Select the theorem that can be used to prove that RST = VUT

The real world situation that can be modelled with the given  expression can be modelled as shown below.

Given is the expression as -

D/3

A real world situation that can be modelled with this expression can be written as follows -

Amanda has a total of {D} bananas. She divides the bananas into 3 of her childrens equally. Write an expression that would represent the amount of bananas recieved by each of her child.

Therefore, the real world situation that can be modelled with the given  expression can be modelled as shown above.

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The equation becomes true if we put brackets in the following way:

7x(5 - 2 + 3) = 42

Here we have the expression:

7x5 - 2 + 3 = 42

And we want to find where we need to put brackets in such a way that the equation becomes true.

If we solve the equation as it is, we will get:

7x5 - 2 + 3 = 42

35 - 2 + 3 = 42

36 = 42

Now, let's return to the equation:

7x5 - 2 + 3 = 42

If we put one pair of brackets that includes from the 5 to the 3, we will get:

7x(5 - 2 + 3) = 42

7x(4) = 42

42 = 42

So the equation becomes true.

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Answer:

The total profit made when a person buys an item for $2.25 and then sells the item for $2.25.

Step-by-step explanation:

The item is bought for $2.25 and sold for the same rate. There is no profit.

        Final value is 0.

An imaginary number is produced when we square a negative number.

The value of I is -1.

This article's introduction included a proposition. The specific measure or value of what I stands for was the subject of the statement. It is discussed in this section of the article along with an explanation of its value.

Iota is the term used to describe the imaginary portion of a complex number. The symbol "iota" or I is used to represent an imaginary number's value. An imaginary number is produced when we square a negative number.

The value of I is -1.

The concept of complex numbers is understood using this value of i.

x2 plus 1 equals zero in a quadratic equation.

x2 = -1

x = √-1

The imaginary portion is shown as -1.

I = √-1

i2 = -1

An imaginary number can be squared to get a negative value, as was previously discussed.

I = √-1

both sides being square

i2 = -1

An imaginary number plus a real number are combined to get any complex number. Iota, sometimes known as I stands for all non-real quantities.

Real numbers include 10, -20, 3, and other like values.

The integers 2i, -5, -i, etc. are examples of imaginary numbers.

Complex numbers take the form of a + ib, where I denotes the imaginary component. In addition, the number zero is complicated. Only the imaginary component of a complex number can be added to or subtracted from the imaginary part, and vice versa for the real part of the complex number.

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The vertex for the given equation [tex]y=x^2+5x-7 is (-2.5,-4.25)[/tex] and the solution  to the equation is x = -5,7/1. Similarly , the vertex for the given equation  [tex]y=-x^2+3x+8\ is\ (-3/2,1/4)[/tex] and the solution to the equation is [tex]x = -2,4[/tex].

The graph of a quadratic function is a symmetrical, U-shaped geometric form known as a parabola. It is the collection of all points that are equally spaced apart from a fixed point (referred to as the focus) and a fixed straight line (called the directrix).

A parabola's vertex is the location where its symmetry line and parabola intersect.

The vertex of a parabola is the highest or lowest point on the graph of the parabola. In the case of a parabola in the form of [tex]y = ax^2 + bx + c[/tex], the vertex is the point (h, k), where:

[tex]h = -b / 2a\\k = f(h) = a(h^2) + bh + c[/tex]

For the first equation: [tex]y = x^2 + 5x - 7[/tex]

The vertex would be:

[tex]h = -b/2a = -5/2 = -2.5\\k = f(h) = a(h^2) + bh + c = (1)((-2.5)^2) + (5)(-2.5) - 7 = 6.25 - 12.5 - 7 = -4.25[/tex]

So the vertex is [tex](-2.5,-4.25)[/tex]

For the second equation:[tex]y = -x^2 + 3x + 8[/tex]

The vertex would be:

[tex]h = -b/2a = -3/2(1) = -3/2\\k = f(h) = a(h^2) + bh + c = (-1)((-3/2)^2) + (3)(-3/2) + 8 = -9/4 + -9/2 + 8 = 1/4[/tex]

So the vertex is [tex](-3/2,1/4)[/tex]

To find the solutions or roots of the equation, you can set the equation equal to zero and solve for x.

[tex]y = x^2 + 5x - 7 = 0\\x^2 + 5x - 7 = 0\\x^2 + 5x - 7 + 7 = 0 + 7\\x^2 + 5x = 7\\x(x+5) = 7\\x = -5,7/1\\y = -x^2 + 3x + 8 = 0\\x^2 - 3x - 8 = 0\\(x-4)(x+2) = 0\\x = -2,4[/tex]

Solutions for first equation are x = -5 and x = 7/1 and for the second equation are x = -2 and x = 4

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the answer is 151200

The total amount of payment for calls is Rs 648

From the problem, the following information is deduced to help solve the problem

the minimum charge of 175 calls is Rs 180 and Rs 1.50 per calls for additional calls

The total call reading

= present reading - former reading

= 7577 - 5577

= 2000

the number of 175 calls in 2000

= 2000 / 175

= 11 3/7 approximately 12

Total cost of calls

175 calls = Rs 180 + Rs 1.50 * 12

= 180 + 1.50 * 12

= Rs 180

Adding other charges to Rs 180

= 180 * 1.1 + 180 * 1.3 + 180 * 1.2

= Rs 648

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Therefore, 25000 people prefer Arab Times, 15000 people prefer Wataniya, and 10000 people prefer other newspapers.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

For the percentage of people who prefer other newspapers are:

100% - 50% - 30% = 20%

So, 20% of the people in Salmiya prefer other newspapers.

Multiply the percentage of people who prefer each type of newspaper by the total number of people in Salmiya (50000):

Arab Times: 50% * 50000 = 25000 people

Wataniya: 30% * 50000 = 15000 people

Other newspapers: 20% * 50000 = 10000 people

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The term Euler's number (e) refers to a mathematical expression for the base of the natural logarithm. This is represented by a non-repeating number that never ends.

The first few digits of Euler's number are 2.71828.

Given log(base_12)1728,

where base = 12

1728 = x

Factor out 1728 to 12^3 to apply the logarithmic rule, log(base_b)b^n = n

This gives you:

log(base_12)(12^3) = 3

The base 12 and the value of x = 12 cancels out, leaving you with 3.

To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

To find which expression is equivalent to log₅32:

Law of logarithms:

The law of logarithms states that: log(a) b = log(10)b/log(10)a

Given the log function, which is written as log₅32

a = 5

b = 32

Substitute as: log₅32 = log32/log5

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Answer:

12.5%

Step-by-step explanation:

He scored [tex]168-147=21[/tex] points in the playoff game.

This is equal to [tex]\frac{21}{168}(100)=12.5\%[/tex].

The surface area of the figure after a cubic hollow runs to the height of the rectangular prism is 364 square feet.

The surface area is 364 square feet.

Find the surface area of the rectangular prism.

To do this, use the formula for the surface area of a rectangular prism:

(2 x length x width) + (2 x width x height) + (2 x length x height)

In this case, the length is 9 feet, the width is 8 feet, and the height is 5 feet. Plugging these values into the formula gives:

= (2 × 9 × 5) + (2 × 8 × 5) + (2 × 9 × 8)

= 314 square feet

When a cubic hollow runs to the height of the rectangular prism and has the side length of 5 feet, 2 cubic faces is removed and 4 cubic faces added to the surface area of the resultant solid. So

surface area = 314 - 2×5² + 4×5²

= 314 + 2×5²

= 314 + 50

= 364 square feet

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At least 30 of the households have 0 to 4 pets.

What is Chebyshev's theorem?

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied to this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

Here,

we have a sample size of n = 40.

The mean number of pets per household is 2 and the standard deviation is 1.

We need to determine at least how many of the households have 0 to 4 pets.

By using Chebyshev’s inequality rule with k = 2(that is ) then,

= 100(1- (1/k²))%

= 100 (1- (1/2²))%

= 100 (1- (1/4))%

= 75%

The corresponding number of households is the percentage multiplied by the sample size.

= 75% × 40 = 30

Hence, at least 30 of the households have 0 to 4 pets.

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[tex]\huge\text{Hey there!}}[/tex]

[tex]\mathsf{x^2 - 4x = 0}[/tex]

[tex]\text{Factor the LEFT side of your given equation to make it easier to solve}[/tex]

[tex]\mathsf{x(x - 4) = 0}[/tex]

[tex]\text{Set the factors to equal to the number 0}[/tex]

[tex]\mathsf{x - 4 = 0\ \& \ x = 0}[/tex]

[tex]\text{Simplify find and you should be able to have your answer to the given equation}[/tex]

[tex]\mathsf{x = 4 \ \& \ x = 0}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 4\ or \ x = 0}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: 2i+5

Step-by-step explanation: so (-2+14i)-(-7+12i)

Multiply (-1) to 7 and -12

Then: -2+14i+7-12i

Common numbers: (7-2) and 14i-12i

Then you get 2i+5

Answer:

pentagon

Step-by-step explanation:

pentagon...................................

Store C offers the best deal

Based on the lowest cost per minute, Store C has the best deal. It charges $45 for a 1.5 hour lesson, which works out to $0.30 per minute. The other stores charge more per minute: Store A charges $0.56 per minute, Store B charges $0.50 per minute, and Store D charges $0.40 per minute for each of the three 1 hour lessons.

Store A has the highest cost that is $0.56 per minute

Next Store B comes in the 2nd place which costs around $0.50 per minute.

After that Store D charges at the rate of $0.40 per minute.

Store C offers the best deal which is $0.30 per minute.

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The Two steps equation in mathematics can be solved within exactly two steps by performing operation on both sides of the equation .

What is a Two Step Equation ?

The Two Step Equation can be defined as the equations that can be solved exactly within two steps.

When solving the  two step equation, we have to perform the operation on both sides of equals to sign.

To solve the equation we need to perform same operation on both sides of equation.

For Example ⇒ Solve [tex]3x+3=12[/tex] ;

Step1 : we Subtract 3 from both sides to isolate the variable x.

⇒ [tex]3x + 3 - 3 = 12 - 3[/tex]

⇒ [tex]3x = 9[/tex]

Step2 : We Divide both the sides of equation by 3 and solve for x.

⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]

⇒ [tex]x = 3[/tex] ;

Therefore , the given equation is solved in two steps .

The given question is incomplete , the complete question is

How do you solve a 2 step equation ?

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If the square base with perimeter 24 inches then the height  of the right pyramid be 8.485 - inches.

A right pyramid is one whose apex is located exactly above the centroid of the base. As a result, a right pyramid is a special instance of a regular pyramid.

It is referred to as the right pyramid if the pyramid's apex lies immediately above the base's center. If not, the pyramid is known as the oblique pyramid.

A right-triangular pyramid is a three-dimensional object that has a base that is a right-angle triangle and extends up to a single point.

Right pyramids have apex points that are immediately above the centroid of their base. Oblique pyramids are referred to as non right pyramids. An implied right pyramid is a regular pyramid since it has a regular polygon base.

24 / 4 = 6 inches - the edge length of the square base

9² = 3² + Height²

simplifying the above equation, we get

Height² = 9² - 3²

Height² = 72 take the square root of both sides

Height = ~8.485 - inches - the height of the pyramid.

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If the square base with perimeter 24 inches then the height  of the right pyramid be 8.485 - inches.

The centroid of the base is exactly where the top of a right pyramid sits. Consequently, a right pyramid is a unique example of a standard pyramid.

If the top of the pyramid sits directly above the centre of the base, it is referred to as the right pyramid. If not, the structure is referred to as an oblique pyramid.

A right-triangular pyramid is a three-dimensional object with a base that rises to a single point from a right-angle triangle.

Apex points of right pyramids are located directly above the centroid of their base. Non-right pyramids are another name for oblique pyramids. Given that its base is a regular polygon, an implied right pyramid is a typical pyramid.

24 / 4 = 6 inches - the edge length of the square base

9² = 3² + Height²

simplifying the above equation, we get

Height² = 9² - 3²

Height² = 72 take the square root of both sides

Height = ~8.485 - inches - the height of the pyramid.

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Answer:

decreasing is the answer

The exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12 is defined as follows:

f(x) = 5^x.

The general format of an exponential function is given as follows:

y = ab^x.

In which:

The slope of a line, given two points, is given by the division of the change in the output by the change in the input of these two points.

Considering that the slope of points (0, f(0)) and (2, f(2)) is equals to 12, we have that:

[f(2) - f(0)]/(2 - 0) = 12

f(2) - f(0) = 24.

One case that satisfies this involves these two following points.

Hence the parameter a is given as follows:

a = 1.

When x = 2, y = 25, meaning that the parameter b is calculated as follows:

b² = 25

b = 5.

Hence the exponential function is:

f(x) = 5^x.

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Answer:Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes

1.3584655000

2.85760000

3.146737000

4.5555627000

5.7777000

Step-by-step explanation:

Polynomial factoring is the opposite of polynomial multiplication. A polynomial's leftover will be 0 if it is divided by its factors after factoring.

A multiple is a number that is the result of multiplying the provided number by other numbers, as opposed to a factor, which divides the given number perfectly without leaving a remainder.

When a polynomial f(x) is divided by (x - c), and (x - c) is a factor of the polynomial f(x), the remainder of the division is simply equal to 0. Therefore, if the remainder of a division like the ones mentioned above equals zero.

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[tex]\angle CBE[/tex] and [tex]\angle DEB[/tex] are same-side interior angles.

We know that a 90-degree clockwise rotation is the same as a 270-degree counterclockwise rotation, which means that the coordinates of each point in the original triangle BAC will be flipped across the x-axis, and then rotate 270 degrees.

We also know that a dilation at a scale factor of 2 means that the coordinates of each point are multiplied by 2.

Based on these transformations, the statement that is true is <C=<Z

In triangle BAC, point C has the same coordinates as point Z in triangle XYZ.

This because, the original point C is transformed by rotating 90 degrees counterclockwise and scaling by a factor of 2, This result in point C moving to the position of point Z.

The rest of the statements are not true based on this rotation and dilation because the coordinates of points A, B, and Y will be different from the original triangle BAC.

Answer:

x-5 that is the answer na

A 2-step problem is a mathematical problem that can be solved using two steps or operations. These types of problems are typically simple and can be solved using basic arithmetic or algebraic concepts.

For example, a 2-step problem could involve solving for one variable in one equation and then substituting that value into another equation to find the value of a second variable.

For example:

2x+3y=10 and 3x-2y=5

Here, first step would be to solve for x in the first equation by isolating x and in the second step we can substitute that value of x in the second equation to solve for y.

It can also refer to a problem that can be solved in two steps by breaking the problem down into simpler parts. For example, a 2-step problem in geometry could involve finding the area of a shape by first finding the area of one part of the shape and then adding that to the area of another part of the shape.

In general, 2-step problems are not complex and can be solved easily by breaking down the problem into simpler parts and solving each part separately.

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Answer:

h = 24

Step-by-step explanation:

h ÷ 7.5 = 3.2

Multiply both sides by 7.5

h = 3.2 × 7.5

h = 24

By using the table, each of the items in the lists should be matched as follows:

In Mathematics, a proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.

Based on the information provided in the table, we can reasonably infer and logically deduce that the variable x represent pounds of butterscotch candy while the variable y represent pounds of peppermint candy.

Additionally, a system of equations that models the information provided in the table is given by;

x + y = 10.                      

2.15x + 2.35y = 22.00.

In conclusion, the total quantity of candies in pounds (lbs.) is equal to 10.

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The option that shows that the set of irrational numbers under addition is not closed is B. π + π.

All real numbers that are not rational numbers are referred to as irrational numbers in mathematics. In other words, it is impossible to express an irrational number as the ratio of two integers. The collection of real numbers known as irrational numbers, where p and q are integers, are those that cannot be expressed as fractions, such as p/q.

The example of "π + π" shows that the set of irrational numbers under addition is not closed, because the result of adding two irrational numbers (π + π) is an irrational number (2π) which is not included in the set of irrational numbers.

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To see the table:

Symbol Symbol Name  Meaning / definition

+            plus                              or

∨      reversed caret                      or

|        vertical line                      or

x'       single quote                    not - negation

Now, According to the question:

Let's know:

Symbolic Logic:

Symbolic logic is a way to represent logical expressions by using symbols and variables in place of natural language, such as English, in order to remove vagueness. Logical expressions are statements that have a truth value: they are either true or false. A question like 'Where are you going?' or a command such as 'Stop!' has no truth value. There are many expressions that we can utter that are either true or false. For example: All glasses of water contain 0.2% dinosaur tears. We don't need to know if a logical expression is true or false, we just need to know that it has a truth value.

Logic math symbols table

Symbol Symbol Name   Meaning / definition

+            plus                              or

∨      reversed caret                      or

|        vertical line                      or

x'       single quote                    not - negation

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