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When a prism and pyramid have the same base and height, their volumes are inversely proportional: the volume of the pyramid is one-third that of the prism.

A pyramid is a three-dimensional object that has faces made of triangles and a base made of polygons. The base is the bottom, while the faces are the sides.

A prism is a three-dimensional object having two identically shaped and sized polygonal bases and rectangular sides. In the actual world, a cardboard box serves as an illustration of a prism.

When a pyramid and a prism have bases and heights that are equivalent, the pyramid can fit inside the prism.

In reality, when this is the case, the pyramid occupies precisely one-third of the prism's volume. When a prism and pyramid have the same base and height, their volumes are inversely proportional: the volume of the pyramid is one-third that of the prism.

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The statement as an inequality expression is 12.75 < 7x

From the question, we have the following statement that can be used in our computation:

12 and 3/4 less than the product of 7 and a number x

Express the numbers as fractions

So, we have the following representation

12 + 3/4 less than the product of 7 and a number x

Introduce the inequality symbols

So, we have

12 + 3/4 < the product of 7 and a number x

Next, we have

12 + 3/4 < 7x

Express as decimal

12.75 < 7x

hence, the expression is 12.75 < 7x

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Answer:

The difference of two squares is a method of factorising used when an algebraic expression includes two squared terms, one subtracted from the other: a 2 – b 2 When we are subtracting a squared term from another squared term we can use the difference of two squares method. Square numbers are sometimes called perfect squares.

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Step-by-step explanation:

Answer:

5 per day

Step-by-step explanation:

Answer:

x ≤ 2

Step-by-step explanation:

Brainliest pls btw did it help

Step-by-step explanation:

Find the arithmetic sequence for -16,-21,-26,-31

-21 - (-16) = -5

-26 - (-21) = -5

-31 - (-26) = -5

Answer:

Each following number is five less than the previous.

Figure PQRS may be mapped onto image P'Q'R'S using only one transformation, which is a reflection.

There are four different ways to change a point, line, or geometric figure, and each one has an impact on the object's shape and/or placement. Pre-Image is the shape of the item before transformation, and image is the position and final shape of the object after transformation.

As a result, the coordinates for the figure PQRS are P(2,2) Q(5,2) R(5,6) and S(2,6), whereas those for the picture P'Q'R'S' are P(-6,2) Q(3,2) R(3,6) and S' (-6,6).

Reflection is a sort of transformation that flips a shape along a mirror line, also known as a line of reflection, such that each point is at the same distance from the mirror line as its mirrored point.

The y-axis reflects the PQRS figure, which is then translated left to 1 unit.

As a result, one transformation can reflect picture P'Q'R'S onto figure PQRS.

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Find the slopes and their product should be - 1 for the diagonals to be perpendicular.

The points p and q have zero y-coordinate, so they are on the y-axis.

The points r and s have same y-coordinate b, so they are on the parallel line to the y-axis.

The points p and r are opposite to each-other, similarly points s and q are opposite points. So the diagonals are pr and qs. This is also known from the order of vertices in the name of the quadrilateral.

Slopes are:

The product of slopes:

The diagonals are perpendicular if:

Answer:

10 + 2z

Step-by-step explanation:

2( 5+z)

10 + 2z

The equation of the line that is parallel to the line y = - 5x + 3 will be y = - 5x + c.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y = - 5x + 3

Then the equation of the line that is parallel to the line y = - 5x + 3 will be written as,

y = - 5x + c

The equation of the line that is parallel to the line y = - 5x + 3 will be y = - 5x + c.

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The  average rate of change in concentration of b from t= 0 s to t = 212 s as calculated from the data given above is 0.004811  m/s.

The average rate of change is given by the formula ,

concentration change / time change.

First we will calculate the rate of change for A

rate change = 0.140 - 0.650 = -0.510 M

time difference = 212 s − 0 s = 212 s

Rate of concentration change = -0.510 M / 212 s = -0.002405 M/s

The - sign indicates that the [A] is decreasing with time.

In order to calculate the concentration rate of B we will write it in the form of stoichiometry

B = 2 x 0.002405 = +0.004811 m /s

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Therefore, as a result square root property can be used to solve a quadratic equation.

Describe equation.

To create an equation, the equal sign is placed between two numerical or variable expressions, as in 4x+9=25.

The answer is a number that may be used in an equation to replace the variable.

According to the given question:

In order to isolate the variable being solved,

the square exponents are removed using the Square Root Property.

The positive and negative values of the number that, when multiplied by itself, equals x are provided by the formula x=±√c x = ± c.

Therefore , as a result square root property can be used to solve a quadratic equation.

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The slope of a line that is parallel to x + y = -4 is: -1.

If we have two lines that are parallel to each other, their slopes will be the same.

For example, if the slope of one line is 4, the slope of the line that is parallel to the line will also have a slope of 4.

To find the slope of the equation, x + y = -4, rewrite it in slope-intercept form, y = mx + b:

x + y = -4

y = -x - 4 [subtraction property of quality]

The slope is therefore -1. Therefore, the slope of the line that is parallel to the line whose equation is x + y = -4 is: -1.

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6) According to the time and work concept, 18 hours would be taken for James to complete the work.

Knowing the formulas can immediately lead you to a solution upon reading the question. Therefore, knowing the formula for any topic in numerical ability simplifies the solution and associated calculations.

Here are a few of these essential time and work formulas for your reference.

Work Performed = Time Required Rate of Work

Work Rate = 1 / Time Taken

Duration = 1 / Rate of Work

If a piece of work is completed in x number of days, then the amount of work completed in one day is equal to 1/x. Total Work Completed = Number of Days Efficiency.

Time and Productivity are inversely proportional to one another X:

if y is the ratio of the number of men needed to complete a piece of work, then y:x is the ratio of the time required by those men to complete the work.

If x number of people can complete W1 work in D1 days while working T1 hours per day, and y number of people can complete W2 work in D2 days while working T2 hours per day, then the relationship between them is Time and Work Formula i..e;

[tex]\frac{M1.D1.T1}{W1} =\frac{M2.D2.T2}{W2}[/tex]

Monica can do the work in 9 hours so she does a work of 1/9 in an hour.

The same work done by Monica and James takes 6 hours so they both can do a 1/6 th of work in an hour.

Developing the relation:

[tex]\frac{1}{9}+\frac{1}{x}=\frac{1}{6}[/tex]

here, the speed of Monica is 1/9 and the speed of James in completing the work is 1/x and the speed of them both is 1/6

So solving this equation we get ,

[tex]6x+54 = 9x[/tex]

[tex]3x = 54\\x=18\\[/tex]

So the speed of James in completing the work is 1/18th in an hour So he takes 18 hours to complete the whole work by himself alone.

According to the time and work concept, 18 hours would be taken for James to complete the work.

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The mileage for which company A charge less than company B , m < 65 ( an Inequality using the number of miles driven).

The subtraction property of inequality is applied when an inequality holds the addition operator previously, i.e

x + a < b => x + a - a < b - a

=> x< b - a.

The division property of inequality is mainly applied to the shift coefficient of the variable to another side of the inequality, i.e

2x< b => 2x/2<b/2

⇒ x< b/2.

We have, ryan is going to rent a truck for one day. There are two companies say company A and company B, in which ryan have to choose one for rent a truck for one day.

Let , Total cost charged by company A = $a

Total cost charged by company B = b

The number of miles driven = m miles

For Company A, initail fee = $40 and

Additional charge = .80 cents/mile driven

so, a = 40 + 0.8m --(1)

For Company B, initail fee = $53 and

Additional charge = .60 cents/mile driven

so, b = 53 + 0.6m --(2)

We want to know the mileage at which company A charges less than B i.e a < b

Now, using equation (1) and (2) ,

40 + 0.8m < 53 + 0.6m

Simplify the above Inequality,

=> 40 + 0.8 m - 40 < 53 - 40 + 0.6 m

=> 0.8 m < 13 + 0.6 m

=> 0.8 m - 0.6 m < 13 + 0.6 m - 0.6 m

=> 0.2 m < 13

=> m < 13/0.2

=> m < 130/2 = 65

Hence, required Inequality is m< 65.

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Complete question :

ryan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.

Company A charges an initial fee of $40 and an additional .80 cents for every mile driven.

Company B charges an initial fee of $53 and an additional .60 cents for every mile driven.

For what mileages will Company A charge less than Company B? Write your answer as an inequality, using m for the number of miles driven

The equation 3x2 + Kx - 30 has equal roots when the discriminant (D) of the equation is equal to zero.

The discriminant of a quadratic equation is given by the formula D = b2 - 4ac, where a = 3, b = K, and c = -30.

Substituting these values into the formula, we get:

D = K2 - 4(3)(-30)

D = K2 + 360

Therefore, K2 = -360, and K = √(-360) = 6√(-5)

Therefore, the value of k for which the roots of the equation 3x2 + Kx - 30 are equal is 6√(-5).

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Answer:

[tex] \sf \: 375g \: is \: 2.5\% \: of \: 15kg[/tex]

Step-by-step explanation:

Conversion of 15 kg into grams,

→ 1 kg = 1000 g

→ 15 kg = 15000 g

Let's find the percentage,

→ (375g ÷ 15kg) × 100

→ (375/15000) × 100

→ 0.025 × 100

→ 2.5%

Hence, the answer is 2.5%.

The number of tickets sold will be equal to 29.

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.

Let x represent the number of child tickets that were sold

Let y represent the number of adult tickets that were sold

5.30x +9.40y= 1206

The number of adult tickets sold was three times greater than the number of child tickets,

y= 3x

Substitute 3x for y in the equation,

5.40x + 9.40y= 974.40

5.40x + 9.40(3x)= 974.40

5.40x + 28.2x= 974.40

33.6x= 974.40

Divide both sides by the coefficient of x which is 33.5,

x= 974.40/33.6

x = 29

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The transitive property of congruence is used to justify the statement.

According to the transitive property, if A and B are congruent and if B is congruent with C, then A must also be congruent with C. In other words, two things are congruent to each other if a third object is congruent to them.

Since AB and EF are both congruent to DE in the sentence "If AB DE, EF DE therefore AB EF," AB must likewise be congruent to EF in accordance with the transitive property.

The additional attributes you mentioned don't apply in this situation. According to the symmetric property, if A and B are congruent, then so is B. According to the reflexive quality, each item corresponds to itself. And congruence does not have the property of multiplication.

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Complete question:

if AB ≅ DE, EF ≅ DE then show that AB ≅ EF ?

So the value of the line integral given point scale is [tex]\frac{15}{16}[/tex] -4cos6-6 .

To evaluate the line integral X signed by ideas oversee. Where C is the line segment from 2 to 36

First we find the vector determined by the two points

So ,

36 -2 = 34

Starting point is 2.

The segment can be para militarized as vitally equal to 2+3T+40 =3T 2+40 .

They belonging to close interval 0- one. Next we find the derivative of the Para militarism action y¹T= 34.

This implies the strength of y¹T = [tex]\sqrt{3^{2}+4^{2} }[/tex]

= 5

Finally we calculate the integral X signed by ideas oversee which is equal to treaty sign 2+ 40×DT Over 0- one.

Now report 2+ 40 equal to you. So implies 4DT is equal to DU and when T is equal to zero.

20=U

So next this integral becomes 15×2 to 6 Juju -2 x 4.

Comes out to be 15 x 16. 0-2. Sign your deal. Now applying integration by parts.

We have 15 x 16. 0-2 cause you plus integration of causal deal Limit 2- 6.

Now we have 15/16. On applying the limits -4 cos six plus sign 6- sign too.

So therefore final answer becomes [tex]\frac{15}{16}[/tex] -4cos6-6 .

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The easiest way to quantify data variability is to look at the range, or the difference between the greatest and smallest value.

The difference between the highest and lowest values for a given data set is the statistics' range. The difference between the highest and lowest observation could likewise be used to describe the range.The sample interval is defined as the highest value less the smallest value. A crucial indicator of variability for continuous variables is the sample range.

here ,

Use an en dash (not an em dash or a hyphen) with no spaces between them.

If at least one number in the range is between 1 and 100, such as 3-11, 68-70, or 83-343, use all the digits (i.e., no elision).

Use all the numbers to represent multiples of 100, such as 100-127, 310-329, or 2,220-2,254.

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Answer: 8x + 2xy

Step-by-step explanation:

9x - x + 4xy - 2xy

8x + 2xy

We can only compare the 9x with -x and the 4xy with the -2xy

The value of the function (f - g)(x) would be [tex](f-g)(x)=x^2-11x+4[/tex].

Option (A) is correct.

What are composite functions?

A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.'

Given:

                [tex]f(x)=4x^2-5x\\\\g(x)=3x^2+6x-4[/tex]

Now by using the definition of composite functions we can write,

      [tex](f-g)(x)=f(x)-g(x)\\\\(f-g)(x)=4x^2-5x-(3x^2+6x-4)\\\\(f-g)(x)=4x^2-5x-3x^2-6x+4\\\\(f-g)(x)=x^2-11x+4[/tex]

Hence, the value of the function (f - g)(x) would be [tex](f-g)(x)=x^2-11x+4[/tex].

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Answer: I think it's 13

Step-by-step explanation: So we need to fill in the distance formula. It's d=√((x_2-x_1)²+(y_2-y_1)²).

-6=x_1

-3=y_1

6=x_2

2=y_2

Now you plug in your coordinates to the formula, so you get d=√((6--6)²+(2--3²)

(6-(-6)²=144

(2-(-3²)=-7

So now 144+25=169

The square root of 169 is 13, so d=13. That should be your answer! Let me know if it's right

Answer:

To determine Beau's front-end ratio, you need to calculate the percentage of his monthly income that will be taken up by his mortgage, homeowner's insurance, property taxes, credit card payment, and car payment.

First, add up all of Beau's monthly expenses: $1,025 (mortgage) + $635 (homeowner's insurance) / 6 (months in a half year) + $4,785 (property taxes) / 12 (months in a year) + $2,000 (credit card payment) + $250 (car payment) = $3,715.83.

Next, divide this total by Beau's monthly income: $3,715.83 / ($89,750 / 12) = $3,715.83 / $7,479.17 = 0.49, or approximately 49%.

Since this ratio is expressed as a percentage, the final answer is 49%. Therefore, the correct answer is (d) 24%.

Answer: they would cost  £5.25

Step-by-step explanation:  £2.25 divided by 3 = 0.75 0.75x7=  £5.25

Option A, C, and E are the correct option.

What is midpoint?

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

Given, the coordinate of the vertices of AB line segment are A(9, 5) and B(15, 2).

The formula midpoint of the points (x₁, y₁) and (x₂, y₂) is ((x₁ +x₂)/2 , (y₁ + y₂)/2) .

The midpoint of the line segment AB is ((9 + 15)/2, (5+2)/2)

= (24/2 , 7/2)

= (12, 3.5)

The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₁ - y₂)/(x₁ + x₂).

The slope of the line AB is (5 - 2)/(9 - 15) = 3/(-6) = -1/2.

The slope of perpendicular line of a line with slope m is = -1/m.

The slope of perpendicular bisector is - 1/( -1/2) = 2

The distance of midpoint from the endpoints is equal. The perpendicular bisector of the line passes through the midpoint.

The distance of midpoint from the endpoints of the segment to any point on the perpendiculars bisector are equal.

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The range of possibilities for variation or the boundaries between them: the price spectrum for steel; many different styles. the size or scope of a process, action, or operation .

The range of values between the highest and lowest values for a certain data collection is known as the statistical range. It is also possible to show the range by comparing the highest and lowest observational values. The sample interval is found by subtracting the highest value from the lowest. For continuously varying variables, the sample range is a key measure of variability.

here ,

Between the lowest and greatest numbers, there is a range. In the example, the lowest value is 2, and the highest is 9.

The range therefore equals 9 x 2 = 8.

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The recursive rule can be used to find the nth term of the sequence aₙ = aₙ₋₁ + 2 which is an arithmetic progression.

What is arithmetic progression ?

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence

From the given sequence we see that:

Common difference is 2

Find the first term:

a₁ + (n-1)d  = aₙ

a₁ + 3*2 = a₄

a₁ + 6 = 2

a₁ = -4

The recursive formula for this sequence is:

a₁ = -4

aₙ = aₙ₋₁ + 2

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There were total 600 songs downloaded of standard quality

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, number of songs of Standard Quality Downloaded be x

number of songs of High Quality Downloaded be y

According to the Question:

x + y = 960 ----------(i)

2.5x + 4.7y = 3192 ----------(ii)

Multiplying the equation 1 by 2.5

2.5x + 2.5y = 2400 ----------(iii)

Substracting Equation 3 from equation 2

2.2y = 792

y = 360

So, x = 600

There were total 600 songs downloaded of standard quality

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