The image of (3, -5) after a dilation with respect to the origin is (15, -25). What is the scale
factor of the dilation?
04
05
06
O 12

The coordinates of the midpoint M of the segment FG is (-2,2).

This question is incomplete, the complete question is;

What is the midpoint M of a line having two endpoints F(-7, 12) and G(3, -8),

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point F (-7, 12)

Point G (3,-8)

To determine the midpoint, plug the given points into the formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( (-7 + 3 )/2, ( 12 + (-8) )/2 )

M = ( ( -4 )/2, ( 12 - 8 )/2 )

M = ( ( -4 )/2, ( 4 )/2 )

M = ( -2, 2 )

Therefore, the  midpoint M of the segment is (-2,2)

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The slope of the line segment that represents the period of time during which the speed decreases is: C: The slope is -10.

The parameters given are:

Starting speed of the car = 55 km/hr

Let us suppose when t=0 , the speed of car was 55 km/hr.

Then car broke down.

The following Data are given regarding car's speed versus the amount of time elapsed from the moment that it began to brake.

Elapsed Time (sec) Speed (mph) → 1 :45 ,2 :35, 3 :25, 4 :15, 5 :15 ,6 :15

Slope of line passing through two points (a, b) and (p, q) is given by the formula:

Slope = (q - b)/(p - a)

Thus, Slope of line passing through two points (1,45) and (2,35) is:

Slope = (35 - 45)/(2 - 1)

Slope = -10

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The inequality expression that can represent the above scenario is
80x + 13600 ≤ 27000.

In mathematics, Inequality is an expression that is used for unequal comparison of two numerical expressions or algebraic expressions.

Instead of an equal sign here, we use signs like Less than (<), Greater than (>), Less than or equal (≤), Greater than or equal (≥), and Not equal (≠), etc.  

Like Linear equations here we use variables like x, y, z .. etc. to represent the unknown quantities or numbers

Here we have

A shipping container will be used to transport several 80-kilogram crates across the country by rail.  

The greatest weight that can be loaded in container is 27000 kilograms.

Other shipments weight = 13600 kilograms  

Let 'x' be the number of crates that can be transported

Weight of 'x' number of crates = 80kg × (x) = 80x  kg

As we know the greatest weight that can be loaded is 27000 kilograms. So here is the total weight of 'x' crates and the other shipment's weight must be less than 27000 kilograms but not more.  

=> 80x + 13600 ≤ 27000

Therefore,

The inequality expression that can represent the above scenario is
80x + 13600 ≤ 27000.

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The first statement is given, the second statement is true because they are vertically opposite angles and the third statement is true by SAS congruency of triangles.

What is congruence of triangles?

Two triangles that are congruent will have precisely the same three sides and three angles.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.

The first statement is true because this is already given in the question.

The second statement is true because ∠KLJ and ∠MLN are vertically opposite angles and we know that vertically opposite angles are always equal. Therefore, the second statement is true.

The third statement is true because of the SAS congruency of triangles.

As we are given ratio of two sides equal to ratio of corresponding sides and the angle between the sides to be equal.

Hence, the two triangles are congruent.

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The likelihood of 8 occurrences in a period of 10 minutes is around 0.091 or 9.1%.

According to the Question

A Poisson distribution issue exists here. The Poisson distribution is a discrete probability distribution that quantifies the likelihood of a certain number of events occurring at a certain average rate, regardless of the interval between occurrences, in a given amount of time or space.

The following formula determines the likelihood that x will occur in a Poisson distribution with parameter λ :

P(x; λ) is equal to x / (λx * e(-λ))!

where

λ = the average number of occurrences within the specified time period.

λ in this situation is 4.2. (the mean number of occurrences in 10 minutes).

In order to determine the likelihood of 8 occurring in 10 minutes:

P(8; 4.2) = (4.2^8 * e^(-4.2)) / 8!

⇒ P(8; 4.2) = 0.091 or 9.1%.

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Answer: A confidence interval is a range of values that is likely to contain the true population value with a certain level of confidence. To determine a 95% confidence interval for the percentage of people who prefer Candidate A, we can use the following formula:

(Sample proportion) +/- (Margin of error)

The margin of error can be calculated using the formula:

Margin of error = (Critical value) * (Standard deviation)

The critical value is a factor used to compute the margin of error. The critical value for a 95% confidence interval is approximately 1.96. The standard deviation is calculated as:

Standard deviation = √((Sample proportion) * (1 - Sample proportion) / (Sample size))

Plugging in the given values:

Sample proportion = 80% = 0.8

Sample size = 45

Margin of error = (1.96) * √((0.8) * (1 - 0.8) / (45))

Step-by-step explanation:

As per the angle sum property, the value of x is 14°

In math the term called angle sum property states that the sum of interior angles of a triangle is 180°.

Here we have the following diagram and we need to find the value of x.

While we looking into the diagram, we have identified the value of the angles are listed as follows:

=> (10x - 11)°

=> (3x - 2)°

=> (3x + 1)°

Now we have to solve this by using the angle sum property then we get,

=> (10x - 11)° + (3x - 2)° + (3x + 1)° = 180°

When we simplify this one then we get,

=> 16x - 12 = 180°

=> 16x = 168°

=> x = 14°

Complete Question

Find the value of x one the following diagram.

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When a number is randomly selected from the set of consecutive integers, it has a 3/4 chance of being divisible by 1995.

A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A chance is a number between zero and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or chance that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed in percentages ranging from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain occurrence relative to all possible outcomes.

given

99-20+1 = 80 potential outcomes.

Now, a number that may be divided by 12 must include the digits 2*2*3.

The realisation that c(c21)(21) = c(c1)c(c+1) is the same as c3c3 is perhaps the trickiest.

The latter statement indicates that you indeed have a group of three consecutive integers that are divisible by 12. Every three consecutive integers must be divisible by three, according to a rule.

The main question is how many of the numbers you choose are divisible by 22=4 22=4.

In this scenario, c can either be 21, 23, 25, 95, 97, 99, so 99212 9921/2 + 1 = 40 OR 20, 24, 26, 92, 96, so 96204 9620/4 + 1 = 20.

Thus, 40+2080 = 60/80 and 40+20/80 = 40/80

60/80 = 3/4

When a number is randomly selected from the set of consecutive integers, it has a 3/4 chance of being divisible by 1995.

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Using the property of median, the values of DC = 16, CQ = 8, FP = 15, and CE = 14.

As DQ = 24, FC = 10, RC = 7.

As we know that the centroid divide each median in the ratio of 2:1.

The diagram of the question is given below:

So, we divide the median DQ in the ratio 2:1

2x + x = 24

3x = 24

Divide by 3 on both side, we get

x = 8

So the length of DC = 16 and CQ = 8

Ac FC = 10 which is 2 part of the ratio 2:1.

So the value of 2x = 10

So x = 5. Now the value of CP = 5

Now the value of FP = FC + CP

FP = 10 + 5

FP = 15

As RC = 7 which is 1 part of the ratio 2:1.

So the value of CE = 2x = 2×7 = 14

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Answer: Let x be the fare of the train, and y be the fare of the bus.

We know that:

x + y = 400 (the total fare of the journey)

And, on the return journey the fare of the bus is hiked by a half of what Talia paid initially, so the fare of the bus on the return journey is:

y * 1.5 = y + (y/2)

And the total fare of the return journey is hiked to 4800, so:

x + y + (y/2) = 4800

We can substitute the first equation into the second equation:

x + (y + (y/2)) = 4800

x + y + (y/2) = 4800

x + (y + (y/2)) = 4800

So, we can solve the system of equations by substituting the first equation into the second equation and solving for x.

x + y = 400

x = 4800 - (y + (y/2))

x = 4800 - y - (y/2)

x = 4800 - y - (1/2)y

x = (4800 - y) - (1/2)y

x = 4800 - (3/2)y

Now we have an equation for x in terms of y. To solve for x, we can use the value of y from the first equation

x = 4800 - (3/2)(400)

x = 4800 - 600

x = 4200

So the train fare is 4200 sh

Step-by-step explanation:

The solution of the absolute value equation:

|x-2|=|4+x|

is  x = -1

Here we want to solve the following equation:

|x - 2| = |4 + x|

A general absolute value function can be rewritten into two equations, in this case these are:

x - 2 = 4 + x

x - 2 = -(4 + x)

The first one has no solution, but the second one does.

x - 2 = -(4 + x)

x - 2 = -4 -x

2x = -4 + 2

2x = -2

x = -2/2 = -1

That is the solution.

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Answer: For your answer you would add like terms so for -5x+x you would get -4x, and for your other you would get 7p.

What it means when you substitute a value into an equation and the result is a true statement is; The solution of the equation

Solving an equation is very synonymous to trying to find the answer to a puzzle. Now, an algebraic equation states that two algebraic expressions are equal.

In order for us to solve an equation, we will have to determine the values of the variable that makes the equation a true statement. Thus, any number that makes the specific equation to be true will be referred to as a solution of the equation.

A solution to an equation is defined as a value of a specific variable that makes a statement to be true when substituted into the equation. Thus, the process of finding the solution to an equation is simply called solving the equation.

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To maximise the area it should be build as a square having side=250 feet each and having area=62500 feet.

what are squares?

A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.

The most important properties of a square are listed below:

Area of square=(side)²

Perimeter of square=4*side

Now,

Given

total fencing available=1000feet

perimeter=1000

4*s=1000

s=250 feet

Therefore,

Area=250^2

=62500 feet^2

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The value of cos v in simplest terms in fraction form is 17/18

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: The triangle ΔXWV with WV=17 , XV=18,

We know cos ∅= base/hypotenuse

here hypotenuse is XV as it is opposite to the right angle. and the base of the triangle is 17

∴ Cos v=17/18

We can also find the measure of the third angle by using the pythogarean theorm as

WX=√18²-17²

   =√35

Hence, The value of cos v in simplest terms in fraction form is 17/18

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Answer:

6

Step-by-step explanation:

4 1/2= 4.5

3/4=0.75

4.5/0.75= 6

just to check, 3/4 x 6 =4.5

The ratio of girls to boys in the 6th grade class of 40 pupils is 18:22.

This can be calculated by first finding the total number of boys in the class. 40-18=22. We then use the formula for ratio, which is the ratio of two or more numbers. In this case, it is the ratio of girls to boys. 18:22. This ratio can also be expressed as 18/22 or 0.818181818181818181818181818181818181818181818182 (to three decimal places). A ratio is a comparison of two numbers and can be used to compare different parts of a whole. It can also be used to compare different groups or classes of people. In this case, it is used to compare the number of girls to boys in a 6th grade class.

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Answer:

The factored form of 4x+16 is (4x + 8)(2). This can be found by using the distributive property, or by using the prime factorization method.

Answer:

P =4.71x-10.6

Step-by-step explanation:

R = 6.91x

C=2.2x+10.6.

P = R - C = 6.91x-2.2x -10.6 =4.71x-10.6

From the figure we see that by the conditions , the figure does not form any Triangle .

A Triangle is defined as the three sided closed figure made up of line segments .

In the figure , the two lines forms a right angle at the base , that means both the line segments are perpendicular ,

and if the two line are perpendicular to the same base then the two line will be called as parallel lines and we know that parallel lines do not intersect .

Therefore , The triangle will form No Triangle as the lines do not meet .

The given question is incomplete , the complete question is

Tell whether the figure given below creates the conditions to form a unique triangle, more than one triangle, or no triangle.

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Answer: To obtain a mixture that is 50% orange juice, you must find the amount of 60% orange juice needed to bring the overall concentration of orange juice to 50%.

We can start by using the formula:

(amount of 60% orange juice) / (amount of 60% orange juice + amount of 30% orange juice) = desired concentration

Let's call the amount of 60% orange juice that we need to add x.

So the equation will look like this:

(x) / (x + 5 gallons) = 0.5

We can then solve for x:

x = (0.5 * x + 0.5 * 5 gallons)

x = 2.5 gallons

So, 2.5 gallons of 60% orange juice must be mixed with 5 gallons of 30% orange juice to obtain a mixture that is 50% orange juice.

Step-by-step explanation:

Answer:

the equation could represent your paycheck at the end of a shift. y is equal to the total amount of money you made, 7 is equal to your hourly wage, and x is equal to the number of hours worked. For example if you worked two hours one day, the equation would be y=7(2), which could be simplified to y=14, so after a two hour shift you would make a total of $14

Step-by-step explanation:

Regarding the addition property of equality, the number would add to both sides of the equal sign to isolate the variable x = 26/7.

What amount would you add to both sides of the equal sign if you were to isolate the variable using the addition property of equality?

The official term for the equality-related characteristic that enables one to multiply both sides of an equation by the same amount. One of the most frequently applied properties for solving equations is this one.

To solve the problem, you would take away 5/7 from both sides.

What is the remedy?

x = 3 and 5/7 or 26/7.

x + 5/7 = 31/7

Subtract 5/7 from both sides of the equation:

x + 5/7 - 5/7 = 31/7 - 5/7

x = 26/7

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Answer:

1: -5/7

2: 26/7

Step-by-step explanation:

The system's total dependability is 0.8813.

The reliability of the individual components determines the overall reliability of multi-component systems.

R = (0.98) (0.96) (0.94)

= 0.8813

The likelihood that a system operates well for a given period of time is known as reliability. When performing this right action:

No maintenance or repairs are necessary. The system correctly complies with the established performance requirements.

The dependability decreases when more time is taken into account for reliability calculations since it obeys the exponential failure rule.

In other words, a system's reliability will initially be high and steadily decline to its lowest level over time.

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The value of the overall reliability of the system is 0.8813.

The possibility that a system will work successfully over a certain time period is referred to as reliability. No repair is necessary or done during this right procedure. The system adheres to the performance standards as specified.

The overall reliability of multi-component systems is determined by the reliability of the individual components.

R = (0.98) (0.96) (0.94)= 0.8813

The possibility that a system will perform well over a particular length of time is referred to as dependability. There is no need for maintenance or repairs while doing this appropriate step. The system satisfies the defined performance criteria.

Because it follows the exponential failure rule, dependability falls as more time is factored into reliability assessments.

In other words, the reliability of a system will begin high and gradually drop to its lowest level over time.

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The factor by which ths speed increases is 2, then the correct option is D.

Here we have the sequence of numbers:

4, 8, 16, 32, 64,  128

Where these have units of miles per hour, but can be ignored, as we only care for the numbers. To get the factor  by which the speed change for each consecutive speeds, we just need to take the pairs of consecutive numbers and take their quotients.

We will get:

8/4 = 2

16/8 = 2

32/16 = 2

etc.

Then the factor is 2, the correct option is D.

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Answer:y=25 x 2 -8

Step-by-step explanation:

25 x 2-8

The solution to the system of equations in this problem is given as follows:

(5,9).

The system of equations for this problem is defined as follows:

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

From the image given at the end of the answer, the solution to the system of equations is given as follows:

(5,9).

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Answer:8

Step-by-step explanation:

dd