assume the following data for a country: total population, 500; population under 16 years of age or institutionalized 120; not in labor force 150 (besides under 16); unemployed 23; part-time workers looking for full-time jobs 10.

The two consecutive natural numbers that satisfy the given equation are 3 and 4.

Let the two numbers be x and x+1

x(x+1) = 1.5x^2

x^2 + x - 1.5x^2 = 0

x^2 - 0.5x = 0

(x-3)(x+0.5) = 0

x = 3, x+1 = 4

The given equation is the product of two consecutive natural numbers, which is equal to 1.5 times the square of the lesser number.

Therefore, we can set up an equation by substituting x for the lesser number and x+1 for the greater number.

x(x+1) = 1.5x^2

We can then simplify the equation by subtracting 1.5x^2 from both sides.

x^2 + x - 1.5x^2 = 0

We can then factor this equation to find the solution.

x^2 - 0.5x = 0

(x-3)(x+0.5) = 0

The solutions to this equation are x = 3 and x+1 = 4. Therefore, the two consecutive natural numbers are 3 and 4.

The two consecutive natural numbers that satisfy the given equation are 3 and 4.

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The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.

1. The equation |x - 3| = 1 can be rewritten as x - 3 = 1 or x - 3 = -1.

2. Solving for x, x = 4 or x = 2.

3. The equation |x - 3| = 4 can be rewritten as x - 3 = 4 or x - 3 = -4.

4. Solving for x, x = 7 or x = -1.

5. The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.

The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7. To find the two endpoints of the line segment, we need to solve for x in the equations |x - 3| = 1 and |x - 3| = 4. The equation |x - 3| = 1 can be rewritten as x - 3 = 1 or x - 3 = -1, and solving for x gives us x = 4 or x = 2. The equation |x - 3| = 4 can be rewritten as x - 3 = 4 or x - 3 = -4 and solving for x gives us x = 7 or x = -1. Therefore, the graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.

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the complete question is

Which of the following is the graph of the region 1 <|x - 3| < 4

As a result, the bus accelerates at a rate of -4 m/s2, and it travels 50 m after applying the brakes.

Bus's initial speed was 72 km/h.

Bus's last speed is 0 km/h.

(Therefore, the bus driver stops)

Bus travel time, t=5 s

To Locate

Bus acceleration and the distance it travels before stopping once the brakes are applied

Solution:

Final velocity is v.

Initial velocity is u.

Acceleration is a.

It takes time.

displacement is s.

Considering that

u = 20m/s

v = 0 m/s

Bus acceleration should be "a"

When using the first law of motion on a bus, we obtain

Let d represent the bus's distance traveled after braking.

a = -4 m/s²

Thus, when we use the third equation of motion on a bus, we obtain

As a result, the bus accelerates at a rate of -4 m/s2, and it travels 50 m after applying the brakes.

d = 50 m

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If this is math, this is undefined because it's impossible to solve.

But in Physics...

Simplify the expression.

−2.3d+4.2h−15

Answer: i hope this helps ..

Step-by-step explanation:

Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ A=20\\ b=6\\ h=4 \end{cases}\implies 20=\cfrac{4(a+6)}{2}\implies 40=4(a+6) \\\\\\ \cfrac{40}{4}=a+6\implies 10=a+6\implies 4=a[/tex]

The correct statement regarding the slope and the intercept of the linear function are is given as follows:

The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour.

The two most important features of a linear function are the slope and the intercept, and their meaning is explained as follows:

The input and output variables for this problem are given as follows:

Two points of the function are:

(0, 8) and (3,6).

Given two points, the slope is calculated as the change in y divided by the change in x, hence:

m = (6 - 8)/(3 - 0)

m = -2/3.

Meaning that the candle's height decays at a rate of 2/3 of an inch an hour.

When x = 0, y = 8, hence the intercept of b = 8 represents the initial height of the candle.

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Answer:

In exact form:

391/28

or

Mixed form:

13 27/28

Step-by-step explanation:

I'm not sure which form you wanted the answer to be so I added both forms. Hope this helps! :)

Hey there!

4 1/4 * 3 2/7

= 17/4 * 23/7

= 17(23)/4(7)

= 391/28

= 13 27/28

Therefore, your answer should be:

13 27/28

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The Surface area this of cylinder with radius 11cm and height 30 cm is 2833.71 cm².

Two parallel, identical bases connected by a curved surface form a 3D solid shape known as a cylinder. Similar to a disc in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases. Perpendicular distance is the measurement separating the two bases, and it is denoted by the letter "h," which stands for height. The distance between the two circular bases' centres and outer edges is known as the cylinder's radius and is denoted by the letter "r".

Surface area of cylinder = 2πr(r+ h)

= 2π11(11+ 30)

= 2833.71 cm²

Thus, the Surface area this of cylinder with radius 11cm and height 30 cm is 2833.71 cm².

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Answer:

13/20

Step-by-step explanation:

Answer:

65/100

Step-by-step explanation:

65/100 because if you try to divide it by 2 u get 32.5

The domain of y = 3 * (2) ^ x is set of all real numbers i.e. (-∞,∞) and the range is (0,∞).

What is domain and range of a function?

The domain is the set or a collection of all the possible values that can go in the function.

The range is collection of all the output values of a function.

Domain

For the given function, the domain is the set of all real numbers because there is no value for 'x' where the function is not defined.

Thus, the domain is (-∞,∞).

Range

For the given function, the values for y range from 0 to infinity.

Therefore, the range is (0,∞).

Hence, the domain of y = 3 * (2) ^ x is (-∞,∞) and the range is (0,∞).

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After evaluating the integral answer is 85/4. thus, option A is the answer.

The given transformation is a change of variables from (x, y) to (u, v). To evaluate the integral using the transformation, we need to use the Jacobian determinant. The Jacobian determinant is the absolute value of the determinant of the matrix of partial derivatives of the transformation.

du/dx = 1, du/dy = 1

dv/dx = -2, dv/dy = 1

The determinant of the matrix of partial derivatives is det(J) = du/dx * dv/dy - du/dy * dv/dx = (1)(1) - (1)(-2) = 3

So the Jacobian determinant is |J| = |3| = 3.

The integral becomes:

R\int \int 5y dx dy = (1/3) R\int \int 5v du dv

where R is the region in the uv-plane that corresponds to the region in the xy-plane bounded by the lines y= -x+1, y=-x+4, y= 2x+2, y= 2x+5

The integral evaluates to (1/3) R\int \int 5v du dv = (1/3) * 85/2 = 85/6 = 85/4

Therefore the correct answer is 85/4

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The force F1 can be expressed as a Cartesian vector, F1 = (F1x, F1y). The other forces acting on the gusset plate can be resolved into x and y components, with F2 = (F2x, F2y), F3 = (F3x, F3y), and F4 = (F4x, F4y).

The force F1 can be expressed as a Cartesian vector, F1 = (F1x, F1y). This vector has two components, the x component F1x and the y component F1y. The other forces acting on the gusset plate can be resolved into x and y components using the same method. For example, the force F2 can be resolved into its x and y components, F2x and F2y, to form the vector F2 = (F2x, F2y). The same applies to F3 and F4, which can be expressed as vectors F3 = (F3x, F3y) and F4 = (F4x, F4y), respectively. The x and y components of each force can be found by using trigonometric functions such as sine and cosine, as well as the magnitude of each force. In this way, each force acting on the gusset plate can be expressed as a Cartesian vector, allowing us to analyze the forces acting on the plate in two-dimensional space.

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Long division is used to divide polynomials, with the leftover being 0 and the quotient being 26x + 26.

To divide the polynomials, we may utilise long division. To begin, divide the dividend's leading term (522) by the divisor's leading term (2). The leftover is 0 and the quotient is 26.

The quotient (26) is then multiplied by the divisor (2) and subtracted from the dividend (522 13z + 3). This yields the value 522 13z - 52.

The leading term of the new dividend (522) is then divided by the divisor's leading term (2). The leftover is 0 and the quotient is 26.

The quotient (26) is then multiplied by the divisor (2) and subtracted from the new dividend (522 13z - 52). This yields a value of 0.

As a result, the final answer is 26x + 26.

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The equation of line in point slope form will be -

y - 5 = - 3(x + 4).

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is a equation of a line → y = -3x + 5 passing through point (-4, 5).

The given equation is -

y = -3x + 5

Slope of the line parallel to this line -

m{p} = - 3

We can write the equation of line in point slope form as -

y - 5 = -3(x + 4)

Therefore, the equation of line in point slope form will be -

y - 5 = - 3(x + 4).

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The evaluation of the expression using the order of operations, indicates the operations that come first as follows;

(5 + 5)² + 15 - 10 Parenthesis

40 ÷ 8 · 4  + 2; Division

4 - 2 + 3 · 5; Multiplication

(3² + 8) ÷ 7 - 5; Parenthesis

The order of operations is a rule that serves as a guide for the correct sequence of performing operations in an equation or expression.  

The evaluation expressions can be presented as follows;

First operation;

(5 + 5)² + 15 - 10

The order of operations, PEMDAS, indicates that we get;

1) Parenthesis first

2) Exponents

3) Multiplication and division

4) Addition and subtraction

Based on the above PEMDAS order of operation, the step that should be completed first is the operation within the parenthesis, which is the addition operation (5 + 5)

The correct option is; Parenthesis

Second expression;

40 ÷ 8 · 4 + 2

The operations in the expression are; division, multiplication, and addition

The order of operations indicates that division, which comes first, from the left, should be performed first. The correct option is therefore;

40 ÷ 8 · 4 + 2; division

Third expression;

4 - 2 + 3 · 5

The subtraction is the first operation from the left, but the order of operations, PEMDAS, indicates that the multiplication, 3 · 5 should be performed first, therefore;

Fourth expression;

(3³ + 8) ÷ 7 - 5

The parenthesis which comes first in the order of operations and first among the operations from left to right comes first

Therefore, the parenthesis comes first;

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The value of g becomes 64% of its value on the surface of the earth when it is at a height of 3200km above the surface, with the radius of the earth being 6400km.

Radius of Earth = 6400 km

Height above the surface of Earth = 3200 km

Gravitational Acceleration on surface of Earth = 9.8 m/s2

Gravitational Acceleration at 3200 km above the surface of Earth = 9.8 x 0.64 = 6.272 m/s2

The gravitational acceleration (g) on the surface of the earth is 9.8 m/s2. This value is constant, regardless of the height of an object above the surface. However, as the height of an object increases, the gravitational force experienced by the object decreases. The radius of the earth is 6400 km, so at a height of 3200 km above the surface, the gravitational acceleration experienced by an object is 64% of its value on the surface of the earth, which is 6.272 m/s2. This is because the gravitational force decreases as the object moves further away from the surface, and at 3200 km the force is only 64% of the force at the surface.

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A line which joins the midpoints of two sides of a triangle is Midsegment

A triangle's midsegment is a line formed by joining any two of the triangle's sides at their midpoints. All three sides of a triangle can be divided (split in half) in any triangle, whether it be right, isosceles, or equilateral. The midpoint of each side is the point that is equally spaced from either vertex.

Triangles can have three midsegments because they have three sides. Any two sides can be joined at their midpoints. Half the length of the base is represented by one midsegment (the third side not involved in the creation of the midsegment). That is the only intriguing aspect. It also:

Is consistently parallel to the triangle's third side; the base

Creates a tiny triangle that resembles the primary triangle.

The area of the smaller, comparable triangle is one-fourth that of the larger triangle.

Half of the original triangle's circumference is contained within the smaller, comparable triangle.

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All, 25%, and 5 are all valid options that can be selected in the Top Values list for a query.

All will display all the values in the query, 25% will display the top 25% of the values, and 5 will display the top 5 values.

To calculate 25%, we can use the formula (value/total)*100. For example, if the total number of values is 20, then 25% would be (20/20)*100 = 100. This would display all 20 values in the query. Similarly, if the total number of values is 50, then 25% would be (50/50)*100 = 100, which would also display all 50 values.

To calculate 5, we can use the same formula (value/total)*100. For example, if the total number of values is 20, then 5 would be (5/20)*100 = 25. This would display the top 5 values in the query. Similarly, if the total number of values is 50, then 5 would be (5/50)*100 = 10, which would also display the top 5 values.

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The cost of excavating a space 81 ft long, 42 ft wide, 9 ft deep at a cost of $36/yd. is $367, 416

The area of the object or space is the space it occupies

The area is denoted by

Area= Lenght * Breadth * Height

Area = 81 * 42 * 9 feet

Area = 30,618 ²

Feet to Yards Converter

From

Foot (ft)

To

Yard (yd)

Feet

ft

Yards

yd

Calculation

Yards to feet ►

How to convert feet to yards

1 yard is equal to 3 feet:

1yd = 3ft

The distance d in yards (yd) is equal to the distance d in feet (ft) divided by 3:

d(yd) = d(ft) / 3

Example

Convert 20 ft to yards:

d(yd) = 20ft / 3 = 6.6667yd

How many yards in a foot

One foot is equal to 0.33333 yards:

1ft = 1ft / 3 = 0.33333yd

How many feet in a yard

One yard is equal to 3 feet:

Remember that 1yd = 3×1yd = 3ft

How to convert 10ft to yards

Divide 10 feet by 3 to get yards:

10ft = 10ft / 3 = 3.33333yd

Feet to yards conversion table

Feet (ft) Yards (yd)

0.01 ft 0.0033333 yd

0.1 ft 0.033333 yd

1 ft 0.33333 yd

2 ft 0.66667 yd

3 ft 1.00000 yd

4 ft 1.33333 yd

5 ft 1.66667 yd

6 ft 2.00000 yd

7 ft 2.33333 yd

8 ft 2.66667 yd

9 ft 3.00000 yd

10 ft 3.33333 yd

20 ft 6.66667 yd

30 ft 10.00000 yd

40 ft 13.33333 yd

50 ft 16.66667 yd

60 ft 20.00000 yd

70 ft 23.33333 yd

80 ft 26.66667 yd

90 ft 30.00000 yd

100 ft 33.33333 yd

Then covert the feet into yards

This shows that 30618 feet = 10206 yards

The cost of each yard is $36/yd.

Then the cost of  excavating the space $36*10206 = $367,416

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The cotangent of an angle is the ratio of the adjacent side length over the opposite side length, which is 9 divided by [tex]\sqrt{57}[/tex] .

The opposite of a tangent is a cotangent. It is the ratio of a right triangle's adjacent side to its opposite side. It may be expressed mathematically as cot, where is the right triangle's angle. The ratio between the adjacent side and the opposite side will be the cotangent of 30°, for instance, if the right triangle's angle is 30°. When you are aware of the side lengths of a right triangle, the cotangent may be used to determine the angle. For instance, the cotangent of the angle is 0.417, which indicates the angle is around 24°, provided you know the lengths of the near side to be 5 and the opposite side to be 12.

In the given question, the ratio of the adjacent side length to the opposite side length is equal to the cotangent of an angle. The neighboring side length in this example is 9 and the opposite side length is the square root of 57. As a result, the cotangent of angle V is equal to 9 divided by 57 squared. This is written as 9/57.

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Answer:

2.64

Step-by-step explanation:

The advantage of a larger sample size is that the estimate covers more ground and is more reliable.Answer:a) 0.6180 b) 0.7817 c) 0.9484 d) 0.994

z = (x - xbar)/σ

Standard deviation = σ = √variance = √[(p)(1-p)/n]

p = population proportion = 0.3

n = sample size

Sample proportion = (x - xbar) = ± 0.04

z = (sample proportion)/(standard deviation)

a) sample proportion = ± 0.04

n = 100

Standard deviation = √[(0.3)(1 - 0.3)/100] = 0.0458

z = ± 0.04/0.0458 = ± 0.873

Using normal probability distribution tables

P(|x- xbar| < 0.04) = P(-0.873 < z < 0.873) = P(z < 0.873) - P(z < -0.873) = 0.809 - 0.191 = 0.6180

b) sample proportion = ± 0.04

n = 200

Standard deviation = √[(0.3)(1 - 0.3)/200] = 0.0324

z = ± 0.04/0.0324 = ± 1.23

Using normal probability distribution tables

P(|x- xbar| < 0.04) = P(-1.23 < z < 1.23) = P(z < 1.23) - P(z < -1.23) = 0.891 - 0.1093 = 0.7817

c) sample proportion = ± 0.04

n = 500

Standard deviation = √[(0.3)(1 - 0.3)/500] = 0.0205

z = ± 0.04/0.0205 = ± 1.95

Using normal probability distribution tables

P(|x- xbar| < 0.04) = P(-1.95 < z < 1.95) = P(z < 1.95) - P(z < -1.95) = 0.974 - 0.0256 = 0.9484

d) sample proportion = ± 0.04

n = 1000

Standard deviation = √[(0.3)(1 - 0.3)/1000] = 0.0145

z = ± 0.04/0.0145 = ± 2.76

Using normal population proportion tables

P(|x- xbar| < 0.04) = P(-2.76 < z < 2.76) = P(z < 2.76) - P(z < -2.76) = 0.997 - 0.0029 = 0.9941

e) the advantage of a larger sample size is that the estimate covers more ground and is more reliable.

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The value of expression is 1 of the equation -8b+15b+14=21b

Two or more expressions with an Equal sign is called as Equation.

The given expression is -8b+15b+14=21b

Minus eight times of b plus fifteen b plus forteen equal to twenty one.

In the given expression b is the variable and minus and plus are the operators.

-8b+15b+14=21b

Take the variable terms on one side and constant on other side.

-8b+15b-21b=-14

-14b=-14

Divide both sides by -14

b=1

Hence, the value of expression is 1 of the equation -8b+15b+14=21b

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[tex]question[/tex]

[tex]answer[/tex]

Hope it's help......✨

The value of expression log₃9 is 2, Option B is correct.

An expression is combination of variables, numbers and operators.

We know that 3 raised to what power equals 9.

We can write this as:

3ˣ = 9

Taking the logarithm of both sides with base 3, we get:

log₃(3ˣ) = log₃ 9

x = log₃9

So, the value of log3 9 is the exponent x that satisfies the equation 3ˣ = 9.

Since 3²= 9, we have:

log₃ 9 = 2

Hence, the value of expression log₃9 is 2.

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The two expressions being cubed are p and q. The expression (p^3 - q^3) is equivalent to cubing both p and q. This means that the expression can be written as (p * p * p - q * q * q). Rewriting it in the form (p^3 - q^3) shows that the two expressions being cubed are p and q.

The expression (p^3 - q^3) is equivalent to cubing both p and q. This means that the expression can be written as (p * p * p - q * q * q). Rewriting it in the form (p^3 - q^3) shows that the two expressions being cubed are p and q.

The expression (p^3 - q^3) is the result of cubing two different expressions, p and q. This is equivalent to multiplying each expression by itself three times. Rewriting the expression in the form (p^3 - q^3) indicates that the two expressions being cubed are p and q. In other words, the expression is the result of taking p and raising it to the third power and then taking q and raising it to the third power. The result is then subtracting q^3 from p^3. This is commonly referred to as cubing both p and q, and the two expressions being cubed are p and q.

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a) Over the intervals (−∞,−9),(-6,-2) and (3,7) the function is increasing.

b) At x-values x=-6 and x=3 the function have local minima.

c) The sign of the function's leading coefficient is negative.

d) The possibility for the degree of the function is 5 or 7.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

A function is said to increasing if the value of y increases as the value of x increases.

From the graph, the function is increasing on (−∞,−9),(-6,-2) and (3,7)

The local minima is a point where the function has minimum value in its local neighbour.

From the graph, the function has a local minima at x=-6 and at x=3.

In the end, the value of f(x) decreases as the value of x increases therefore the sign of the function's leading coefficient is negative.

The graph intersects the x-axis 2 times and also the function have 5 turning points both the these information indicates that the function is of 5 degrees or 7 degrees.

Therefore, interval, local minima, coefficient value and degree of function is obtained.

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The solution of the system is (4, 2).

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

We have the system of inequalities:

x + y ≥ 6

x ≥ 4

To find the solution:

Solve as a system of equations.

x + y = 6

And x = 4.

Then y = 2.

Therefore, (4, 2) is the solution of the system.

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Answer:The solution of the system is (4, 2).

What are systems of inequalities?

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

We have the system of inequalities:

x + y ≥ 6

x ≥ 4

To find the solution:

Solve as a system of equations.

x + y = 6

And x = 4.

Then y = 2.

Therefore, (4, 2) is the solution of the system.

Step-by-step explanation:

The simplified form of the expression  (2x⁵ + 3y⁴)(- 4x² + 9y⁴)

is 36y⁸ - 8x⁷ + 18x⁵y⁴ - 12x²y⁴.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, A multiplication of two polynomials (2x⁵ + 3y⁴)(- 4x² + 9y⁴).

= 2x⁵(- 4x² + 9y⁴) + 3y⁴(- 4x² + 9y⁴).

= - 8x⁷ + 18x⁵y⁴ - 12x²y⁴ + 36y⁸.  (multiplication of the same base is the

                                                                                addition of exponents)                                                                                                              

= 36y⁸ - 8x⁷ + 18x⁵y⁴ - 12x²y⁴.

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The value of x is 1.75 and y is 5. The solution is obtained using properties of congruent triangles.

What is a congruent triangle?

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 triangles are congruent by SAS congruency because

AC = CD (Given)

∠ACB = ∠DCE ( Vertically opposite angles)

BC = CE  (Given)

Thus, Triangle ABC ≅ Triangle DEC

Since, the triangles are congruent, therefore

⇒AC = CD

⇒4y-6 = 2x+6   ...(1)

Also, BC = CE

⇒3y+1 = 4x

⇒(3y+1)/4 = x    ...(2)

Now, substituting the value of x in (1), we get,

⇒4y-6 = 2(3y+1)/4+(6)

⇒4y-6 = (6y+2 +24)/4

⇒16y-24 = 6y+2 +24

⇒10y = 50

⇒y = 5

Now putting the value of y in (2), we get

⇒(3(2)+1)/4 = x

⇒7/4 = x

⇒ x = 1.75

Hence, the value of x is 1.75 and y is 5.

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The amount that Junior would be charged for interest, given his credit card APR would be B. $44.29

To calculate the amount of interest charged on a credit card balance, you can use the formula:

Interest = (APR / 365 days) x Balance x Days in the billing period

In this case, the APR is 21.99% and the monthly balance is $2, 416.91.

The APR must be converted to a decimal, so 21.99% becomes 0.2199

So, the Interest = (0.2199 / 365) x 2, 416.91 x 30

= $ 44.29

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