Which two triangles are congruent? Complete the congruence statement.
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Rectangle ABCD is a square.

Relation between rectangle and square?

Squares and rectangles each have four straight sides. However, a square's and a rectangle's mathematical characteristics are very dissimilar. For instance, a common distinction is that squares have equal sides on each side, whereas only the opposite sides of a rectangle are equal.

Radius of circle R = 4cm

let sides of rectangle is a,b

let rectangle be ABCD in which AB =CD= a , AC=BD=b

ACD is right angled triangle on C.

Then,

\(AD^{2} =AC^{2} +CD^{2} \\\\8^{2} =b^{2} +a^{2} \\\\64=b^{2} +a^{2} \\\\b^{2} =\sqrt{64-a^{2} }\)------(1)

Area of rectangle = Area of ΔACD + ΔABD

                             = \(\frac{1}{2} \times a\times b + \frac{1}{2} \times a\times b\)

Area of rectangle = a×b

by eqn (1)

             Area = \(a\times (\sqrt{64-a^{2} } )\)

For maximum area

\(\frac{dA}{da} =0\\\\a \times \frac{1}{\sqrt{64-a^{2} } } (-a)+(\sqrt{64-a^{2} } )\times(1)=0\)

\(\sqrt{64-a^2} -\frac{a^2}{\sqrt{64-a^2} } =0\\\\\frac{64-a^2-a^2}{\sqrt{64-a^2} } =0\\\\64-2a^2=0\\\\a^2=32\\\\a=\sqrt{32} \\\\In (1) eqn\\b=\sqrt{64-a^2} \\\\b=\sqrt{64-32} \\\\b=32\)

So, a=b

Means Rectangle ABCD is a square.

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 z =  3  or z = \(\frac{In q^{12} }{In q^{4} }\)   is the value of z in linear equation.

What in mathematics is a linear equation?

a ) Simplify using exponent rule with same base  = a\(a^{n} . a^{m} = a^{n + m}\)

Based on the given conditions, corresponding exponents are equal                                                                              = \(3^{2 + x} = 3^{7}\)

Rearrange unknown terms to the left side of the equation                                                                           = 2 + x = 7

 Calculate the sum or difference                                                                               x = 5

b) Calculate the power 5764801 + \(7^{y}\) = 117649

Rearrange unknown terms to the left side of the equation

         7^{y} = 117649 - 5764801

The equation is not defined.

c)  the equations  z =  3  or z = \(\frac{In q^{12} }{In q^{4} }\)

   answer    z =  3  or z = \(\frac{In q^{12} }{In q^{4} }\)

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The probability of the event that the second dice is not smaller than the first dice is 15/36.

It's simple to rule out every option:

First die is a 1, and the second die wins 5/6.

First die is a 2, and the second die wins 4/6.

First die is a 3, and the second die wins 3/6.

First die is a 4, and the second die wins 2/6.

First die is a 5, and the second die wins 1/6.

First die is a 6, winning with a score of 0/6.

In total, 15 out of the 36 results favor the second die. All of these might be tabulated.

So the probability of the event that the second dice is not smaller than the first dice = 15/36

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The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

The correct sequence of project phases is Definition - Planning  - Performance. The correct answer is B.

This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.

Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.

Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.

Therefore the sequence of project phase is  Definition - Planning  - Performance The correct answer is B.

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Answer:

$807.39

Step-by-step explanation:

\(\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given:

Substitute the given values into the compound interest formula and solve for A:

\(\implies A=500\left(1+\dfrac{0.04}{12}\right)^{12 \cdot 12}\)

\(\implies A=500\left(1.00333333...\right)^{144}\)

\(\implies A=500\left(1.61478492...\right)\)

\(\implies A=807.392461...\)

Therefore, Alyson will have $807.39 (nearest cent) in her account at the end of 12 years.

To determine if a high school's claim of having unusually high math SAT scores is justified, we can compare the sample mean with the population mean using a z-score.

The average math SAT score is given as 514 with a standard deviation of 113. A random sample of 60 students from the high school yielded a sample mean of 531. By calculating the z-score and comparing it to the range of usual events, we can assess the validity of the high school's claim. To determine if the high school's claim is justified, we calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n))

Where:
x is the sample mean (531),
μ is the population mean (514),
σ is the population standard deviation (113),
and n is the sample size (60).

Substituting the values into the formula: z = (531 - 514) / (113 / sqrt(60))
Calculating the z-score gives us a value. By comparing the z-score to the range of usual events, we can determine if the high school's claim is justified. The range of usual events is typically within ±2 standard deviations from the mean. If the z-score falls within this range, it suggests that the sample mean is not significantly different from the population mean, and the claim of unusually high scores may not be justified.

Please note that the provided explanation assumes a normal distribution and the use of a one-sample z-test.

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we can take the two equations and divide them

so is option 4

\(\frac{3}{8}x = 32\)

multiply both sides by the reciprocal

x = 85⅓

We would expect her to make about 85 business calls in a month.

Step-by-step explanation:

The equation means "3/8 of the unknown total is 32"

When we multiply 3/8 by its reciprocal, it becomes 1 and cancels on the left.

8/3 times 32 is a mixed number, so it is reasonable to round it to a whole number of calls.

.

I hope I read this question correctly. The coding for the fraction made it a bit confusing.

the statement "there are arbitrarily many different mathematical functions that interpolate a given set of data points" is false.

Interpolation is the process of constructing a mathematical function that passes through a given set of data points. However, not every set of data points can be interpolated by a unique function. For example, if we have two data points (x1, y1) and (x2, y2) where x1 ≠ x2, then there exists a unique linear function f(x) = mx + b that passes through these two points.

However, if we have three or more data points, there may be multiple functions that interpolate the data. Nevertheless, there are some conditions that can guarantee the uniqueness of the interpolating function, such as if the data points are the values of a polynomial of degree n or less, then there exists a unique polynomial of degree n or less that interpolates the data.

Therefore, the statement "there are arbitrarily many different mathematical functions that interpolate a given set of data points" is false. The number of possible interpolating functions depends on the properties of the data points and the type of function used for interpolation.

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1 pound of jelly beans cost $1.75

1 pound of almonds cost $2.75

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

From the table,

We can make two equations:

Cost of jelly beans = x

Cost of almonds = y

First purchased:

9x + 7y = 37

Second purchased:

3x + 5y = 17

Now,

9x + 7y = 37 _____(1)

3x + 5y = 17 ______(2)

Using the elimination method.

Multiply 3 into (2).

9x + 7y = 37

9x + 15y = 51

(-)     (-)      (-)

       -8y = -14

           y = 14/8

           y = 7/4 = 1.75

And,

9x + 7y = 37

9x + 7 x 1.75 = 37

9x + 12.25 = 37

9x = 37 - 12.25

9x = 24.75

x = 2.75

Thus,

Cost of 1 pound of jelly beans = $1.75

Cost of 1 pound of almonds  = $2.75

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The given statement "The LCM of 2 numbers is the product of the two numbers" is false because the LCM of 2 numbers does not have to be product of the numbers involved.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b in mathematics and number theory.

The statement is "never" true. The LCM (Least Common Multiple) of two numbers is the smallest multiple that is common to both numbers, whereas the product of two numbers is simply the result of multiplying the two numbers together.

For example, the LCM of 2 and 3 is 6, whereas the product of 2 and 3 is 6. But the LCM of 2 and 4 is 4 , whereas the product of 2 and 4 is 8.

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The expression will be 5 + 11x.

What is an expression?

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible to compare expressions to phrases. In English, a phrase by itself may contain an action, but it does not constitute a whole sentence.

Explanation: 3 + 7

Let the number to be "x"

Step 1 : the number is multiplied by - 8

           So, -8 x

Step 2 : subtracted from the sum of 5 and 3 times the number

       So,  (5 +3x) - (-8x)

           = 5+3x + 8x

           = 5 + 11x

Hence, The final expression will be 5 + 11x.

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The angle in standard position which is coterminal with an angle in standard position measuring 152 is -208 degrees.

To find the angle, follow these steps:

So, the angle in standard position that is coterminal with an angle measuring 152 degrees is -208 degrees.

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Answer: ($8.96 / 7) * 5                        or $6.40

Step-by-step explanation: You need to find the price for one watermelon then multiply it by 5 to find the price of 5.

yes, because the midpoints (a+c) = b

Given that the line's equation is y=x.

B and C are the two points on this line.

( a+ c, b) is the midpoint of B and C.

We can see from this that using the midpoint formula

a + c = \(\frac{x1+x2}{2}\)

b=\(\frac{y1+y2}{2}\)

Because both points are on y=x, we get

x1=y1, x2=y2.

As a result, x1 = a+c and 2y1 = 2b or y1 =b.

Because x1=y1, we have a+c =b.

In other words, the coordinates of the midpoint satisfy the equation y=x.

Thus, the answer is

because (a+c) = b

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Therefore, the solution set for the system is the point (1.8, 5.2).

A graph is a collection of points, called vertices (or nodes), and a set of connecting lines, called edges, that connect pairs of vertices. Graphs are often used to represent relationships between objects, such as roads between cities, social connections between people, or links between web pages.

Graphs can be classified based on their properties, such as whether they are directed or undirected, whether they have loops (edges that connect a vertex to itself), or whether they are connected (all vertices can be reached from any other vertex).

by the question.

To solve this system of equations graphically, we need to plot the lines represented by each equation on a coordinate plane and find their intersection point (if it exists).

First, let's rearrange the first equation to solve for y:

\(y = (2/3)x + 4\)

Now, we can plot this line by finding two points on it. For example, when x = 0, y = 4, and when x = 3, y = 6. We can then connect these points with a straight line.

\(y < 4x\). This is an inequality, so we'll shade the region below the line y = 4x. To plot the line itself, we can again find two points on it. When x = 0, y = 0, and when x = 1, y = 4. Connecting these points.

we need to shade the region below this line, since y is less than 4x. This region includes all points on the coordinate plane that satisfy y < 4x. We can shade it by drawing a dotted line along the line y = 4x and shading the region below.

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Answer:

There are 4 prime numbers.

Step-by-step explanation:

The prime numbers are: 151, 157, 163, 167

You just need to know what numbers are prime numbers.

Answer:

4 prime numbers

Step-by-step explanation

A prime numbers is a natural number greater than 1 that is not a product of two smaller natural numbers. For example, 5 is a prime number because it is multiplied by 1 and itself. On the contrary, 4 is not a prime number because it is multiplied by 2. Remeber 1 is not a prime number because it has only 1 factor and prime numbers have exactly 2 factors. Therfore the prime numbers in between 150 and 170 are.... 151, 157,163, and 167.

             The 4 prime numbers between 150 and 170 are:

                                     151, 157, 163, 167

Answer:

110°

Step-by-step explanation:

Let the third angle be x. All the angles in a triangle add up to 180°. From the previous statement, we can write the equation:

25° + 45° + x = 180°

70° + x = 180°

x = 110°

The angle 2π/7 in its standard position is added as an attachment

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

Angle = 2π/7

The coordinates of this point can be found by using the formula for converting from polar to rectangular coordinates:

x = cos(2π/7)

y = sin(2π/7)

So, we have

x = 0.62

y = 0.78

As an ordered pair, we have

(0.62, 0.78)

This means that we plot (0.62, 0.78)

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Perimeter of Rectangle is 44m

A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.

According to the given information

Area of Rectangle = l × b

Area of Rectangle = 105 \(m^{2}\)

Length of one side = 7 m

Let the length of the adjacent side = b

Area of Rectangle given = 7 × b

                     105   = 7 × b

                       b    =  \(\frac{105}{7}\)

                       b   = 15 m

Perimeter of Rectangle given = 2( l + b )

                                        = 2 ( 7 + 15 )

                                        = 2 × 22

                                        = 44m

Perimeter of Rectangle is 44m

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Answer:

188 kids in intermediate, 100 juniors, and 13 children that attend primary school.

Step-by-step explanation:

K there are 300 kids.

5/8 are intermediate, so 5/8 * 300 = 187.5, you can't have half a kid, so we can round to 188 kids are intermediates.

1/3 are juniors, so 1/3 * 300 = 100 are juniors.

The rest are primary:

(1)-(5/8 + 1/3)= 1/24

Thus, 1/24 are primary students, so 1/24 * 300 = 12.5 and again we will round up to 13 children in primary classes.

I am not sure if this is answering your question since you don't specifically have one listed.

Radius A = 3

Radius B= 9

Scale factor = Radius A / Radius B = 3/9 = 1/3

Scale factor = 1/3

Answer:

The cone has a volume of approximately 982.5 cubic centimetres.

* That answer sounds off to me, but I'm not sure.  You might want to run through the logic yourself and see if you get the same results.

Step-by-step explanation:

The volume of a cone is one third that of a cylinder with the same height and base radius. In other words:

\(v = \pi r^{2} \frac{h}{3}\)

But before using that, we need to know the value of h, height.  What we are instead given is the slant height, or the length from tip to edge.

We can use that slant height along with the base radius to get the cone height, as the three of them are the edges of a right triangle, with slant height being the hypotenuse.

To get the height then we can say

\(h = \sqrt{s^{2} - r^{2}}\)

Where h is height, s is slant, and r is radius.

\(h = \sqrt{14.8^{2} - 14^{2} }\)

\(h = \sqrt{219.04 - 196}\)

\(h = \sqrt{23.04}\)

\(h = 4.8\)

A very squat cone indeed.

Now we can plug that and the radius into the actual cone equation:

\(v = \pi (14cm)^{2} \frac{4.8cm}{3}\\= \pi 196cm^2 * 1.6cm\\\approx 985.2 cm^3\)

Answer:

Area of triangle RST = 95 in² (Approx)

Step-by-step explanation:

Given:

Side a = 22 in

Side b = 13 in

Perimeter = 50 in

Find:

Area of triangle

Computation:

Side c = Perimeter - Side a - Side b

Side c = 50 - 22 - 13

Side c = 15 in

Heron's formula:

s = Perimeter / 2 = 50 / 2

s = 25 in

Area of triangle = √s(s-a)(s-b)(s-c)

Area of triangle = √25(25-22)(25-12)(25-15)

Area of triangle = √25(3)(13)(10)

Area of triangle = 5√390

Area of triangle = 5 × 19(approx)

Area of triangle RST = 95 in² (Approx)

Answer:

D.95 on edge

Step-by-step explanation:

In a study examining the effect of ignoring text messages on distraction, the variable "trying to ignore text messages" would be the independent variable, whereas the variable "amount of distraction" would be the dependent variable.

The independent variable is the one that is manipulated or controlled by the researcher. In this case, the researchers are interested in studying the effect of attempting to ignore text messages, so they would manipulate the participants' behavior in relation to text messages (e.g., asking them to ignore the messages or not).

The dependent variable, on the other hand, is the variable that is measured or observed to determine the effect of the independent variable. Here, the researchers would measure the amount of distraction experienced by the participants as a result of trying to ignore the text messages.

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Answer:

The second set

Step-by-step explanation:

The second set is not a function because there is an input with more than one output.

The given values are: In 5 = 1.609, In 7 = -1.946. We have to find In 245 with the help of a calculator.The given values are in logarithmic form of base ‘e’.We know that:ln(ab) = ln(a) + ln(b)ln(a/b) = ln(a) - ln(b)ln(a^n) = n * ln(a)Using the above laws of logarithm, we can write:In 245 = In (5 * 7 * 7) = In 5 + In 7 + In 7= 1.609 - 1.946 - 1.946≈ -1.283

The natural logarithm function is commonly written as ln(x). When we write this, we mean the logarithm with base e. For example, ln(1) = 0, since e^0 = 1. Also, ln(e) = 1, since e^1 = e. The natural logarithm is the inverse of the exponential function e^x.The given values are: In 5 = 1.609, In 7 = -1.946. We have to find In 245 with the help of a calculator. The given values are in logarithmic form of base ‘e’.Using the above laws of logarithm, we can write:In

245 = In (5 * 7 * 7) = In 5 + In 7 + In 7= 1.609 - 1.946 - 1.946≈ -1.283

Therefore, In 245 ≈ -1.283

In this problem, we used the logarithmic properties of logarithms to calculate In 245. We used the values of In 5 and In 7, and then we combined them with the help of the logarithmic laws to find the value of In 245. The final answer that we got with the help of a calculator was In 245 ≈ -1.283.

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The matching answers and corresponding colors for the holiday lights are: (Slope: 3) Dark Blue, (Slope: -4) Violet, (Slope: 1/4) Red.

To find the slope of a line passing through two points \((x_1, y_1)\ and\ (x_2, y_2)\), we can use the formula:

Slope = \((y_2 - y_1) / (x_2 - x_1)\)

Let's calculate the slopes for each pair of points:

1. (8, 3) and (10, 9):

Slope = (9 - 3) / (10 - 8) = 6 / 2 = 3

2. (2, -3) and (1, 1):

Slope = (1 - (-3)) / (1 - 2) = 4 / (-1) = -4

3. (-4, -8) and (-8, -9):

Slope = (-9 - (-8)) / (-8 - (-4)) = (-9 + 8) / (-8 + 4) = -1 / (-4) = 1/4

Now let's compare the slopes to identify the matching answers:

1. Slope: 3 (Dark Blue)

2. Slope: -4 (Violet)

3. Slope: 1/4 (Red)

Thus, the corresponding colors for the holiday lights would be:

1. Dark Blue

2. Violet

3. Red

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