The Pythagorean Theorem Part 2 Quiz

The area of the triangle PQR is 12 square units

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

J(–2, 2), K(–2, 6), and L(–8, 2),

Reflection and rotation are rigid transformation

This means that

Area of PQR = Area of JKL

So, we have

Area = 1/2 * |x1y2 - x2y1 + x2y3 - x3y2 + x3y1 - x1y3|

So, we have

Area = 1/2 * |-2 * 6 + 2 * 2 + -2 * 2 + 8 * 6 - 8 * 2 + 2 * 2|

Evaluate

Area = 1/2 * |24|

So, we have

Area = 12

Hence, the area is 12 square units

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Step-by-step explanation:

what is the difference between the x- values ?

and what is the difference between the y- values ?

a transformation means a simple shift. so, addition of subtraction. no multiplication or such.

1 to -1 ? -2

-1 to -3 ? -2

5 to 3 ? -2

6 to 6 ? 0

3 to 3 ? 0

-2 to -2 ? 0

so, the transformation is (-2, 0)

If the length of the rectangular plot  is 180m , then the width of the rectangular plot is 51.2 m .

The Area of square plot is ⇒ Area = (Side) × (Side),

In this case, Side is = 96m,

So , the area of the square plot is : A = 96m x 96m = 9216 m² .

The Area of  Rectangular Plot is ⇒ A = (Length) × (Width) ;

We know that the area of the rectangular plot is the same as that of the square plot,

that means ⇒ Length × Width = 9216 m² ;

We also know that Length = 180m, so we substitute this value in the equation above ;

⇒ 180m × Width = 9216 m² ;

Dividing  both sides by 180m ;

we get ;

⇒ Width = 9216/180 ;

⇒ Width = 51.2 m ;

Therefore, the width of the rectangular plot is 51.2 meters.

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The given question is incomplete , the complete question is

In exchange of a square plot of side 96 m, a man wants to acquire a rectangular plot of 180m long and of the same area of the square plot .

Find the width of the rectangular plot .

A) 145.86 + 79.6 = 225.46

Rounding off the first number to 100 places, 145.86 becomes 145.86000

Rounding off the second number to 10 places, 79.6 becomes 79.60000

So the rounded answer is 145.86000 + 79.60000 = 225.46000

Estimated answer: 225

The answer is reasonable.B) 2450.21 - 599.36 = 1851.05

Rounding off the first number to 100 places, 2450.21 becomes 2450.21000

Rounding off the second number to 10 places, 599.36 becomes 599.36000

So the rounded answer is 2450.21000 - 599.36000 = 1851.05000

Estimated answer: 1850

The answer is reasonable.C) 922.58 - 398.99 = 523.59

Rounding off the first number to 100 places, 922.58 becomes 922.58000

Rounding off the second number to 10 places, 398.99 becomes 398.99000

So the rounded answer is 922.58000 - 398.99000 = 523.59000

Estimated answer: 523

The answer is reasonable.D) 2351.85 + 89 = 2440.85

Rounding off the first number to 100 places, 2351.85 becomes 2351.85000

Rounding off the second number to 10 places, 89 becomes 89.00000

So the rounded answer is 2351.85000 + 89.00000 = 2440.85000

Estimated answer: 2440

The answer is reasonable.

2 , 3, 5 all are that prime of 30

5×6

Answer:

See proof below

Step-by-step explanation:

We will use the SAS condition for congruency of two triangles

SAS (Side-Angle-Side)

If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

In the two triangles ΔHIK and ΔJIK we have
m∠4 = m∠3  (given)

HK ≅ KJ

IK is the common side

So the two sides HK and IK are equal and the included angles ∠4 and ∠3 are also equal

So by SAS, the two triangles are equal

So m∠2 = m∠1

which means IK bisects ∠HIK

The area of a rectangle is 35x^2 + 12x  - 36

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

To determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given that the length of the rectangle is (7x − 6) and the width is (5x + 6).

Thus the width be (5x + 6).

So, the length = (7x − 6)

So,

Area of rectangle = (7x − 6) (5x + 6).

= 35x^2 + 42x -30x - 36

= 35x^2 + 12x  - 36

So, The area is 35x^2 + 12x  - 36

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Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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If the order of choices matter, then;

Number of ways = 20

Also, if order of choices does not matter, then;

Number of ways = 10

Total number of choices = 5

Object choices = 2

By method of permutation

Number of ways =  5! / (5-2)!

Number of ways = 5! / 3!

Number of ways = 5 x 4

Number of ways = 20

Total number of choices = 5

Object choices = 2

By method of combination

Number of ways =  5! / (5-2)! 2!

Number of ways = 5! / 3! 2!

Number of ways = 5 x 4 / 2

Number of ways = 20 / 2

Number of ways = 10

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At 9:00 a.m., the rate of people entering the amusement park is 533 people per hour, while the rate of people leaving the amusement park is 67 people per hour.

(1) At 9:00 a.m., the rate of people entering the amusement park is given by the derivative of the entering function, which is:

f'(t) = 400 + 200cos(πt/12).

At t = 9, this rate is 400 + 200cos(π*9/12) = 400 + 200cos(3π/4) ≈ 533 people per hour.

(2) At 9:00 a.m., the rate of people leaving the amusement park is given by the derivative of the leaving function, which is:

g'(t) = 200 - 200cos(πt/12).

At t = 9, this rate is 200 - 200cos(π*9/12) = 200 - 200cos(3π/4) ≈ 67 people per hour.

the complete question is :

both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.? (2) how fast are people leaving the amusement park at 9:00 a.m.?

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The IR spectrum described could be an alkyl chloride with a carbonyl group, such as chloroform ([tex]CHCl_{3}[/tex]).

The IR spectrum described suggests the presence of several functional groups in the compound.

The strong, broad band in the 3600 to 3100 inverse centimeter range corresponds to the stretching vibration of the O-H bond in alcohols, while the strong, spiked peak in the 3000 to 2800 inverse centimeter range corresponds to the stretching vibration of the C-H bond in alkanes. The weak peak near 1850 inverse centimeters corresponds to the stretching vibration of the C=O bond in ketones, while the sharp peak near 1640 inverse centimeters corresponds to the stretching vibration of the C=C bond in alkenes.

The series of spiked bands in the 1500 to 1200 inverse centimeter range corresponds to the bending vibrations of the C-H bond in alkanes, while the two strong bands at 990 and 910 inverse centimeters correspond to the stretching vibration of the C-Cl bond in alkyl chlorides.

Based on this information, the compound that matches the IR spectrum described could be an alkyl chloride with a carbonyl group, such as chloroform ([tex]CHCl_{3}[/tex]).

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Create a proportion using the given information to determine how long it will take for Cheryl's phone battery to totally drain. Total time divided by the remaining charge's percentage equals the remaining time (total charge)

Enter these values because Cheryl is aware that the battery will continue to operate for 1.5 hours at a 55% charge. 1.5 / 0.55 = (total time) / 1 = (total time) / (total charge) (amount of time left) / (remaining percentage of the charge)

When we calculate the total amount of time, we get:

Time: 2.727 hours (1.5 / 0.55 × 1) * 1

To determine how long the battery will survive after fully charged, we may simply reverse the rate of discharge:

Total time / Total charge / (time left) / 1 = Total time / 100 (time left) = Total time / 100 (time left) (percent charge remaining)

The battery's lifespan after being completely charged is as follows:

(Total time) / 100 divided by the remaining time gives us 2.727 / 100 or 0.02727 hours.

As a result, after 1.64 minutes, or 0.02727 hours, Cheryl's phone battery will be fully charged.

Therefore,  It takes 2.727 hours for Cheryl's phone battery to totally drain at a constant rate.

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Yes, it is possible for a system of linear equations with fewer equations than variables to have no solution. For example, consider the system of linear equations: x + y = 1, x + 2y = 3, x + 3y = 4.

The system of linear equations given is:

x + y = 1

x + 2y = 3

x + 3y = 4

This system has two variables (x and y) but only three equations. We can add and subtract the equations to see that the first two equations imply that y = 2, but the third equation implies that y = 1. This is a contradiction, so there is no solution to the system.

To solve this system, we can use techniques such as elimination or substitution. For example, we can subtract the first equation from the second equation to eliminate x, and get:

[tex]x + 2y - (x + y) = 3 - 1[/tex]

[tex]y = 2[/tex]

Similarly, we can subtract the first equation from the third equation to eliminate x, and get:

[tex]x + 3y - (x + y) = 4 - 1[/tex]

[tex]2y = 3[/tex]

[tex]y = 3/2[/tex]

However, we obtained two different values for y, which is a contradiction. As a result, the equation system cannot be solved. In other words, there is no pair of values of x and y that satisfy all three equations simultaneously.

Geometrically, this means that the system of equations represents three planes in three-dimensional space. However, these planes do not intersect at a common point, so there is no solution to the system.

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The linear function giving the amount remaining after buying x cups of coffee is given as follows:

A(x) = -3x + 15.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Each cup of coffee costs $3, hence the slope m is given as follows:

m = -3.

(for each cup purchased, the balance decays by $3).

Hence:

A(x) = -3x + b.

Buying 4 cups of coffee, the balance is of $3, hence the intercept b is obtained as follows:

3 = -3(4) + b

b = 15.

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The possible lengths for the third side could be: any length between 1 inch and 12 inches (but not equal to either 8 inches or 5 inches) any length greater than 12 inches

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

Given ,

Lance is drawing a triangle. He draws one side that is 8 inches long and another side Se that is 5 inches long.

The third side of the triangle can be any length that satisfies the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So, in Lance's triangle, if the first side is 8 inches long and the second side is 5 inches long, then the third side must be less than 8 + 5 = 13 inches.

So, the possible options for the third side are:

6 inches

7 inches

9 inches

10 inches

11 inches

12 inches

13 inches or longer.

Therefore, The possible lengths for the third side could be: any length between 1 inch and 12 inches (but not equal to either 8 inches or 5 inches) any length greater than 12 inches

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Answer:

Bank a/c Dr

To cash a/c

(Being deposited cash into bank)

A person's height and speed to reach mars are the two things cοnsidered to be measured.

Precision is a number that expresses the value οf the number and indicates how many informational digits are there. Fοr instance, 3.14 is an approximation οf pi that is reasonable and accurate. Hοwever, the precision digit, which is 3.199, is less than the precise digit.

1. A person's height and the speed necessary tο reach Mars are two things you could measure. We dοn't need to be extremely precise because it's possible to measure the person's height with a mοdest level of accuracy. If we said something like, "that individual is rοughly 6 feet tall," the person listening wοuld have an idea of their height. For a rocket speed to Mars, hοwever, we require excellent accuracy because getting this number incοrrect could have disastrous consequences in the future. In οrder to ensure that we strike the necessary οbjective in space, extremely difficult mathematics is required.

2. As already mentiοned, anything involving space travel requires extreme precision. The spacecraft might sοmehow crash if the calculations are off. Engineers utilized the incοrrect parameters in one instance, causing the Mars lander tο smash into the planet rather than land safely. Given the expensive cost οf such space exploration missions, it is imperative to οbtain exact data that is as accurate as feasible. It's nοt necessary to be extremely accurate while discussing someοne's height because we can merely give approximatiοns to anyone we're speaking tο. Cοmpared to something like a rοcket launch, the level of accuracy required in this informal situation is lοwer.

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The probability that there will be less than two days between manufacturing production line outages is approximately 0.553, or 55.3%.

We need to make some assumptions in order to calculate the probability that the time intervals between manufacturing production line breakdowns will be shorter than two days. Assume that the intervals between breakdowns have an exponential distribution with a mean of 3.5 days (1/2 times per week).

The probability that an interarrival time is fewer than two days can be calculated using the exponential distribution formula as follows:

P(X < 2) = 1 - e(-2/3.5)

where "X" stands for the duration in between breakdowns.

When we condense the expression, we get:

P(X < 2) = 0.553

Therefore, The probability that there will be less than two days between manufacturing production line outages is approximately 0.553, or 55.3%.

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Answer: $14.20

Step-by-step explanation:

the 42.60 has to be given to three people equally, (two makers and yourself).

42.60/3 = $14.20/person

Answer: $14.20

Step-by-step explanation:

Since you share with 2 other people, there are 3 people (including yourself) that are entitled to the tip.

∴ $42.60/3= $14.20 each.

You get $14.20

Hope this helps :)

The expression that is equivalent to x² +7x+12 ÷ x²+8x+15 is (x + 4) ÷ (x + 5)

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

x² +7x+12

÷

x+8x+15

Express properly

So, we have

x² +7x+12 ÷ x²+8x+15

Factorize each expression

This gives

(x + 4)(x + 3) ÷ (x + 5)(x + 3)

Cancel out the common factor

(x + 4) ÷ (x + 5)

Hence, the expression is (x + 4) ÷ (x + 5)

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When we solve the provided question, the equations will be - > x = 1/2 y + 5

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is commonly only one parameter, which also provides as the symbol. For instance, 2x - 4 = 2.

Here, the equations will be -

x = 1/2 y + 5

2x + 3y = 14

2(1/2y + 5) +3y = -14

y = -6    

and x 2

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The number of different sandwich possibilities is 1081.

To calculate this, we must use the multiplication principle. We will begin by calculating the number of possibilities for the bread, meat, and cheese. There are 6 different breads, 4 different meats, and 4 different cheeses. So, there are 6 x 4 x 4 = 96 possible combinations for the bread, meat, and cheese. Next, we must calculate the number of possibilities for the condiments. Since we are allowing repetition for the condiments, we can calculate the possibilities by multiplying 12 (the number of condiments) by itself. So, there are 12 x 12 = 144 possibilities for the condiments. Lastly, we can multiply 96 (the number of bread, meat, and cheese combinations) by 144 (the number of condiment combinations). This yields 1081 different sandwich possibilities.

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Angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let the triangle be ABC.

The angle A is 27 degrees.

The angle B is 75 degrees,

We need to find the angle of C

From Angle sum property the sum of three angles is 180 degrees.

∠A+∠B+∠C=180

27+75+∠C=180

102+∠C=180

∠C=78 degrees.

Hence, angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.

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Complete Question below:

In Triangle ABC, angle A is 27 degrees, angle B is 75 degrees then the angle C?.

The percentage of people who took less than 30 seconds to complete

the task 84.4%.

The diagram shows us how many people finished the task in what time.

40 people finished in 5-10 seconds.

40 people finished in 10-15 seconds.

30 people finished in 15-20 seconds.

30 people finished in 20-25 seconds.

25 people finished in 25-30 seconds.

25 people finished in 30-35 seconds.

25 people finished in 35-40 seconds.

25 people finished in 40-45 seconds.

15 people finished in 45-50 seconds.

That is what the diagram is telling us, and what "frequency" means in this case.

Therefore,

In total, 255 people participated.

only the last 2 groups took longer than 40 seconds.

Therefore,

The estimate of how many took less than 40 seconds is

255 - 25 - 15 = 215 people.

215 people are how many % of 255 :

100% = 255

1%  = 100%/100

     = 255/100

     = 2.55

215 is a many % as how often 1% fits into these 215 :

215 / 2.55 = 84.31372549%

                 ≈ 84.4%

Complete Question:

Times taken to complete a task. Here is a histogram showing the times taken to complete a task.

40- Estimate the percentage of 35 people who took less than 40 seconds to complete the task.

Give your answer to 1 decimal place.

Frequency Density : 1 5 0 5

Time (Density) :

10 15 20 25 30 35 40 45 50

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The probability of receiving two heads and one tail is 3/8, or 0.375.

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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The height of the tree before it got broken  is given as 72.43 feet

we have

the angle made at 45 degrees

The top touched the ground from 30 feet

we have tan 45 = x / 30

1 = x /30

x = 30

cos 45 = 1 / √2

1 / √2 = 30 / y

y = 30√2

the height = x + y

= 30 + 42.43

= 72.43

The height of the tree before it was broken is 72.43 ft

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The sum of the geometric sequence for this problem is given as follows:

S = 665.

The sum of the first n terms of a geometric sequence of first term [tex]a_1[/tex] and common ratio q is given by the equation presented as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

The parameters for this problem are given as follows:

[tex]a_1 = 32, n = 6, r = 1.5[/tex]

Hence the sum is obtained as follows:

S = 32 x (1 - 1.5^6)/(1 - 1.5)

S = 665.

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The two point baskets are 16 and the three point basket is 1.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a basketball player scored 50 points.

Let the two point baskets be x and the three point baskets be y.

The total number of baskets made was 17.

Here, x+y=17 -------(i)

During last nights game all two point and three point baskets.

Now, 2x+3y=50 -------(ii)

Substitute x=17-y in the equation (ii), we get

2(17-y)+3y=50

34-2y+3y=50

y=16

Substitute y=16 in equation (i), we get

x=1

Therefore, the two point baskets are 16 and the three point basket is 1.

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B .The value of f(x) is increasing for each unit decrease in x  about the graph is correct.

What is the graph of exponential function?

The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines

Exponential function f(x) is given

According to given graph, The value of f(x) is increasing for each unit decrease in x

Therefore, The statement, The value of f(x) is increasing for each unit decrease in x about the graph is correct.

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