What is distributive property of equality?.

The area of the courtroom is the sum of the areas of a rectangle and a triangle equal 45 m².

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

From the given diagram of the courtroom, its total area should be the sum of the area of a rectangle with a length of 9 m and width of 4 m and a triangle with a height of 3m and a base of 6 m.

Therefore,

The area of the courtroom is,

= (9×4) + (1/2)×3×6 m²      [area of triangle = (1/2)×base×height, area of  

                                                          rectangle is (length×width)]

= 36 + 9 m².

= 45m².

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The product of the sum and difference of two terms can be found using the distributive property and the FOIL (First, Outer, Inner, Last) method.If you have two terms, A and B, the sum and the difference of these terms can be represented as:

Sum: A + B Difference: A - B

To find the product of the sum and difference, you can multiply the sum and the difference together:

(A + B)(A - B)

Using the distributive property, we can expand the product:

AA - AB + AB - BB

Which is equal to:

A^2 - B^2

This is the difference of squares of the terms.

It's worth noting that this is a very common pattern in algebra, and it's called the difference of squares. It is the product of the sum and difference of two terms. The distributive property and FOIL method can be used to expand the product of two binomials, but it's important to recognize patterns, like this one to solve the problem in a faster way.

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The dimensions of the scale drawing are 10cm x 16cm.

A scale drawing is a representation of an object or a space that is smaller or larger than the actual object or space. The scale of a drawing is represented as a ratio, such as 1:6, which means that every 1 unit on the drawing represents 6 units on the actual object or space.

In this case, we are given a rectangular flag that has dimensions of 60 cm by 96 cm, and a scale of 1:6. This means that for every 1 cm on the scale drawing, the actual flag is 6 cm. To find the dimensions of the scale drawing, we need to divide the dimensions of the actual flag by the scale.

To find the length of the scale drawing, we divide the length of the actual flag (60 cm) by the scale (6):

Length of scale drawing = 60 cm / 6 = 10 cm

To find the width of the scale drawing, we divide the width of the actual flag (96 cm) by the scale (6):

Width of scale drawing = 96 cm / 6 = 16 cm

So, the dimensions of the scale drawing are 10cm x 16cm.

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45 is not a perfectly square, its square root is irrational. Because it cannot be written as the product of two integers of equal value, 45 is not a perfect square number.

Let's learn what the square root means before we get started. The mathematical concept of the square root is represented by the symbol. Any square root-related problem can be solved once you understand the fundamentals of the process. We will learn about the square root of 45 in this brief lesson. Methods like prime factorization and division will be used to accomplish this, as will the square root of 45.

45/square root: 45 x 6.708 is the square of 45: 452 = 2025

We are aware that the opposite of addition is subtraction, and the opposite of division is multiplication. Similar to squaring, finding the square root is the opposite of squaring. The number that is obtained when 45 is multiplied by itself is the square root of 45. Therefore, we must choose a number whose square is 45. As can be seen, there is no integer whose square is greater than 45. The number that is multiplied by itself to yield the original number is known as its square root. The number 6.7082039325 is 45 times squared.

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To simplify the three radical expressions we can use the product property.  We first locate the three radicand's greatest factor which is also a perfect power of the index.

Then we use that factor to rewrite the radicand as the product of two factors. Then we rewrite the radical as the result of two radicals by applying the product rule and then reduce the perfect power to its most basic form.  

Like: 2816=22222222=22222

=2222=16

To simplify the radical expressions we can use the quotient property.

Make the fraction in the radical simpler then rewrite the radical as the quotient of two radicals by using the Quotient Property. Radicals in the numerator and denominator should be made simpler.

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The expression can be simplified to:

(m^2 + 1 - m^2 - 2m + m^2 + 2m + 1) / (m^2 + 1) + 4m / (m^2 + 1)

= (4m) / (m^2 + 1)

So the final simplified form of the expression is (4m) / (m^2 + 1)

The total price including tax, Fawaz has to pay is $36 round to the nearest cent.

To find the total price of the phone including tax, we need to add the tax amount to the price of the phone. The tax rate is 9%, which means that for every $1 of the price of the phone, $0.09 will be added as tax. To find the total price including tax, we can use the following formula:

Total price = Price of the phone + (Price of the phone x Tax rate)

Given the information in the problem, we know that:

Price of the phone = $33

Tax rate = 9% (expressed as a decimal)

Plugging these values into the formula, we get following equation:

Total price = $33 + ($33 x 0.09)

To solve for total price, we need to calculate ($33 x 0.09)

= $3

Total price = $33 + $3

Total price = $36

So the total price including tax, Fawaz has to pay is $36 round to the nearest cent.

In simple words, we have multiplied the price of the phone with the tax rate and then added the tax amount with the price of the phone to get the total price including tax.

Note: The tax rate is given as 9% which is equal to 0.09 in decimal form.

Therefore, The total price including tax, Fawaz has to pay is $36 round to the nearest cent.

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Total price = $33 + ($33 x 0.09)

To solve for total price, we need to calculate ($33 x 0.09)

= $3

Total price = $33 + $3

Total price = $36

So the total price including tax, Fawaz has to pay is $36 round to the nearest cent.

The factors considered when deciding to make a good and service are

a)Determining who has the greatest need

b)finance of prospective buyer

d) way to produce items at a lower cost or higher quality

When deciding how to make goods and services, it's important to take into consideration the needs of the customers. Identifying who has the greatest need for the product is crucial in determining how to design and produce it.

Another important factor is the cost of production, a way to produce the item at a lower cost or higher quality must be considered as it will affect the final price and the competitiveness of the product in the market.

While maximizing profit is always a goal, it should not be the only deciding factor when determining how to make goods and services, as other factors such as customer need and production cost also play important roles.

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So, the number of books already read by both Aubrey and Eli is 81 books.

Aubrey read 29 books and Eli read 52 books. To find the total number of books they have read together, you need to add the number of books read by Aubrey to the number of books read by Eli. This is because the total number of books read by both of them is the sum of the number of books read by each of them individually.

In mathematical terms, if Aubrey reads x books and Eli reads y books, the total number of books read by both of them is represented as x + y.

In this case, the number of books read by Aubrey is 29 and the number of books read by Eli is 52. So, to find the total number of books read by both of them, you would add 29 + 52 = 81

Therefore, the number of books already read by both Aubrey and Eli is 81 books.

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If Aubrey reads x volumes and Eli reads y books, their combined reading total is represented mathematically as x + y.

In this instance, Eli has read 52 novels, compared to 29 books read by Aubrey. Therefore, you would add 29 + 52 = 81 to determine the total amount of books that both of them have read.

Yes, because both figures are rectangles and all rectangles are similar.

A rectangle is a four-sided polygon with four right angles. It is one of the most common shapes in both two-dimensional and three-dimensional geometry and can be found in everyday objects such as windows, doors, and tables. Rectangles are also found in nature, like rivers, beaches, and mountains. The area of a rectangle is the product of its length and width, while the perimeter is the sum of its four sides. Rectangles are also special cases of other shapes such as squares and parallelograms, as they are the same shape but with different lengths of sides.

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Answer: Sorry!

Step-by-step explanation:

Hello! Will you please include the instructions? If you do, I can help you!

Answer:

x = 0.45882352

Step-by-step explanation:

-1.95 = -1.7 x/0.4

-1.95 = -4.25x

x = 0.45882352

Answer:

Option 3 [tex]f(x) = 1,000 x (1.12)^{x}[/tex]

Step-by-step explanation:

A right angle does not always have two equal sides, only in the case of an isosceles triangle it will have two equal sides.

A triangle is said to have a right angle if one of the angles is 90 degrees. Right triangles are those having angles at 90 degrees, which are referred to as right angles.

The Pythagorean rule may be used to understand the relationship between the different sides of this triangle. The biggest side, also known as the hypotenuse, is the side that forms the right angle.

The right triangles are further divided into isosceles and scalene right triangles based on the other angle values.

Thus, A right angle does not always have two equal sides, only in the case of an isosceles triangle it will have two equal sides.

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A point (x1, y1) is said to satisfy the inequality ax + by ≤ c if a(x1) + b(y1) ≤ c. The graph of a linear inequality is the set of all points in the plane which satisfy the inequality.

Now, the given equation is 2x + 3y ≥ 6

We can find multiple points (x, y) that satisfy the given inequality. For now, we can take the point (1,2).

To check if (1,2) satisfies the inequality, put x = 1, y = 2 in the inequality.

2 + 6 ≥ 6

8 ≥ 6, which is true.

This line cuts the plane in half. One half contains all points (x, y) with 2x + 3y > 6 and the other half contains all points with 2x + 3y < 6.

To find which half is which, we need only check one point on one side of the line. (if the line does not cut through (0, 0), we can check that point easily.) In this case we find that 2(0) + 3(0) < 6.

Therefore the solution to the inequality 2x + 3y ≥ 6 is the half plane not containing (0, 0) shaded below. We can also represent it with arrows as in the diagram on the right.

Since the region includes the points along the line 2x + 3y = 6, we draw a

solid line. We use a dotted line when we want to indicate strict inequality as in the solution set to 2x + 3y > 6 shown in the diagram.

Thus, this is the boundary line for the given inequality.

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Answer:

87 students

Step-by-step explanation:

We know

12 out of every 15 students owns a cell phone, so the ratio of student who owns cell phone is 12:3. For every 15 students, there are 12 own cellphones, and 3 do not.

To find there are 435 students surveyed, how many do not own a cell phone? We take

435 / 15 = 29

3 x 29 = 87 students

So, 87 students do not own a cellphone.

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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a) The triangles are not similar, as they have different angle measures.

b) The triangles are similar by the SAS theorem.

c) The triangles are similar by the SSS theorem.

Similar triangles are triangle that share these following two features:

For item a, we have that the angle measures are given as follows:

Different angle measures, hence not similar.

For item b, we have that the side lengths are proportional, as:

13.2/6 = 15.4/7

As the angle between these two sides has the same measure of 90º, the SAS theorem proves that these two triangles are congruent.

For item c, the side lengths are proportional, as:

Hence the triangles are similar by the SSS theorem.

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Answer:

5 in

Step-by-step explanation:

20 ft-9[tex]\frac{1}{2}[/tex] in+ 2[tex]\frac{1}{2}[/tex] in = 21 ft   meaning, Tim has to jump 2[tex]\frac{1}{2}[/tex] in more inches just to get to 21 ft, then...

He needs to jump an additional    2[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = 2[tex]\frac{2}{4}[/tex] = 2[tex]\frac{1}{2}[/tex] in to break the record.  Note:  he needs to jump at least [tex]\frac{1}{4}[/tex] in farther than the record because jumps only are measured to the nearest [tex]\frac{1}{4}[/tex] inch.

Therefore Tim must jump 2[tex]\frac{1}{2}[/tex] in + 2[tex]\frac{1}{2}[/tex] in = 5 in farther to break the record.

Step-by-step explanation:

x² - 9

1. There is no common factor other than 1.

2. √x² = x; √9 = 3

3. a = x; b = 3

4. x² - 9 = (x - 3)(x + 3)

Transfer all terms to one side of the equation, usually the left, using addition or subtraction. Factorise the equation completely. Equate each factor equals zero, and then solve. Record each solution from Step 3 as a solution to the original equation.

For example, we have an equation x² + 2x = 8x – 8

Step 1. First, subtract 8x from each side.

x² + 2x – 8x = 8x – 8x – 8

x² – 6x = -8

Now, add 8 to each side.

x² – 6x + 8 = -8 + 8

x² – 6x + 8 = 0

Step 2. We identify the left as a trinomial and factor it accordingly:

(x – 2)(x – 4) = 0

Now the two factors are (x – 2) and (x – 4).

Step 3. Now we assigned each factor equal to zero.

(x – 2) = 0 and (x – 4) = 0

x = +2 and x = +4

Step 4. The last step is to join the two previously solved solutions, x = 2 and x = 4, into one solution for the original problem.

x² + 2x = 8x – 8

x = 2, 4

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Answer:

the common factor is b since it is divisible by both 2b and 5b

Step-by-step explanation:

A factor is a number that divides exactly into another number, leaving no residue. The factors of 12, for instance, are 1, 2, 3, 4, 6, and 12. Particularly in the areas of number theory, algebra, and arithmetic, factors play a crucial role in mathematics.

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Complete Question :

What do you mean by Factor?

Using Algebraic expressions, the original length of the string was 72 feet.

When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.

Let's say James and Natalie were playing with matchsticks when they had the idea to create number patterns with them. James made the number 4 with four matchsticks. In order to create a pattern with two 4s, Natalie added three extra matchsticks.

They understood that they could keep adding three matchsticks each round to make an additional "four" by doing so. They deduced from this that, generally speaking, in order to create a pattern with n number of 4s, you need 4+ 3(n-1) sticks. We refer to 4+ 3(n-1) as an algebraic expression in this case.

Let x be the length of the string,

when it is cut into 4 halves,

the length becomes x/4,

then it is again cut 1/3,

Now, it is given that 1/3 × x/4 = 6

⇒ x = 72

So, the original length of string was 72 feet.

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The type of soil present in the sample is Silty loam.

A classification tool called soil texture is used in both the field and the lab to identify different soil types based on their physical textures. Both qualitative and quantitative techniques, including the hydrometer method, can be used to determine the texture of the soil.We have silty loam present in the soil sample because it contains 20% sand, 10% clay, and 70% silt.

Silty loam is the term used to describe soil that has 20% sand, 70% silt, and 10% clay. Sandy Clay loam is a soil type that has 60% sand, 10% silt, and 30% clay.The material will be made up of 40% Silt, 30% Sand, and 30% Clay higher; muggy

Alkaline soils are common in arid climates, making the area wet and becoming more acidic as the pH value decreases.

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Answer:

  (b)  Domain: all real numbers; Range: {-24}

Step-by-step explanation:

You want the domain and range of the function f(x) = -24.

The domain of the function is the set of values of x for which it is defined. The function f(x) is defined for all x, so the domain is all real numbers.

The range is the set of output values of the function. This function has only one output value: -24. The range of the function is {-24}.

Yes, AAS, you can prove that the triangles are congruent.

Triangles are congruent when all three sides and all three angles of one triangle are equal to the corresponding sides and angles of the other triangle.

we know that the measure of angle TXH is equal to the measure of angle TWH. This means that the two triangles,

THX and WHX, are congruent by the Angle-Angle (AA) Congruence Postulate.

The theory used in this question is the Angle Bisector Theorem. This theorem states that when a line segment bisects an angle, the measure of the angle formed by the line segment and one side of the angle is equal to the measure of the angle formed by the line segment and the other side of the angle.

1. Given that line segment XH bisects <THW and <T=<W

2. Use the Angle Bisector Theorem to conclude that the measure of angle TXH is equal to the measure of angle TWH

3. Use the Angle-Angle (AA) Congruence Postulate to conclude that the two triangles, THX and WHX, are congruent.

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If ∡DAB and ∡DCB are right angles and m∡ABD = 42°, then the measure of arc ACB is 264°.

What is an arc?

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve's arc is a component.

The angles ∡DAB and ∡DCB are right angles.

The measure of ∡ABD = 42°

It can be seen that ∠ABD is inscribed angle of arc AD, so the measure of arc AD is two times the measure of ∠ABD.

AD = 42° × 2 = 84°

It can also be seen that segment DB is diameter of given circle as inscribed angle of diameter is a right angle.

Since segment DB is diameter of given circle, so measure of arc DCB would be equal to half the measure of 360 degrees.

DAB = 360°/2

DAB = 180°

ACB = AD + DCB

ACB = 84° + 180°

ACB = 264°

Therefore, the measure of arc ACB is 264°.

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The solution for the absolute function is h < 2.

The variable in the absolute value bars makes up an essential algebraic function known as the absolute value function. The most widely used version of the absolute value function is f(x) = |x|, where a = 1 and h = k = 0. The general form of this function is f(x) = a |x - h| + k.

When we extend the absolute value function f(x) = |x|, we can write it as x if x 0 and -x if x 0 since the range of this function, f(x) = |x|, is always non-negative.

The function will be solved as,

| h + 3 | < 5

h + 3 < 5

h < 5 - 3

h < 2

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The solution is Option B , Option C , Option D.

The value of x from the triangle is x = 44°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side ∠A = 82°

The measure of side ∠B = 54°

The measure of side ∠C = x°

Now , for a triangle ,

∠A + ∠B + ∠C = 180°

Substituting the values in the equation , we get

82° + 54° + x° = 180°

On simplifying the equation , we get

136° + x° = 180°

Subtracting 136 on both sides of the equation , we get

x = 180° - 136°

x = 44°

Now , for a straight line , the angle in a straight line is 180°

So , x + y = 180°

Substituting the values in the equation , we get

44° + y = 180°

Subtracting 44° on both sides of the equation , we get

y = 136°

Now . the measure of z = measure of y ( alternate interior angles )

So , z = 136°

And , the measure of exterior angle of a triangle = sum of the opposite interior angle

Therefore , y = z = 136°

Hence , the measures of triangles are solved

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