Find the value of X and Y. Write your radical in simplest form. Exact answers only.
to
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y = (x - 4) (x - 4) The factored quadratic function (x - 2) has a vertex with an x-coordinate of 3, and two unique roots.

The study of mathematics covers numbers and their variations, equations and related structures, shapes and their locations, and locations where they can be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)

Vertex form of a quadratic equation: (h,k) is vertex

y = a(x-h)^2 + k

The x of the vertex needs to equal 3

y = a(x-3)^2 + k

y = (x-3)^2 - 1

y = x^2 -6x + 8

y = (x - 4) (x - 4) The factored quadratic function (x - 2) has a vertex with an x-coordinate of 3, and two unique roots.

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Total discount ticket at the amusement park were 51. If 75% of the sold ticket were discounted tickets and if the amusement park sold 68 tickets in all.

Total number of ticket sold = 68

75% of them were discount tickets, = 75 × 68/100

= 51 tickets

So 51 tickets were discount tickets and (68-51) = 17 tickets were without discount tickets. We can also calculate the without discount ticket by a different method. Remaining 25% tickets were the without discount tickets. So,

= 25 × 68/100

= 17 Tickets

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The area of the triangle GHJ is 48 square units.

The area of a triangle can be found using the formula:

Area = (1/2) * base * height.

In this question, we are given that triangle GHJ has a base of 12 units and a height of 8 units. To find the area of the triangle, we simply substitute these values into the formula and solve.

Area = (1/2) * 12 * 8 = 48 square units

To be more specific, first, we multiply the base and height together to get 12*8 = 96. Then we divide 96 by 2 to get 48. Therefore, the area of triangle GHJ is 48 square units.

It's important to note that the base and height of a triangle must be perpendicular to each other in order for the formula to be accurate. Also, the unit of measurement used for the base and height must be consistent, otherwise, the area calculated will not be correct.

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A triangle GHJ has a base of 12 units and a height of 8 units. What is the area of the triangle GHJ?

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The slope of the green line is -4/3.

The correct option is C.

What is the slope of the line?

The slope of a line is a measure of how steep the line is and the direction it is going. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on the line.

The slope of a line is often represented by the letter "m" and can be calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

It is given that the lines graphed below are parallel.

We know that if two line having slopes m₁ and m₂ are parallel, then

m1 = m2

In other words, the slopes of two parallel lines are the same.

The slope of the red line is -4/3 and it is parallel to the green line. It means the slope of red and green line are the same.

The slope of green line = Slope of the red line

The slope of the green line = -4/3

Hence, The slope of the green line is -4/3.

The correct option is C.

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The slope of the green line is -4/3. The correct option is C.

What is the slope of the line?

The slope of a line is a measure of how steep the line is and the direction it is going. It is defined as the ratio of the "rise" (the change in the y-coordinate) to the "run" (the change in the x-coordinate) between two points on the line.

The slope of a line is often represented by the letter "m" and can be calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

It is given that the lines graphed below are parallel.

We know that if two line having slopes m₁ and m₂ are parallel, then

m1 = m2

In other words, the slopes of two parallel lines are the same.

The slope of the red line is -4/3 and it is parallel to the green line. It means the slope of red and green line are the same.

The slope of green line = Slope of the red line

The slope of the green line = -4/3

Hence, The slope of the green line is -4/3.

The correct option is C.

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To obtain how fast the ball traveling 2 seconds after it is thrown, we differentiate the position equation with respect to time once;

dh(t) =  d  (-16[tex]t^{2}[/tex] + 40t +5 )

dt        dt

dh(t) = -32t  + 40

dt

with t= 2:

h'(2) =-32 (2) +40

h'(2) =-24 ft/s.

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The amount of diesel remaining after traveling more than 28 miles will always be greater than or equal to 0.

If a vehicle uses diesel fuel, the amount of diesel remaining after traveling more than 28 miles will depend on the efficiency of the vehicle and the total capacity of the tank. We can express this as an inequality by saying that the diesel remaining will always be greater than or equal to 0.

diesel remaining ≥ 0

The amount of diesel remaining after traveling more than 28 miles will always be greater than or equal to 0.

The amount of diesel remaining after traveling more than 28 miles will depend on the efficiency of the vehicle and the total capacity of the tank. We can express this as an inequality, which states that the diesel remaining will always be greater than or equal to 0. This means that no matter how far the vehicle has traveled, there will always be some diesel left in the tank.

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The Volume of shape Q is 25,600 cm³.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared.

Let z be the scale factor

x be the surface area of shape Q

and, y be the surface area of shape P

So, z²=x/y

we have,

x = 2880 cm², y= 720 cm²

z² = 2880/720

z² = 4

z = 2

Now, If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

z³ = x/y

We have z= 2 and y = 3200 cm³

So, 2³ = x/3200

x = 8×3200

x = 25,600 cm³

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The ratio between the weights, giving how much Piglio is heavier than Whiskers, is given as follows:

1.5.

The ratio between two amounts a and b is obtained applying the proportion between these two amounts, that is, dividing a by b, as follows:

Ratio = a/b.

Which gives how many times greater the measure a is than the measure b, if the ratio is greater than 1.

The weight for each cat in this problem is given as follows:

The ratio between the weights of Piglio and Whiskers is given as follows:

Ratio = 4/2.67

Ratio = 1.5.

Meaning that Piglio is 1.5 times heavier than Whiskers.

Whisker's weight is given as follows: 2 and 2/3 kg.

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The length of side of the cube with 181 square inches surface area is 5.5 inches

The information that was provided indicates that the surface area of the cube is 181.5 square inches. A cube's surface area is calculated as the square of the length of each side multiplied by 6. The formula to use in order to get the total surface area of a cube is = 6a²

Where "a" represents the side of the cube.

As a result, 6a² = 181.5 square inches

a² = 181.5/6

a² = 30.25

a² = √30.25

a = 5.5 inches

Therefore, each face of the cube is 5.5 inches on a side.

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The number of the cans that is produced is 5832.

We know that the term direct proportion has to do with a case in which one of the variables is increasing and the other is also increasing along side. This implies that the two variables can be seen to increase at the same time.

We have that the relationship of the process can be given as shown in question in simple format as; y = 243x where;

x = Number of hours

y = Number of cans

After 24 hours, we have;

y = 243(24)

y = 5832

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By using the ratio formula, the number of doughnuts that will be consumed of 8 students in the time period of 9 minutes is 24 doughnuts.

The ratio formula compares the connection between two quantities or numbers. In this case, we are given that:

2 students can eat 4 doughnuts in 6 minutes

By using the ratio formula, 1 student can eat = 4/2 = 2 doughnuts in 6 minutes

It takes an average student about 3 minutes to consume a doughnut using the formula= 6/2 = 3 minutes

In one minute, the amount of doughnut can be consumed by a student is 1/3 of a doughnut

This method can be used to predict how many doughnuts 8 students can consume in 9 minutes:

X = 8 x 9 x (1/3) = 24 doughnuts

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The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.

What is perimeter?
A boundary is a closed path that encompasses, encircles, or delimits a two-dimensional shape or a one-dimensional length. A circle's or an ellipse's perimeter is its outermost portion. Numerous applications in real life involve the perimeter calculation. The radius of a shape's edge is known as the perimeter. By summing the lengths of the sides of various forms, discover how to calculate the perimeter. By multiplying the lengths of the sides, one can always get a shape's perimeter. The area surrounding an object is called its perimeter. An enclosed garden is one example at your home. The distance around anything is called its perimeter. A 200-foot fence will be needed for a yard that is 50 feet by 50 feet.

Ratio factor of  A to B = 7:2

Proportion between the perimeters = 7/2

We now understand that a shape's perimeter equals the sum of all its sides. Consequently, using the values from the provided figure, enter the following expression:

A1 / 9+5+9+12 = 7/2

A1 = (7*35)/2

A1 = 122.50 units.

The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.

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Answer: The exponential form should be 10⁵=9x+1 instead of 9x+1=10⁵

Step-by-step explanation:

The exponential form of a logarithm should be the other way around.

The set of properties for inequalities is as follows:

1. Additive characteristics of inequality

2. Inequality's subtraction property

3. The inequality's multiplication property

4. The unequal division property

5. Converse Property

An inequality is a relationship between two expressions that can be described mathematically and can be represented by any of the following symbols: >, <, ≤, ≥, =, and ≠.

The set of properties for inequalities is as follows:

1. Additive characteristics of inequality: The inequality remains the same even if both sides are given the same value.

2. Inequality's subtraction property: The inequality remains the same even after deducting the same amount from each side of it.

3. The inequality's multiplication property: Take p and q, two positive numbers. When p and q are both multiplied by the same positive value, the inequality stays the same. However, the inequality changes when p and q are both multiplied by the same negative value.

4. The unequal division property: Take p and q, two positive numbers. When p and q are both divided by the same positive number, the inequality is unaffected. However, the inequality is reversed when p and q are split by the same negative value.

5. Converse Property: According to the converse property, all we need to do to reverse the inequality symbol is flip the number.

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Polygonal Modeling: a type of 3D modeling that uses points, lines, and polygons to create a 3D object. NURBS Modeling: a type of 3D modeling that uses mathematical equations to create smooth curves and surfaces. Subdivision Modeling: a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes.

1. Polygonal Modeling: This type of 3D modeling uses points, lines, and polygons to create a 3D object. The polygons are connected together to create the 3D shape, and then textures and colors can be applied to the shape. This type of modeling is often used to create characters and environments for video games and animations.

2. NURBS Modeling: NURBS stands for Non-Uniform Rational B-Splines. This type of 3D modeling uses mathematical equations to create smooth curves and surfaces. NURBS modeling is often used for creating organic shapes such as cars and furniture.

3. Subdivision Modeling: Subdivision modeling is a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes. This type of modeling is often used for creating characters and creatures for video games and animations.

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The time taken by 5 large solar panels and 3 small solar panels to charge a car, found using the unitary method, is 576 minutes.

The unitary approach is a method for problem-solving that involves first determining the value of a single unit, and then determining the necessary value by multiplying the single unit value.

Given

Time taken by 2 large solar panels to charge a car = 240 minutes

Time taken by 2 large solar panels to charge a car

       = Time taken by 6 small solar panels to charge a car = 240 minutes

The unitary method can be used to find the charging times of 1 large and 1 small solar panel.

The time taken by 1 solar panel is greater than time taken by 2 large and 6 small solar panels.

Time taken by 1 small solar panel = 240 * 6 = 1440 minutes

Time taken by 1 large solar panel = 240 * 2 = 480 minutes

Therefore the time taken by 5 large solar panels and 3 small solar panels to charge a car = (480/5)+ (1440/3) =96 + 480= 576 minutes.                    

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The velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: V(x)=0.9×4.4√x

Thus if x=100feet or 30.47 m putting this value in the equation we get

V(30.47)=0.9×4.4√30.47

             = 21.86 m/sec

Hence, the velocity of the object dropped from a height of 100 feet is equal to 21.86 m/sec

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Answer:

Drew is incorrect

Step-by-step explanation:

Let the number be x such that if the product of the number and 4 is 1.08 then

x * 4 = 1.08

Divide both sides by 4

x = 1.08/4

= 0.27

Drew is incorrect because the result (1.08) has 2 decimal places and not one like he concluded. The number of digits before the decimal point for the numbers being multiplied must be 2.

The length of the beach towel is 4.135 feet.

Area of a two dimensional shape is the total region which is bounded by the object's shape

Given that

Hugo needs a total of 22.23 square feet of terry cloth to make a beach towel and a beach bag.

Total area of the terry cloth = 22.23 square feet

The beach bag requires 5.13 square feet of cloth.

Area of cloth for beach bag = 5.13 square feet

Area of the cloth for beach towel = 22.23 - 5.13 = 17.1

Area of the beach towel is 17.1 square feet.

Assuming the towel is square shape,

(Length of the towel)² = 17.1

Length of the towel = √(17.1) = 4.135

Hence the length of the beach towel is 4.135 feet.

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The grouping symbols commonly used in mathematics are the following:

Now, According to the question:

What are the 4 types of grouping symbols?

The grouping symbols commonly used in mathematics are the following:

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

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So on solving the provided question we can say that we know that all angles of  Quadrilateral is 90, 4x - 2 = 90; x = 22

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

we know that all angles of  Quadrilateral is 90

4x - 2 = 90

4x = 88

x = 22

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To find the equation of the line, we can use the two points on the line.

An equation is a mathematical statement that expresses the relationship between two or more variables, or a condition that two or more expressions must satisfy. An equation typically involves an equal sign, with an expression on either side of the sign. The expressions on each side of the equation can contain constants, variables, functions, operations, and other mathematical symbols. Equations are used to solve problems in mathematics, physics, engineering, chemistry, economics, and other scientific and practical fields.

The distance between a point (P) and a line (L) can be found using the following formula:
d = |(ax + by + c)|/√(a^2 + b^2)

where (a, b, c) are the coefficients of the line equation, and (x, y) are the coordinates of the point.

To find the equation of the line, we can use the two points on the line. Let's say these two points are (x1, y1) and (x2, y2). We can calculate the equation of the line using the following formula:

a = (y2 - y1)/(x2 - x1)
b = -1
c = y1 - ax1

Using these equations, we can easily calculate the distance between the point and the line.

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The number of solutions which the system of equations has is: A. no solution.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (0, 4), a linear equation of the first line can be calculated in slope-intercept form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (5 - 4)/(3 - 0)(x - 0)

y = x/3 + 4

For the second line, we have:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 1 = (1 + 1)/(6 - 0)(x - 0)

y = x/3 + 1

In conclusion, the system of linear equations has no solution because it represents parallel lines.

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The value of k in the equation is  3x + e^(x^2-3x/2)

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

y = 2ln(k - 3x) + x^2 - 3x

The x-axis is the set of points where y = 0. To find where the curve crosses the x-axis, we need to solve the equation y = 0 for x.

y = 2ln(k - 3x) + x^2 - 3x

so

0 = 2ln(k - 3x) + x^2 - 3x

We can re-arrange this equation to solve for x:

x^2 - 3x + 2ln(k - 3x) = 0

Now we can use the quadratic formula to find x.

x = (3 +/- sqrt(3^2 - 4(2ln(k - 3x))))/2

Now we know that there is only one root, we can pick the positive value and solve for k using k-3x = e^(x^2-3x/2)

k = 3x + e^(x^2-3x/2)

This is the final solution for k.

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No, the square root of 1 is 1, but 1 is not equal to the square root of 1. The square root of a number, represented by the symbol √, is a value that, when multiplied by itself, gives the original number.

For example, the square root of 4 is 2, because 2 x 2 = 4. In the case of 1, the square root is also 1, because 1 x 1 = 1.

In mathematics, the square root of a number is always non-negative, real number. It is positive for positive numbers and zero for zero. So, in short, the square root of 1 is 1, but 1 is not equal to the square root of 1. It is just a value that gives 1 when multiplied with itself.

It's important to note that the square root is not a number but an operator, an action which you perform on a number. The square root of a number is a value that, when multiplied by itself, gives the original number.

In this case, the square root of 1 is 1, which means that 1 multiplied by 1 is 1.

Also, it's worth mentioning that there are two types of square roots: principal square root and non-principal square roots. Principal square root is the positive value of the square root and non-principal square roots are the negative value of the square root.

In this case, the square root of 1 is 1, which is the positive value of the square root.

In conclusion, the square root of 1 is 1, and it is the positive value of the square root, but 1 is not equal to the square root of 1, as the square root is a value that gives the original number when multiplied by itself.

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Circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

Thus, circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.

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Circle, triangle, rectangle, rhombus, square, and trapezoid are the 5 common geometric shapes.

Any building, whether open or closed, with a specific shape and characteristics composed of lines, curves, and points is referred to as a geometric shape. Squares, rectangles, circles, cones, cylinders, spheres, and so on are a few examples of well-known geometric forms. Each of these forms has specific characteristics that set them apart from other shapes.

Figures enclosed by a boundary created by combining a specific number of curves, points, and line segments are referred to as geometric forms. Every shape has a distinctive name like a circle, square, triangle, or rectangle, for example. In everyday life, we are surrounded by a variety of fundamental geometric forms, such as the triangle-shaped pizza slice, rectangle-shaped doors and windows, and many more.

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The random variable X represents the length of each engineering conference, and is measured in days.

The normal distribution should be used for this problem, as the underlying population is normal. The normal distribution is a continuous probability distribution that is characterized by a symmetric bell-shaped curve. It is a useful model for events that follow a normal or Gaussian pattern, such as the lengths of engineering conferences.

c. i. The 95% confidence interval for the population mean length of engineering conferences is (3.38, 4.50) days.

ii. The graph of the 95% confidence interval for the population mean length of engineering conferences is shown below.

iii. The error bound for the 95% confidence interval is 0.77 days. This can be calculated using the formula: Error Bound = 1.96*(standard deviation/√sample size). In this case, the error bound is calculated as: 1.96 * (1.28/√84) = 0.77.

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