Congruent Triangle Proofs. List reasons for the statements. Prove PQR congruent to STR and prove JKL is congruent to NKM 35 points!!

Answer: Let x be the measure of the angle in degrees. Then, the measure of its supplementary angle is 180 - x degrees.

We are told that the angle measures 153.4 degrees more than its supplementary angle. Using this information, we can set up an equation:

x = (180 - x) + 153.4

Simplifying this equation, we get:

2x = 180 + 153.4

2x = 333.4

x = 166.7

Therefore, the angle measures 166.7 degrees, and its supplementary angle measures:

180 - x = 180 - 166.7 = 13.3 degrees

We can check that the angle and its supplementary angle add up to 180 degrees:

166.7 + 13.3 = 180

So our solution is correct.

Step-by-step explanation:

Answer:

Where is the picture???

Step-by-step explanation:

The scale factor between the original and resulting points is equal to 4 / 3.

In this problem we find a representation of a quadrilateral and its image depicted in Cartesian plane. According to the statement, the coordinates of the original and resulting points are, respectively:

B(x, y) = (- 3, 6), B'(x, y) = (- 4, 8)

Then, the scale factor can be found by means of the following formula:

B'(x, y) = k · B(x, y)

(- 4, 8) = (- 3 · k, 6 · k)

k = 4 / 3

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Given:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

now , put the given values of x = -2 nd y = 5 in equation :

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:-45

Step-by-step explanation:

first plug in the x and the y values

4(-2)(5)-(-2+7)

The start using pemdas to simplify

*or bodmas depends on what you learned

Then you should arrive to this

4(-2)(5)+ -(5)

-8(5)+ -5

-40-5= -45

Hope that helps

The center of this circle is (3,0) and its radius is 3.

It is required to find the center and radius of the circle.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

Given that: (X-3)^2+y^2=9

The equation of a circle in standard form is:

(x -a)² + (y-b)² = r²

The x-coordinate of the center is a the y-coordinate of the center is b

, and r is the radius.

In this case,

a=3

b=0

and

r=3.

Hence, the center of this circle is (3,0) and its radius is 3.

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Answer:57

Step-by-step explanation:

274 students had not signed up for any of the three courses.

A counting method called the inclusion-exclusion principle is used to determine how many items there are in the union of two or more sets. The basic concept is to start by counting the components in each set, but we then need to adjust for any items that are in multiple sets. The number of elements in the intersection of any two sets must be subtracted in order to make this repair, and the items in the intersection of any three sets must be added back in. When it comes to combinatorics and probability theory counting difficulties, the inclusion-exclusion principle is a helpful tool.

The total number of students signed up for the course is:

73 + 54 + 34 = 161

This includes multiple courses together. To get the accurate number we subtract the number of students that signed up for 2 courses.

(17 + 9 + 9) + 4 = -22 + 4 = -18

The negative count means we have overcounted, so we need to subtract this number from the total number of surveyed students:

292 - 18 = 274

Hence, 274 students had not signed up for any of the three courses.

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Given, P(X=15) and using the probability mass function we get

(27C15)(0.546)¹⁵(1-0.546)²⁷⁻¹⁵=0.1523

What is Probability?

Probability is simply how likely something is to happen. The occurrence of an event will be in the range of 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

What is the Probability mass function?

The probability distribution of a discrete random variable, or probability mass function, gives the potential values and the corresponding probabilities. 

According to the problem,

Let X be the random variable of interest, on this case we know that:

 X∼Binom (n=27,p=0.546)

The probability mass function for the Binomial distribution is given as:

                              P(X)=(nCx) (pˣ) (1-p)ⁿ⁻ˣ,

                              here,

                                      (nCx) =  n !/(n-x)!( x)!

For finding Probability and by using the mass function :

P(X=15) = (27C15)(0.546)¹⁵(1-0.546)²⁷⁻¹⁵ = 0.1523

The value of p will be 0.546

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Answer:

To find the area of the shaded segment of the circle, we need to first find the area of the sector formed by the 60 degrees angle, and then subtract the area of the triangle formed by the radii and the chord.

The formula for the area of a sector of a circle is:

A_sector = (θ/360) x πr^2

where θ is the central angle in degrees, and r is the radius.

Substituting the given values, we get:

A_sector = (60/360) x π x 18^2

A_sector = 113.04 cm^2

Next, we need to find the area of the triangle formed by the radii and the chord. To do this, we need to first find the length of the chord using the formula:

c = 2r sin(θ/2)

where θ is the central angle in radians.

Converting the given 60 degrees angle to radians, we get:

θ = 60 x (π/180) = π/3 radians

Substituting the values, we get:

c = 2 x 18 x sin(π/6)

c = 18√3 cm

Now, we can find the area of the triangle using the formula:

A_triangle = (1/2) x base x height

where the base is the chord length c, and the height is half the length of the chord, which is:

h = r - r cos(θ/2)

Substituting the values, we get:

h = 18 - 18 cos(π/6)

h = 18 - 9√3 cm

Therefore, the area of the triangle is:

A_triangle = (1/2) x 18√3 x (18 - 9√3)

A_triangle = 243 cm^2

Finally, the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

A_shaded = A_sector - A_triangle

A_shaded = 113.04 - 243

A_shaded = -129.96

However, the result is negative because the triangle is larger than the sector in this case. Therefore, there is no shaded area in this situation.

Step-by-step explanation:

Answer:

Mean = 325.6

Range = 80

Median = 49

Step-by-step explanation:

Mean= All numbers added dividend by 10 (amount of digits)

Range= Highest number minus lowest number

Median= Middle number (process of cancellation)

Current yield = 4.51%

The price of a bond is equal to the future cash flows' present value, discounted at the appropriate discount rate—the yield to maturity.

The price of a bond is the amount that investors are willing to spend on an existing bond. Bond prices are stated as a percentage of face (par) value in the online offering table and statements you get.

Current Yield=Annual Cash Inflows/Market Price

Annual cash flow is 4.75% of 100 = $4.75

Market Price of Bond = $105.25

Current Yield = 4.75/105.25

=4.51%

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The answer in a fraction or whole number. is P(odd) = 1/3.

Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  

The number below the line is called the denominator.  It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection

According to the fundamental principle of fractions, a fraction retains its value whenever its numerator or denominator were multiplied by a single non-zero number. It can be used to multiply or divide two fractions.

Only 3 is odd among the integers 2, 3, and 4. As a result, there is a 1/3 chance of selecting an odd number (1 out of 3).

P(odd) is equal to 1/3 as a result.

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The Area would be 4ft because 2x2=4 its basic multiplication,

And I don't really understand why you also put 6ft but if you're saying 2ft x 6ft then that would be 12ft.

Hope that helps <3

Answer:

you go queen

Step-by-step explanation:

yas

Answer:

C. Simple interest involves interest calculated only on the principal. Compound interest is interest computed on the original principal as well as on any accumulated interest.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this problem, we need to standardize the values using z-scores and then find the area under the standard normal distribution curve between those z-scores.

First, we need to find the z-scores for the values 3.2 and 6.2 using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For x = 3.2:

z = (3.2 - 5.2) / 1 = -2

For x = 6.2:

z = (6.2 - 5.2) / 1 = 1

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. The area represents the probability of a randomly chosen Fluorescent lighbulb lifetime being between 3.2 and 6.2.

Using a standard normal distribution table, we can find that the area between z = -2 and z = 1 is approximately 0.8186.

Therefore, the probability that a randomly chosen Fluorescent lighbulb lifetime will be between 3.2 and 6.2 is approximately 0.8186 or 81.86%.

Answer:

6.25 seconds

Step-by-step explanation:

Using the the equation

h = 100t − 16t^2

The ball hits the ground, when h = 0, solving below equation:

100t − 16t^2 = 0

4t(25 - 4t) = 0

t = 0 seconds, this is the starting point when ball was hit

25 - 4t = 0 ⇒ 4t = 25 ⇒ t= 25/4 = 6.25 seconds later the ball hits the ground

The yield to maturity (YTM) of the bonds is 10.77%.

To calculate the yield to maturity (YTM), we need to use the following formula:

YTM = [(Annual Interest Payment + (Par Value - Market Price) / Years to Maturity) / (Par Value + Market Price) / 2] x 100%

Where:

Annual Interest Payment = Coupon rate x Par value

Par value = RM1,000

Market Price = RM980

Years to Maturity = 3

Coupon rate = 10%

First, let's calculate the annual interest payment:

Annual Interest Payment = Coupon rate x Par value = 10% x RM1,000 = RM100

Next, we can substitute the given values in the formula:

YTM = [(100 + (1,000 - 980) / 3) / (1,000 + 980) / 2] x 100%

YTM = 10.77%

Therefore, the yield to maturity (YTM) of the bonds is 10.77%.

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1) The amount is 307 g

2) The rate of change is 0.088

3) The time taken  is 8 days

Exponential decay is a mathematical process in which the value of a quantity decreases over time or space at a rate proportional to its current value.

We know that the exponential decay can be given by;

N =No[tex]e^-0.088t[/tex]

After 3 days;

N =400[tex]e^-0.088(3)[/tex]

N = 307 g

The rate of change after 3 days;

307 = 400[tex]e^-3r[/tex]

307/400 = [tex]e^-3r[/tex]

0.7675 =[tex]e^-3r[/tex]

-3r = ln(0.7675)

r = ln(0.7675)/-3

r = 0.088

1/2(400) = 400[tex]e^-0.088t[/tex]

200/400 = [tex]e^-0.088t[/tex]

1/2 =[tex]e^-0.088t[/tex]

t = ln0.5/-0.088

t = 8 days

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With given linear equations of lines, the straight lines AB and CD are not  parallel.

What is a linear equation?

In mathematics, a linear equation is an equation that can be written in the form:

y = mx + b

where "y" and "x" are variables, "m" is the slope of the line, and "b" is the y-intercept, which is the point where the line crosses the y-axis.

A linear equation represents a straight line on a graph and describes a linear relationship between two variables. The slope "m" determines how steep the line is, while the y-intercept "b" determines where the line crosses the y-axis.

Now,

To determine if the lines AB and CD are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.

The slope of a line is given by the coefficient of "x" in its equation when it is written in the form of y = mx + b, where "m" is the slope.

For line AB, we have:

OA = 3x + 7y

OB = 5x + 6y

Subtracting the equation for OA from the equation for OB, we get:

OB - OA = (5x + 6y) - (3x + 7y)

= 2x - y

So the slope of line AB is:

m_AB = (change in y) / (change in x) = -2 / 1 = -2

Now, for line CD, we have:

CD = 6x - 3y

So the slope of line CD is:

m_CD = (change in y) / (change in x) = -3 / 6 = -1/2

Since the slopes of line AB and line CD are not equal, i.e., m_AB ≠ m_CD, we can conclude that the lines are not parallel to each other.

Therefore, the geometrical relationship between the straight lines AB and CD is that they are not parallel to each other.

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Answer:

To find the average speed in miles per hour, we need to divide the total distance by the time taken:

Average speed = Total distance / Time taken

Average speed = 234 miles / 6 hours

Average speed = 39 miles per hour

Therefore, Nathan's average speed was 39 miles per hour.

Step-by-step explanation:

Answer:

Nathan drove an average of 39mph

Step-by-step explanation:

r=d/t

rate=234/6

234+6=240

240/6=40

Because we added a six, we need to subtract one:

40-1=39

Nathan drove an average of 39mph

The cost price of an item is the sum paid to acquire it or the cost at which it was produced. The cost price is denoted by the letter C.P. 

we made money when we sold a product we used the formula are :

we lose money while selling a product. we used formula are :

The profit (gain) percentage and selling price are :

The loss percentage and SP are :

The required correct match for the given problem has been shown below.

A number system is described as a process of composing to designate digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other symbols in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
3 2/7 = 23/7 = 3.2                      between 3 and 4
-3 7/8 = -31/8 = -3.875               between -3 and -4

-3/8 = -0.375                             between 0 and -1
-0.9                                          between 0 and -1
1/7                                             between 0 and 1.

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The value of x is 47 from the given figure.

An angle is formed when two straight lines or rays meet at a common endpoint.

The sum of angles is 180 degrees from the figure.

x-2+x-2+x-2+x-2=180

Add the like terms

4x-8=180

Add 8 on both sides

4x=188

Divide both sides by 4

x=188/4

x=47

Hence, the value of x is 47 from the given figure.

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The Simple Interest is $112.5

What is Simple Interest?

Simple Interest is is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.

Simple Interest = P * R * T/100

Where P = Principal = $2500

Rate = 1.5%

Time = 3 years

Simple Interest = 2500 * 1.5 * 3/100

Simple Interest = 11250/100

Simple Interest = $112.5

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When Five dozen eggs cost R60 [r/dozen], the value of R is 3600.

The term "dozen" or "dz" refers to a group of twelve.

Because there are roughly 12 lunar cycles (or months) in each solar cycle (or year), the number 12 may be one of the earliest primitive integer groupings. Twelve is useful because it has the most divisors among numbers up to its double, a characteristic that is only true of the numbers 1, 2, 6, 12, 60, 360, and 2520.

The duodecimal system, also known as the dozenal, was developed in Mesopotamia and uses the number twelve as its base (see also sexagesimal). By counting each finger bone with one's thumb, one can quickly count in base-12 on their hands.

Given 5 dozen of egg costs = R/60

That is

5 × 12 = R/60

60 = R/60

R = 60 × 60

R = 3600

Thus, When Five dozen eggs cost R60 [r/dozen], the value of R is 3600.

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Complete question:

Five dozen eggs cost R60 [R/dozen]. Find the value of R.

Therefore , the solution of the given problem of  expressions comes out to be option C. 69x is the right response.

Calculations like multiplying, dividing, joining, and presently removing are required. If they were put together, it would say: An equation, some statistics, and a mathematical formula A statement of truth is composed of values, components, and mathematical processes like additions, subtractions, errors, subdivisions, and arithmetic formulas. Words and phrases can be evaluated and analysed.

Here,

The formula 21x + 19(2x) + 2(5x) can be made simpler as follows:

=> 21x + 38x + 10x = 69x

Maliq's total scores can therefore be written as 69x.

To determine which decision is equivalent to 69x, we can also look through the answer options.

A.

=> (21+19)2x + 10x = 40(2x) + 10x = 80x + 10x = 90x,

which is not equivalent to 69x..

B. 42x and 69x are not equal.

C. 69x is the same as 69x.

D. The sum of

=> (21+19+2)(x+2x+5x) = 42(8x) = 336x does not equal 69x.

Therefore, C. 69x is the right response.

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The surface area of the pyramid, given the dimensions of the pyramid can be found to be 1, 188 m ²

The surface area of a pyramid can be found by the formula :

= Base area of pyramid + 12 x ( Perimeter of the base x Slant height )

The surface area of this pyramid is :

= ( 6 x 6 ) + 12 x ( ( 6 + 6 + 6 + 6 ) x 4 )

= 36 + 12 x ( 24 x 4 )

= 36 + 12 x 96

= 1, 188 m ²

In conclusion, the surface area of the pyramid is 1, 188 m ².

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The sum of the first 30 consecutive whole numbers is 465.

What are consecutive numbers?

Consecutive numbers are numbers that follow each other in order without interruption, with a difference of 1 between each two adjacent numbers. For example, 3, 4, 5, 6, and 7 are consecutive numbers.

The formula n x (n+1)/2 is used to find the sum of the first n consecutive whole numbers because it provides a quick and efficient way to calculate the sum without having to add all the numbers individually.

To understand why the formula works, consider the sum of the first n numbers: 1 + 2 + 3 + ... + (n-1) + n. We can rewrite this sum in reverse order, starting with n and working down to 1: n + (n-1) + (n-2) + ... + 2 + 1.

If we add these two expressions together, we get:

(1 + n) + (2 + n-1) + (3 + n-2) + ... + (n-1 + 2) + (n + 1)

Notice that each pair of terms in parentheses adds up to n+1. There are n/2 pairs of terms, so the sum of the first n numbers is:

n/2 x (n+1)

Simplifying this expression gives the formula:

n x (n+1)/2

So to find the sum of the first 30 consecutive whole numbers, we can substitute n=30 into the formula:

30 x (30+1)/2 = 15 x 31 = 465

Therefore, the sum of the first 30 consecutive whole numbers is 465.

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The amount of water left in the cubical tank would be; 3040000 mm³

A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.

We know that Volume of a cube = a³ ; a = size of edge

Volume of cubical tank = 12³

= 1728 cm³

Now, Half filled cube = 1728 / 2

= 864 cm³

Volume is f rectangular tank :

V = length x width x height

V = 10 * 8 * 7 = 560 cm³

Volume of water left in cubical tank will be;

(864 - 560) = 304cm³

1cm³ = 1000mm³

Therefore,

304cm³ = 304 x 1000 = 3040000mm³

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