A rectangle has side lengths, in centimetres, of r and r-3
a)Write a sentence to explain why r>3.
b)The perimeter of the rectangle is smaller than 26 cm. Use this information and your answer to part a) to write a double inequality for r.

Considering that the larger triangle is the image of the smaller triangle after a dilation whose center is at (-2,1), the scale factor that was used in the dilation is 2.

Dilation is a technique for creating comparable figures that have their size reduced or increased by certain scaling factors.

Hence, the dilation of a triangle involves decreasing or increasing their sizes by a scale factor.

Considering the larger triangle which is the image of the smaller triangle after a dilation with center at (-2,1);

Scale factor = 5 - 1 / 1 - (-1)

Scale factor = 4 / 2

Scale factor = 2

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When you try to solve an equation and receive a variable or a number equal to itself, you know it has an endless number of solutions.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

If you try to solve an equation and receive a variable or a number equal to itself, you know it has an endless number of solutions.

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You buy 3 tickets. You spent $225 to buy the tickets.

What is an equation?

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Given that there are two planes to buy tickets.

First plane offers $75 per ticket.

The other plan offers $180 plus $15 per ticket.

Assume that you buy x number of tickets.

According to the first plane, the total cost of x number of tickets is y = $75x.

According to the second plane, the total cost of x number of tickets is y = $180 + 15x

The system of equations is

y = $75x .....(i)

y = $180 + 15x  ....(ii)

Using the substitution method solve the equations.

The solution of the equations represents the total cost for the two options is the same.

Putting y = 75x in equation (ii)

75x = 180 + 15x

Subtract 15x from both sides:

75x - 15x = 180

60x = 180

Divide both sides by 60:

x = 3

Putting x = 3 in equation (i)

y = 75 × 3

y = 225

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The expression for pressure is P = k/V and pressure is 50 pounds per square inch.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

Given pressure and volume are inversely proportional to each other

P ∝ 1/V

P = k/V

given when pressure p = 25 pounds per square inch

then volume V = 400 cubic inches

25 = k/400

k = 10,000

and when  V = 200 cubic inches

then P = k/V

P = 10000/200

P = 50 pounds per square inch

Hence pressure is 50 pounds per square inch.

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If the two rates​ continue, the number of hours when the prices of the two stocks would be the​ same is equal to 1.85 hours.

In order to write a system of algebraic equation to describe this situation, we would assign variables to the price of Stock A and the price of Stock B after a certain number of hours respectively, and then translate the word problem into algebraic equation as follows:

For the price of Stock A increasing at the rate of ​$0.11 each hour, an algebraic equation which models it is given by:

T = 12.81 + 0.11x

For the price of Stock A decreasing at the rate of ​$0.16 each hour, an algebraic equation which models it is given by:

T = 13.31 - 0.16x

Equating the two algebraic equations, we have:

12.81 + 0.11x = 13.31 - 0.16x

0.11x + 0.16x = 13.31 - 12.81

0.27x = 0.5

x = 0.5/0.27

x = 1.85 hours.

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Answer:

China = 6018 / 1339 = 4.49

US = 5093 / 307 = 16.59

Russia = 1704 / 140 = 12.17

India = 1293 / 1157 = 1.12

Japan = 1246 / 127 = 9.81

Germany = 858 / 82 = 10.46

Canada = 614 / 33 = 18.60

The common factors for 48,36,−12 48 , 36 , - 12 are 1,2,3,4,6,12 1 , 2 , 3 , 4 , 6 , 12 . The GCF for the numerical part is 12.

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The quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions.

That means if we are given a function of the form: f(x) = u(x)/v(x),

we can find the derivative of this function using the quotient rule derivative:

f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]2

Where:

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Answer:

6x + 8y = 13. 8y = 13 - 6x.

y = (13 - 6x) / 8.

f(x) = (13 - 6x) / 8.

x = (13 - 6f-1(x)) / 8.

8x = 13 - 6f-1(x).

6f-1(x) + 8x = 13 S

Since 1214 is a four digit number and you have fewer than 10 blocks it is not possible to represent 1214 in any other way.

With fewer than 10 place value blocks, it would not be possible to show the number 1214 using standard place value notation, as you would need at least 4 blocks to represent the ones, tens, hundreds, and thousands place. Each block would represent a different place value, such as ones, tens, hundreds, and thousands. Each block would have a different numerical value, such as 1, 2, 1, and 4, respectively. Since 1214 is a four digit number and you have fewer than 10 blocks it is not possible to represent 1214 in any other way.

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Answer:  liquidity reasons

Step-by-step explanation:

Banks sell credit cards and personal loans to customers to increase their profits, deepen customer relationships, generate more revenue, and compete in the market.

A loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations, etc.

Banks will try to sell credit cards and personal loans to customers for a few reasons:

Profit: Banks earn money by charging interest on loans and credit cards. By selling these products to customers, banks can earn significant profits.

Customer retention: By offering loans and credit cards to customers, banks can deepen their relationships with them and increase customer loyalty.

Increased revenue: Offering loans and credit cards can help banks generate more revenue from customers.

Market competition: Banks face intense competition from other financial institutions, including credit unions and online lenders.

Hence, banks sell credit cards and personal loans to customers to increase their profits, deepen customer relationships, generate more revenue, and compete in the market.

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The area of a triangle with the base 4.8 cm and height 3.6 cm is 8.64 cm².

Therefore the answer is 8.64 cm².

The area of a triangle can be calculated using the formula:

Area = (1/2) x base x height

In this case, the base of the triangle is 4.8 cm and the height is 3.6 cm. Plugging these values into the formula, we get:

Area = (1/2) x 4.8 x 3.6

Area = (1/2) x 17.28

Area = 8.64 cm²

So the area of the triangle is 8.64 square centimeterS.

It's important to note that the formula for area of triangle uses the concept of base and height. A base is a side of the triangle and height is the perpendicular distance from the base to the opposite vertex.

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On solving the provided question, we can say that from the provided graphs, we have Domain = [(-4, 0) to  (-3, 1)]

Mathematicians  use the graphs to logically convey facts or values using the visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

from the provided graphs, we have  

domain of the function

Domain = [(-4, 0) to  (-3, 1)]

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The gradient or slope of the line is given by the equation m = -3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P = P ( -1 , 0 )

Let the second point be represented as Q = Q ( 0 , -3 )

Now , the slope of the line passing through the points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -3 - 0 ) / ( 0 - ( -1 ) )

On simplifying the equation , we get

Slope m = -3/1

Slope m = -3

Hence , the slope of the line is m = -3

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Answer:

y=7

Step-by-step explanation:

Answer: y=7

Step-by-step explanation:

15-8=7

y=7

On solving the provided question, we can say that The perimeter of the Isosceles  triangle is 8 + 4v'5+ 4[tex]\sqrt{2}[/tex]= 8 + 8[tex]\sqrt{2}[/tex] = +[tex]\sqrt{2}[/tex])

A triangle with two sides that have the same length is said to be isosceles. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The hypotenuse is 8 so the equal sides are x lets say.

Now, by Pythagoras Theorem

x^2 + x^2 + = 8^2

x^2 = 64/2

x = [tex]4\sqrt{2}[/tex]

The perimeter of the triangle is 8 + 4v'5+ 4[tex]\sqrt{2}[/tex]= 8 + 8[tex]\sqrt{2}[/tex] = +[tex]\sqrt{2}[/tex])

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The ratio A:D = 1:64

A ratio is the comparison of two amounts of the same unit which shows the amount of one present in the other.

Given that A:B = B:C = C:D if C:D is 1:4, we need to find A:D.

So, we proceed as follws

A:B = B:C = C:D

⇒ A/B = B/C = C/D = 1/4

So, we have that the equation

A/B = 1/4

This implies that

A = B/4

Also, we have that the equation
B/C = 1/4

This implies that

B = C/4

Finally, we have that

C/D = 1/4

This implies that

C = D/4

Since A = B/4, B = C/4 and C = D/4,

Substituting C into B, we have that

B = C/4

= (D/4)/4

B = D/16

Since A = B/4, substituting this B into A, we have that

A = B/4

= (D/16)/4

A = D/64

So, A/D = 1/64

⇒ A:D = 1:64

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The number of hours until the city is locked down is given as follows:

229 hours.

The function for this problem is defined as follows:

p(t) = 0.004t³ + 0.001t + 1.

For which the variables are given as follows:

The rate of change of the infection in 72 hours = 3 days is given by:

p'(3).

The derivative of the function is given as follows:

p'(t) = 0.012t² + 0.001.

After the instantaneous rate after 3 days is given as follows:

p'(3) = 0.012(3)² + 0.001

p'(3) = 0.109.

The city will lock down when p'(t) = 10 x p'(3) = 1.09 that is:

0.012t² + 0.001 = 1.09.

0.012t² + 0.001 - 1.09 = 0.

Hence the time in days is obtained as follows:

0.012t² = 1.089

t² = 1.089/0.012

t² = 90.75

[tex]t = \sqrt{90.75}[/tex]

t = 9.53 days.

Each day is composed by 24 hours, hence the time in hours is obtained as follows:

9.53 x 24 = 229 hours. (rounding to the nearest whole integer).

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Based on the information in the bar graph, the number of students of the next 140 asked will select football rather than track and field as their favorite sport is, 35

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

Mike asked 200 students to select their favorite sport and then recorded the results in the bar graph

the percentage of students who selects football is,

Percentage = (50/200)×100

Percentage =  25%

If we consider in same percentage students will select football in next 140 students,

then,   number of those students will be,

25 = (a/140)×100

a = 35

Therefore, the number of students is, 35

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By applying the formula x=-b/2a to find the quadratic's vertex, the result can then be used to replace y in the original equation.

To convert standard form to vertex form,

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Answer: "C. 0.9604.

Step-by-step explanation: The correct answer is The probability that at least one of the alarm clocks will wake her up is 0.9604. Heather has a very important test to take in the morning. So she wants to be sure that she will wake up in time, so she sets two alarm clocks.

The function whose vertex is on the y-axis is f(x) = (x – 2)(x + 2).

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Write each of the functions in the form of ax² + bx + c

Vertex of the function.

= ( -b/2a, f(-b/2a) )

Now,

f(x) = (x – 2)²

x² - 2x + 4

a = 1, b = -2, c = 4

-b/2a = 2/2 = 1

f(1) = -2

Vertex = (1, -2)

f(x) = x(x + 2)

x² + 2x

a = 1, b = 2, c = 0

-b/2a = -2/2 = -1

f(-1) = -1(-1 + 2) = -1

Vertext = (-1, -1)

f(x) = (x – 2)(x + 2)

x² + 2x - 2x + 4

x² + 4

a = 1, b = 0, c = 4

-b/2a = 0

f(0) = (0 -2)(0 + 2) = -4

Vertex = (0, -4)

f(x) = (x + 1)(x – 2)

x² - 2x + x - 2

x² -  x + 2

a = 1, b = -1, c = 2

-b/2a = 1/2

f(1/2) = (1/2 + 1)(1/2 - 2) = 3/2 x -3/2 = -9/4

Vertex = (1/2, -9/4)

Thus,

The vertex (0, -4) is on the y-axis.

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Answer: In order to solve this problem, you should use the Pythagorean theorem. Since FG is perpendicular to OP, and OP and OQ are radii of the same circle, then triangle OFG is a right triangle. Similarly, triangle ORS is also a right triangle. By using the Pythagorean theorem, you can find that:

OF = sqrt(OP^2 + FG^2) = sqrt(19^2 + 40^2) = sqrt(361 + 1600) = sqrt(1961)

and

OS = sqrt(OQ^2 + RS^2) = sqrt(19^2 + 37^2) = sqrt(361 + 1369) = sqrt(1740)

Therefore, the length of the segment connecting the feet of the altitudes is:

OF + OS = sqrt(1961) + sqrt(1740) = 27.2

So the answer is A. 27.2

Step-by-step explanation:

The probability the spinner landing on 5 is 0.125. The result is obtained by dividing the number of favorable outcomes by the number of events.

Probability is a numerical description of how possible an event to happen. Tha value of probability is between 0 to 1. Zero probability means something is impossible to happen. Probability 1 shows certainty.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

A spinner is divided into 8 equal sections numbered 1 to 8. Find the probability that the spinner lands on number 5!

From the information, we have:

P(A) = n(A) / n(S)

P(A) = 1/8

P(A) = 0.125

Hence, the probability that the spinner lands on number 5 is 0.125.

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If the elements in the pairs are related to each other then the pair is called as Ordered Pair an if the elements in the pair are not related then the pair is called as Unordered Pair .

The Ordered Pair is defined as a pair of elements having specific importance for order of their placements.  

Also, the ordered pairs are used to represent elements that have a relation between them .

The Ordered pairs are usually used  to represent a point on a coordinate plane.

The Unordered Pair is a set of the form (a,b) that have two elements "a and b" that have no particular relation between them,

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Answer:

Yes, the sides 7cm, 24cm and 25cm form a right angle triangle.

This is because the sides of a right angle triangle must follow the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 7cm and 24cm are the two legs and 25cm is the hypotenuse.

Step-by-step explanation:

Residual Value should not be more than 5% of Cost of Asset i.e Rs. 5000 and accordingly the amount to be adjusted shall be Rs.

What Exactly Is Residual Value?

The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.

A good residual value is what?

Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.

                 A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.

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Answer:

median = 4.5

Step-by-step explanation:

the median is the middle value of the data set arranged in ascending order. If there is no exact middle value then it is the average of the values either side of the middle

express the values in ascending order ( smallest to largest )

2 , 3 , 4 , 5 , 6 , 8

           ↑

the middle is between 4 and 5 , then

median = [tex]\frac{4+5}{2}[/tex] = [tex]\frac{9}{2}[/tex] = 4.5

Answer:-2

Step-by-step explanation:

2(x-4) + 3x -x^2

2(2-4)+ 3(2) - 2^2

2(-2)+ 3(2)-2^2

-4+6-4=

-2