, wherein it describes a hard and fast degree 0 (which is not always empty). The empty set may also be referred to as the void set.

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Complete Question:

Is A={x:x²=4 and 3x=9} an empty set justify your answer?

The length of TW is given as follows:

TW = 17.4 units.

The length TW is the hypotenuse of a right triangle of sides WU and UT.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The side lengths are given as follows:

Hence the length TW is obtained as follows:

(TW)² = 12.6² + 12²

[tex]TW = \sqrt{12.6^2 + 12^2}[/tex]

TW = 17.4 units.

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The number one more than 79 is 80.

Number:

Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. [1] Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number. The most common number system is the Hindu-Arabic number system, which can represent any number using combinations of 10 basic numeral symbols called digits.  In common parlance, a number is indistinguishable from the number it represents.

Greater than Number:

It is a mathematical term used to compare two quantities and to establish a relationship between two quantities in which one term is greater than the other. The terms greater than, less than, and equal are used to compare two numbers, amounts, or amounts. Each term has a separate letter. B. "greater than" is represented by ">", "equal to" is represented by "=", and "less than" is represented by "<".

According to the Question:

To better understand this question,

It can be expressed as 1 more than 79, 1 more than 79, 1 more than 79, 79 plus 1.

Thus,

1 more than 79 is the same as 79 plus 1. So the answer for 1 greater than 79 is calculated as:

Therefore,

1 + 79 = 80.

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The graph of the function f(x)=-x+3,x<=-3 and f(x)=-x^(2)+6,x>-3 is given attachment.

A function is a procedure or a relation that links each element of a non-empty set A, at least, to one element of a different non-empty set B. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain, respectively. f = {(a,b)| for all a ∈ A, b ∈ B}

If each element of set A has exactly one image in set B, then the relation is said to be a function.

A function is a relation from a non-empty set B such that its domain is A and no two different ordered pairs in f share the same first element.

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When you substitute a number for each variable and simplify it is called a Substitution method.

I will demonstrate how the substitution method works. Suppose we have the following systems of linear equations with two variables:

Equation 1:  3x + 2y = 11

Equation 2:  -x + y = 3

By solving these two equations we get x=1 and y=4.

The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation. We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.

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A battery is a nice illustration. Atoms have had their electrons chemically removed in batteries. Because the positive ions and electrons are stored at the opposing ends of the battery, there is a potential difference between the two ends.

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Answer:

question is not mentioned properly

Step-by-step explanation:

i can answer but first what's the question

Answer:

there's nothing there?

Their age now are 13 years old for Jerry and 18 years old for Tom.

As per data given, Tom age now = 5 + Jerry age now. After time = 2 year, Tom age : Jerry age = 4 : 3. We can determine their age now by substitute methods as follow:

After 2 years = Tom age  : Jerry age = 4 : 3

Tom age now + 2 : Jerry age + 2 = 4 : 3

Substitute Tom age now to jerry age now from first formula, so:

Tom age now + 2 : Jerry age now + 2 = 4 : 3

5 + Jerry age now + 2 : Jerry age now + 2 = 4 : 3

3 ( 5 + Jerry age now + 2)  = 4 (Jerry age now + 2)

21 + 3 Jerry age now = 4 Jerry age now + 8

Jerry age now = 21 - 8

Jerry age now = 13 years old

Find the tom age from first formula

Tom age now = 5 + Jerry age now

Tom age now = 5 + 13

Tom age now = 18 years old

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Option (a) represents the correct answer i.e. The value of g(f(9)) is -4.

What is a function?

A relation known as a function connects members of one set in a specific way to those of another set.

Given, f(x)=√x-5 and g(x) = -x²

here, g(f(x)) = g(√x-5 )

                  = - (√x-5)²

 So,  g(f(9)) = - (√9 - 5)²

                   = - (3-5)²

                   = -4

Hence, Option (a) is correct.

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Option (a) represents the correct answer i.e. The value of g(f(9)) is -4.

a mathematical phrase, rule, or law that establishes the link between an independent variable and an outcome variable (the dependent variable). An input and also an output are linked by a function. It functions similarly to a machine with an input or an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "

Given, f(x)=√x-5 and g(x) = -x²

here, g(f(x)) = g(√x-5 )

                 = - (√x-5)²

So,  g(f(9)) = - (√9 - 5)²

                  = - (3-5)²

                   = -4

Hence, Option (a) is correct.

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Using trigonometric identities to simplify the expression, we have sec²(π/2 - x) (sin²(x)-sin⁴(x)) = cos²x

Trigonometric identities are equations that contain the trigonometric ratios.

Since we have the trigonometric expression sec²(π/2 - x) (sin²(x)-sin⁴(x))

We desire to simplify it as follows.

sec²(π/2 - x) (sin²(x)-sin⁴(x))

Using the trigonometric identity sec²(π/2 - x) = 1/cos²(π/2 - x), we have that

sec²(π/2 - x) (sin²(x)-sin⁴(x)) = 1/cos²(π/2 - x) × (sin²(x)-sin⁴(x))

Also, using the fact that cos²(π/2 - x) = sinx, we have that

1/cos²(π/2 - x) × (sin²(x)-sin⁴(x)) = (sin²(x) - sin⁴(x))/sin²x

Factorizing out sin²x, we have that

(sin²(x) - sin⁴(x))/sin²x = (sin²(x)(1 - sin²(x))/sin²x

= 1 - sin²x

= cos²x

So, sec²(π/2 - x) (sin²(x)-sin⁴(x)) = cos²x

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Answer:

10.25x+17y ≥ 50

Step-by-step explanation:

10.25x is how much shirts you can buy

17y is how much pants you can buy

50 is the total money you can spend

HOPE THIS HELPED!

The inequality that represents the situation is 10.25x + 17y ≤ 50.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

You go to a store to buy clothes.

The shirt cost 10.25$ each and the pants cost $17 each.

Let x equal the number of shirts and y equal the number of pants you buy. you can only spend up to $50 at the store.

That means,

10.25x + 17y ≤ 50

Therefore, the inequality is 10.25x + 17y ≤ 50.

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Answer: 8, 9, 10

Step-by-step explanation:

Set [tex]x=1, 2, 3 \implies x+7=8, 9, 10[/tex].

It will cost Caden $5445 to paint the outside walls and roof of the warehouse.

The superficial area can be calculated using the following formula:

2 (lh +wh + lw )

2 (38 x 45 + 30 x 45 +38 x 30)

2 (1710 + 1350 + 1140)

2 x  4200

8400 square foot

Now, let's subtract the area of the floor that will not be painted.

30 x 38 = 1140

8400 - 1140 = 7260 feet to be painted

7260 x 0.75 = $5445

Based on this, the total cost to paint the area desired is $5445.

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The probability that the next two customers would both select popcorn is 1/78.

Probability is the odds that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. The more likely it is that the event would occur, the closer the probability value would be to one.

The probability that the next two customers would both select popcorn = number of popcorns / total number of snacks x [(number of popcorns / total number of snacks) - 1]

Total number of snacks = 3 + 4 + 6 = 13

2/13 x 1/12 = 1/78

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Answer:

I think it's -2

Step-by-step explanation:

because it keeps going down by 2 and 4-2=2 so its -2