In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation.

Answer:

12.7 inches

Step-by-step explanation:

We know that the length of a diagonal is :

[tex]d=a\sqrt{2}[/tex]

Here d = Diagonal of a square

a = Side of a square

Given:

The perimeter of a Square is 36 inches.

Since the formula for the perimeter of a square is 4a

Thus, 4a = 36

⇒ a = 36÷4 = 9 inches

Now,

d = 9×√2 = 12.7 inches

Hence the length of a square is 12.7 inches.

Area formula: A = (base)(height)

A = 24 x 16

= 384 cm^2

The volume of the composite figure is 408 cm³

An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.

The volume of the composite figure is:

Volume = area of base * height

Substituting:

Base area = (14 * 3) + (1/2)(5 + (14-6))(7 - 3) = 68 cm²; height = 6 cm

Volume = area of base * height = 68 cm² * 6 cm = 408 cm³

The volume is 408 cm³

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[tex]\cfrac{1}{6}+\cfrac{3}{4}-\cfrac{2}{3}\implies \cfrac{(2)1~~ + ~~(3)3~~ - ~~(4)2}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{2+9-8}{12}\implies \cfrac{3}{12}\implies \cfrac{1}{4}[/tex]

The function will be g(x ) = x² + 2

A function is a special form of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation rather than a function is depicted in the above graph since one is mapped to two different values.

But, if one were instead mapped to a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly.

The function machine receives the x-values as input. After finishing its operations, the function machine produces the y-values. Any function may be the one within.

g(x) = x2 + 2

Now we need to but this in vertex form.

If you graph this equation, you will see that the vertex is (0,2). Plug this in to (h,k) in the equation. The value of a is just 1 because you didn't multiply by anything during the transformation.

So you get g(x) = (x-0)2 + 2 = x2 + 2

This ends up just being the same as the standard form of the equation

Hence, The function will be g(x ) = x² + 2

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Zeros, vertex, and end behavior can all be used to determine the height that the golf ball travels from its initial location to the point where the golf ball starts falling towards the ground.

Graph is a data structure that consists of a set of nodes and edges that connect those nodes. Nodes are used to represent entities, such as people, places, or objects, and edges are used to represent the connections between those entities. Graphs are used to represent relationships between data, such as in networks, social media, and biological systems. Graphs can also be used to represent mathematical equations, as in function graphs.

Zeros, or x-intercepts, are the points where the graph of the quadratic function crosses the x-axis. The vertex is the highest point of the graph and can be used to determine the peak of the golf ball's trajectory. Finally, the end behavior of the graph can be used to determine how the graph will change as x increases or decreases without bound. This can be used to determine the point at which the golf ball begins to fall towards the ground.

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The width of the rectangle is calculated as: 11 inches

The formula for area of a rectangle is:

A = l*w.  

Since the area is 33 in², then;

33 = x(x + 8) would be the equation to solve for x.

Now, you need to put the equation in standard form.  

x² + 8x - 33 = 0.

To complete the square you need to add 33 to both sides.  

Now you have x² + 8x = 33  

Take the coefficient for the x term (8) and divide by 2.  Now square it.  That would be 4², so 16.  

Now you have x² + 8x + 16 = 49

(x + 4)² = 49

Take  the square root of both sides and you have;

x + 4 = 7.  

Therefore, x = 3 (the short side) and 11 is the long side.

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The only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.

What is a valid triangle?

A valid triangle is a three-sided polygon that satisfies the following conditions:

The sum of the lengths of any two sides of the triangle is greater than the length of the third side.

The lengths of all three sides of the triangle are greater than zero.

Adam should use the dimensions 40 in., 44 in., 58 in. for a triangular frame to form a right triangle.

To determine if a right triangle can be formed, we need to check if the Pythagorean theorem is satisfied, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the longest side (the hypotenuse).

Let's check each set of dimensions:

For 25 in., 60 in., 65 in.:

25^2 + 60^2 = 625 + 3600 = 4225

65^2 = 4225

The Pythagorean theorem is satisfied, so a right triangle can be formed. However, this triangle is not a valid option for Adam because the lengths are too short for building walls.

For 40 in., 44 in., 58 in.:

40^2 + 44^2 = 1600 + 1936 = 3536

58^2 = 3364

The Pythagorean theorem is not satisfied, so a right triangle cannot be formed using these dimensions.

For 50 in., 110 in., 130 in.:

50^2 + 110^2 = 2500 + 12100 = 14600

130^2 = 16900

The Pythagorean theorem is satisfied, so a right triangle can be formed.

For 130 in., 50 in., 60 in.:

50^2 + 60^2 = 2500 + 3600 = 6100

130^2 = 16900

The Pythagorean theorem is satisfied, so a right triangle can be formed.

Out of the options given, only the dimensions 50 in., 110 in., 130 in. and 130 in., 50 in., 60 in. satisfy the Pythagorean theorem, but both are too large for building walls.

Therefore, the only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.

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Therefore , the solution of the given problem of expressions comes out to be  16 ounces are equal to 1 pound.

There is a need for mathematical operations like multiplying, splitting, joining, and currently removing. If they were combined, it would read as follows: A mathematical formula, some data, and an equation Values, elements, and mathematical operations like additions, deductions, errors, subdivisions, and algebraic formulas all go into making a declaration of truth. It is possible to assess and analyse words and sentences.

Here,

=> 6x - 3 is an expression that is equal to 3(2x-1).

We can spread the 3: to see why this is true.

=> 3(2x-1) = 6x - 3

There are 5,280 feet in a mile, as the saying goes.

5280 feet make up a mile.

Simply put, this phrase means that 5,280 feet is equal to 1 mile.

One way to say "there are 16 ounces in a pound" is:

A pound weighs 16 ounces.

Simply put, this phrase means that 16 ounces are equal to 1 pound.

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The correct descriptions of the right-hand and left-hand behavior of the graph of the polynomial function y = 2x^2 - 3x + 5 are:

Right-handed actions: As x +, y +

Left-handed actions: As x -, y +

The positive coefficient of the x2 term (2) causes the parabola on the graph of the polynomial function y = 2x^2 - 3x + 5  to open upwards.

The y-values of the function approach positive infinity as x approaches negative infinity (i.e., x -), and vice versa. This is known as the left-hand behaviour of the graph.

As x approaches positive infinity (i.e., x → +∞), the y-values of the function also approach positive infinity (i.e., y → +∞). This is referred to as the graph's right-hand behaviour.

As a result, the following statements accurately describe the right-hand and left-hand behaviour of the graph of the polynomial function y = 2x^2 - 3x + 5 :

Right-handed actions: As x +, y +

Left-handed actions: As x -, y +

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The answer is "no," the ordered pair (4, 28) is not a solution of the equation.

A solution of an equation is a value or set of values that makes the equation a true statement when substituted for the variable(s) in the equation.

To determine if the ordered pair (4, 28) is a solution of the equation 7 = y - 5x, we need to substitute the values x = 4 and y = 28 into the equation and check if it is a true statement:

7 = y - 5x

7 = 28 - 5(4) // Substitute x = 4 and y = 28

7 = 28 - 20

7 = 8

The statement 7 = 8 is not true, which means that the ordered pair (4, 28) is not a solution of the equation 7 = y - 5x. Therefore, the answer is "no," the ordered pair (4, 28) is not a solution of the equation.

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Answer:

d

Step-by-step explanation:

Answer:

The question is incomplete.

Step-by-step explanation:

Answer: (2,0) = (-2,-2) (2,2) = (-2,0) (1,0) = (-3,-2) (0,2) = (-4,0)

Step-by-step explanation:

The solution with the concern of the given problem of circle and tangent is the picture showing the relation between a circle and a line.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

1.

In the question, we are given Circle with center F and tnagent ED to the circle.

2.

The image is of the circle and tangent.

3.

The picture describes the circumference of the circle. when unfolding the circle comes in form of a straight line.

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Answer: B

Step-by-step explanation: Expressions that include x within the denominator can be solved to find values that cannot be expressed within the domain of the graph. Because there are clear vertical asymptotes at x=1 and x=5, the graph is formed around these areas. The main difference between B and C is that in order for the answer to be C, the graph must pass through y=1, and the graph displayed does not represent that.

Consequently, y = (4/5)x - 4 is the equation of the line with a slope of 4/5 and a y-intercept of (0,-4).

Slope is a mathematical term that describes how steep a path is. It gives an explanation of the rate of rise or decline of the line as it moves horizontally along the x-axis. The percentage of the difference in the y-coordinate to the change in the x-coordinate at all between the two locations on a line is known as the slope of the line. In other terms, it is the line's "rise" over its "run". The letter "m" stands for slope, and the following formula is used to determine it:

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

given

In slope-intercept form, a line's equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Given that the y-intercept is (0, -4) and the slope is 4/5, we can enter these numbers into the slope-intercept form to obtain:

y = (4/5)x - 4

Consequently, y = (4/5)x - 4 is the equation of the line with a slope of 4/5 and a y-intercept of (0,-4).

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Using Pythagοras theοrem, The length οf the bridge needed tο cοnnect Main Street and Secοnd Street is apprοximately 4.53 miles.

A basic geοmetry theοrem that deals with the sides οf a right triangle is knοwn as the Pythagοrean theοrem. Accοrding tο the theοrem, the square οf the length οf a right triangle's hypοtenuse—its lοngest side—is equal tο the sum οf the squares οf the lengths οf the triangle's οther twο sides, which are referred tο as its legs.

The fοllοwing is hοw the theοrem is written in mathematical nοtatiοn:

[tex]c^2 = a^2 + b^2[/tex]

Where a and b are the lengths οf the οther twο sides (legs) οf the right triangle and c is the length οf the hypοtenuse. The Pythagοrean equatiοn is a cοmmοn fοrm fοr expressing this relatiοnship.

Pythagοras, an ancient Greek mathematician, is credited with discοvering the Pythagοrean theοrem, which bears his name. It has several uses in physics, engineering, mathematics, and οther disciplines.

Tο determine the length οf the bridge needed tο cοnnect Main Street and Secοnd Street, we need tο find the distance between the twο streets.

We can dο this by using the Pythagοrean theοrem, which states that in a right triangle, the square οf the length οf the hypοtenuse (the lοngest side) is equal tο the sum οf the squares οf the lengths οf the οther twο sides.

In this case, we can think οf the bridge as the hypοtenuse οf a right triangle, with Main Street and Secοnd Street fοrming the οther twο sides. We can then use the Pythagοrean theοrem tο find the length οf the bridge as fοllοws:

Length οf the bridge = square rοot of ([tex]3.4^2 + 3^2[/tex])

= square roοt of (11.56 + 9)

= square roοt of 20.56

= 4.53 miles (rounded to twο decimal places)

Therefοre, the length of the bridge needed to cοnnect Main Street and Second Street is apprοximately 4.53 miles.

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Answer:

Step-by-step explanation:

14.7 N

Therefore, unitary method solution is in order to have enough turf to cover the amphitheatre, the city must purchase at least 6 pallets of it.

Take the lengths of this minute subsection and split the sum by two to complete a task using a variable unitary technique. The unit technique, in a nutshell, removes a wanted item both from the specific sets and color subsets. For instance, 40 pencils will cost Rs/kg ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality.

Here,

A is equal to (70)2/4, which is 15,386.78 square feet.

We split the area by the area covered by each roll of turf to determine the quantity of rolls necessary to cover this area:

Rolls Equals A / Rolls' surface area

Given that the size per roll is 30 square feet, we have:

15,386.78 rolls divided by 30 equals 512.89 rolls.

Ceil(number of rolls / 100) = minimal number of pallets

the smallest number larger than or equal to x, ceil(x), is. If we replace the value we discovered with the quantity of rolls, we get:

Ceil (512.89 / 100) = Ceil (5.1289) = Minimum number of boxes = 6

Therefore, in order to have enough turf to cover the amphitheatre, the city must purchase at least 6 pallets of it.

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The expression cos(a-b) is equivalent to cos(a)cos(b) + sin(a)sin(b), while the expression cos(a)cos(b) - sin(a)sin(b) is equivalent to cos(a+b).

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of the properties of trigonometric functions such as sine, cosine, and tangent, which are used to calculate the angles and sides of triangles.

in the given question,

The expression cos(a-b) is equivalent to cos(a)cos(b) + sin(a)sin(b), while the expression cos(a)cos(b) - sin(a)sin(b) is equivalent to cos(a+b).

Therefore, we can rewrite the expression cos(a-b) as cos(a)cos(b) + sin(a)sin(b) and then compare it to the expression cos(a)cos(b) - sin(a)sin(b) by changing the sign of the second term in the first expression:

By comparing these two expressions, we can see that they are very similar, except that the sign of the second term is different. Specifically, we have:

So, we can say that the values of cos(a-b) and cos(a)cos(b) - sin(a)sin(b) are related by the sign of the sin(a)sin(b) term. If the sign is positive in the first expression, then it is negative in the second expression and vice versa.

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Using the rules of writing a pattern, we found the missing numbers and found the pattern:

52, 62, 72, 82

What is a pattern?

A pattern in mathematics is a series of recurring figures, shapes, or numbers. Any kind of event or thing can be connected to a pattern. A pattern has a rule that identifies the items that are part of the pattern and those that are not. There are many distinct kinds of patterns, including word patterns, logic patterns, image patterns, and number patterns. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series. The number of patterns can be limitless or finite.

We are asked to find the missing digits to complete the pattern.

5_, 62, _2, _2

So the numbers have two digits.

For this pattern, the last three numbers end with the digit 2.

So the first number should be 52.

Now the difference between 52 and 62 is 10.

Since the last two numbers also have an ending digit as 2, the difference between two consecutive numbers should be 10.

Then the pattern is:

52, 62, 72, 82.

Therefore using the rules of writing a pattern, we found the missing numbers and found the pattern:

52, 62, 72, 82

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binary operation has at most one identity element.

A binary operation is a mathematical operation that takes two elements from a set and combines them to produce a third element in the same set. In other words, it is an operation that involves two operands, which can be numbers, variables, or other mathematical objects.

Let's suppose that a binary operation "⋆" has two identity elements "e" and "f", where "e" and "f" are distinct. This means that for any element "a" in the set on which the binary operation is defined, we have:

a ⋆ e = a and f ⋆ a = a (since "e" and "f" are identity elements)

Now, let's consider what happens when we apply the binary operation "⋆" to "e" and "f":

e ⋆ f = f (since "e" is an identity element)

e ⋆ f = e (since "f" is an identity element)

This means that "f = e", which contradicts our assumption that "e" and "f" are distinct. Therefore, it is not possible for a binary operation to have two distinct identity elements.

Hence, we can conclude that a binary operation has at most one identity element.

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Answer:

If the marlin weighs over 1,500 pounds, and it "dresses out two thirds of that," that means that the weight of the meat that can be harvested from the marlin is 2/3 of 1,500 pounds, or 1,000 pounds (since 2/3 x 1,500 = 1,000).

If the price per pound is thirty cents, then the total value of the meat is 1,000 x 0.30 = $300.

Let me solve it down for you :)

The shape is a cuboid, so its dimensions will be:

[tex] \sf \: Surface \: area \: of \: cuboid = 2(lb + bh + hl)[/tex]

[tex] \sf \: S.A. = 2(12 \times 5 + 5 \times 10 + 12 \times 10)[/tex]

[tex] \sf \: S.A. = 2(60+ 50 + 120)[/tex]

[tex] \sf \: S.A. = 2(230)[/tex]

[tex] \sf \: S.A. = 460 \: {m}^{2} [/tex]

Dimensions of the cuboid:

[tex] \sf \: Volume = l \times b \times h[/tex]

[tex] \sf \: Volume = 12\times 5 \times 10[/tex]

[tex] \sf \: Volume = 600 \: {m}^{3} [/tex]

Convert m to cm, according to the question:

600 Cubic meter =

600,000,000 Cubic Centimeters

An equation can be solved by finding the value of the variables.

Solving an equation involves finding the value(s) of the variable(s) that make the equation true. The process for solving an equation depends on the type of equation and the specific instructions or conditions given.

1) 18 - a/16 = 17

18 - a = 16 * 17

18 - a = 272

a = 18 - 272

a = -254

2) 15 - n/-10 = -21

15 - n = (-21) * (-10)

15 - n = 210

n = 15 - 210

n = -195

3) 12 + y/-20 = 18

12 + y = 18 * (-20)

y = -372

4) c + 17/-26 = -5

c + 17 = (-5) (-26)

c = 113

5) 3c + 12 = 36

c = 36 - 12/3

c = 8

6) 1/5 f - 9 = -24

1/5 f  = -24 + 9

1/5 f = -15

f = -15 * 5

f = -75

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The approximate diameter of the tin would be 12.9 centimeters.

Diameter is a straight line passing through the center of a circle, or any other curved shape, and connecting two points on the circumference. It is the longest line that can be drawn within a circle and its length is twice the radius. It is also used in measuring the size of objects and distances in the universe. The term is also used in geometry to refer to the size or width of a triangle, square, or other shapes.

To measure the diameter of a tin which is 750 gram, one needs to use a ruler or measuring tape. First, one needs to weigh the tin using a scale or balance. Once the weight is known, it can be used to calculate the approximate diameter of the tin.

To find the diameter, one needs to use the formula: Diameter = 2 x (cube root of volume). The volume of the tin can be calculated by multiplying the weight of the tin (in grams) by 0.52.

Therefore, for a tin weighing 750 grams, the approximate volume would be 390 cubic centimeters. To find the diameter, one needs to take the cube root of 390, which is 6.47.

Therefore, the approximate diameter of the tin would be 12.9 centimeters.

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The true statement of the inequality is (d) Yes, because the total cost is $305, and $305 ≤ $315.​

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

The cost of each gift is $55

So, we have

5(55+4) +10 <= $315

When expanded, we have

305 <= $315

The above inequality is true

Hence, the solution is (d)

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Answer:

See Picture

Step-by-step explanation:

The original sin(x) function starts at (0,0) and oscillates around the x-axis between y=1 and y=-1, intercepting it in intervals of π.

To graph sin(x)-2 then, we simply need to graph a sin(x) function 2 units lower.