The sum of the interior angles of a polygon is 20 x 180.

Work out the number of sides of the polygon.

sides

The x-intercept of the graph of y = x² - 4x + 4 is x = 2.

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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Answer:

Kumain ka Ng pansit para ka Maka sagot

Step-by-step explanation:

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The amount of money in the account after 6 years is $68,847.56

To solve this problem, you can use the formula for compound interest,

where V is the final value of the account, P is the initial principal, r is the annual interest rate (expressed as a decimal), and t is the number of years the money is invested.

The formula for compound interest, V = Pe^(rt) is used to calculate the future value of an investment. It takes into account the effect of compounding, which means that interest is earned not only on the initial investment but also on the accumulated interest over time.

Plugging in the given values, we have

V = 51200e^(0.0546) = 51200e^0.324. e^0.324 is approximately 1.38, so the final value of the account is 512001.38 = $68,847.56

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The distance and bearing of the boat from its original location are about 183.33 miles, N71.97°E

A bearing is a description of the amount by which a north or south headed line is deflected in the eastern or western direction.

The initial direction in which the boat is traveling = Due east

The distance the boat travels in the direction due east = 130 miles

The distance the boat travels in the direction N38°E = 72 miles

Therefore;

The distance the boat has traveled from its original location is found using the law of cosines as follows;

The included angle between the 130 miles distance the boat travels east and the 72 miles distance the boat travels N38°E = 90° + 38° = 128°

Let d represent the distance of the boat from its original location, we get;

d² = 130² + 72² - 2 × 130 × 72 × cos(128°) ≈ 33609.1828181

d ≈ √(33609.1828181) ≈ 183.33

The distance of the boat from its original location is about 183.33 miles

Let the angle formed by the direction of the boat to its destination and the path the boat travels east, according to the law of sines, we get;

183.33/(sin(128°) ≈ 72/(sin(B))

(sin(B)) ≈ 72 × (sin(128°))/183.33

m∠B ≈ arcsin(72 × (sin(128°))/183.33) ≈ 18.03°

The bearing of the boat from its original location is; N(90° - 18.03°)E = N71.97°E

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A right triangle is formed by the provided sides 6 cm, 10 cm, and 8 cm

Given that a triangle has sides measuring 6 cm, 10 cm, and 8 cm.

The question is whether a right triangle is formed by the specified sides.

The Pythagorean theorem states that the sum of the squares of the base and height is equal to the square of the hypotenuse.

Hypothesis 2 Equals Base 2 plus (Altitude)2

Make the hypotenuse 10 cm long.

Specify 6 cm for the base and 8 cm for the perpendicular.

(Hypotenuse)2 LHS (Hypotenuse)

RHS: (Base)2 + (Altitude)2 (Base)2 + (Altitude)2 = (6)2 + 2 = (10)2 = 100 (8)

LHS = RHS: 2 = 36 + 64 = 100

The sides provided meet the requirements for a right triangle.

As a result, a right triangle is formed by the provided sides.

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If triangle JKL is dilated by a scale factor of 3,cos(bº)=4/5.

Trigonometric By definition, ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

If you know the lengths of two of the triangle's sides, you can use trigonometric ratios to get the measurements of one (or both) of the acute angles.

tan(b)=P/B=3/4

sin(b)=P/H=3/5

cos(b)=B/H= To find

B=4, H=5

cos(b)=4/5

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Therefore , the solution of the given problem of algorithm comes out to be the halting problem can be demonstrated to be indecidable and so unsolvable.

A method for performing calculations or solving problems is known as an algorithm. Algorithms act as a thorough set of instructions that step-by-step direct hardware- or software-based processes through a series of planned activities. In every aspect of IT area, algorithms are utilized regularly.

Here,

The halting problem is one of the most popular unsolved issues. It poses the following inquiry:

Does M halt when it is given the input w for an arbitrary Turing machine over the parameters alphabet = a, b and an arbitrary string w over

 The halting problem can be demonstrated to be indecidable and so unsolvable.

Therefore , the solution of the given problem of algorithm comes out to be the halting problem can be demonstrated to be indecidable and so unsolvable.

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The required statement is RS/VU = ST/UT and angle S is congruent-to angle U. Option A is correct.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

The figure of the triangle is not given the quesiton, An figure is attached after the solution regarding the solution,

From diagram,
Consider the triangle RST and triangle VUT

ST/UT = 2

∠S = ∠U both are of 90°
RS/VU = 2.

So, triangles are similar by the SAS similarity theorem.

Thus, the required statement is RS/VU = ST/UT and angle S is congruent-to angle U. Option A is correct.

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Number of pens  x=10.

Number of pencils  y=30.

The Five Principles are: freedom, efficiency, mutuality, responsibility, and quality. Victoria that she always incorporates The Five Principles into her conversations with other businesses, government officials, and other partners and leaders. The writing core is tougher and leaves a lighter trace on the paper as the number increases.

Let number of pens =x

And number of pencils =y

⇒ x+y=40

⇒(5+y)+(x−5)=4x

⇒3x=y

Substituting in above equations ;

⇒x+3x=40

⇒x=10

⇒y=30

∴number of pens =x=10

⇒number of pencils =y=30

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The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.

Now, According to the question:

Let's know:

What is Horizontal lines?

If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.

The equation is y = 4.

The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.

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The commission on the sale would be $62.5

To find the commission on a sale, you can use the following formula:

Commission = Sale Amount x Commission Rate

Sale Amount: the total value of the sale

Commission Rate: the percentage or decimal value of the commission rate (e.g. 5% = 0.05)

The commission on a sale can be calculated by multiplying the total sale amount by the commission rate.

In this case, the commission on a 1,250 sale with a commission rate of 5% would be:

= 1,250 x 0.05

= 62.5

So the commission on the sale would be $62.5

It's also worth noting that commission rate is given as a decimal and not a percentage. 5% is 0.05 as decimal.

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To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate.

A point is identified by its ordered pair of (x, y). The first number represents the x-coordinate, while the second represents the y-coordinate.

To graph a point, you draw a dot at the coordinates of the ordered pair. It's usually a good idea to begin at the beginning.

An ordered pair of integers, such as an x-coordinate, which is a number on the x-axis, and a y-coordinate, which is a number on the y-axis, can be used to identify each point. Parentheses are used to indicate ordered pairings (x-coordinate, y-coordinate). The starting point is at (0,0).

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Both the x- and y-axes have negative values in this quadrant.

The x-axis in the fourth quadrant has positive values, whereas the y-axis has negative numbers.

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from 1st through 4th and marked by Roman numerals: I (+; +), II (; +), III (; ), and IV (+; ).

The intersection of the x-axis (the horizontal number line) and the y-axis divides the coordinate plane into four equal pieces in the cartesian system (the vertical number line). These four regions are known as quadrants because they each account for one-quarter of the coordinate plane.

The third quadrant, known as Quadrant III, is located in the bottom left quadrant.

The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant.

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To solve x easily, shift the variables to one side, and shift all the other values including constants to the other side.

Solve for x means finding the value of x in an equation involving one variable that is x or with different variables like finding x in terms of y. Whatever the case is you are required to find  the value of x, for which the given equation holds true.

For example, if the equation is given as: 2x - 50 = 4

Now solve the tjis equation for x by keeping the term with variable x to one side, and shifting all the other values such as constants to the other side.

now

2x = 4 + 50

2x = 54

x = 54/2

x= 27

This is the required value of x which is obtained after solving the equation for x.

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Answer: 8

Step-by-step explanation:

Its a fish tank no fish can escape. So 10-2 because 2 fish died and that is 8.

So you have 8 fish.

Hope this helps

The cost  of hiring a van for 5 days is $235.

In this question, we have been given an equation c = 10 + 45d that represents the cost in pounds of hiring a van for days.

here c = cost in pounds

d = number of days

We need to find the cost  of hiring a van for 5 days.

Substitute the value d = 5 in given equation.

c = 10 + 45d

c = 10 + (45 × 5)

c = 10 + 225

c = 235 dollars

Therefore, the cost for 5 days is 235 dollars

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The equation 11 = −4x²−x³ is a cubic polynomial.

Polynomial:

A polynomial is an algebraic expression containing indefinites and constants. Polynomials can be thought of as dialects of mathematics. They are used to represent numbers in almost all areas of mathematics, and are used in specific areas of mathematics such as mathematics  Critical analysis. For example, 2x + 9 and x2 + 3x + 11 are polynomials.

Cubic Polynomial:

The cubic polynomial is the polynomial with the largest exponent of the variables. H. Order of variables as 3. Based on the degree, polynomials are divided into four types: zero polynomials, linear polynomials, second order polynomials, and third order polynomials. The general form of a cubic polynomial is p(x): ax³ + bx² + cx + d, where a ≠ 0. where a, b, and c are coefficients and d is a constant, all of which are real numbers. An equation involving a cubic polynomial is called a cubic equation. Examples of cubic polynomials are p(x): x³ − 5x² + 15x − 6 and

r(z): πz³ + (√2)10.

Now,

A cubic polynomial is a polynomial of degree 3. A cubic polynomial has the form f(x)=a₃x³ +a₂x² +a₁ x+ a₀

​Here, the polynomial 11 = −4x² −x³

or x³+4x² +11 = 0 is a polynomial of degree 3 with coefficients a₁ = 0,

a₂ =4, a₃​ =1 and constant a₀= 11.

Hence, 11 = −4x² −x³  is a cubic polynomial.

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Answer:

208

Step-by-step explanation:

60 percent of 520 is 312

520 subtract 312 is 208

Answer:

208

Step-by-step explanation:

(520)-60% of 520

(520)-3×104

520-312

=208

Hope it helps you

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The equation equivalent to the equation x + y = 3 is 6x + 6y = 18.

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

Example:

2x + 4 = 9 is an equation.

We have,

x + y = 3

Multiply 6 on both sides.

6x + 6y = 18

Thus,

The equation that is equivalent is 6x + 6y = 18.

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a. 26%

sorry if wrong...

if r(x) = x² and r(x) = 4, then the value of x = ± 2

Equal means same in all aspects, whereas equivalent means similar but not identical. For example, 2 is said to be equal to 2 but equivalent to 1 + 1.

For example y = x+5 and the same y = 2x+7

then we can say that x+5 Is also equal to 2x+7

2x+7 = x+5

then x = -2

similarly r(x) = x²

thesame r(x) = 4

this means that x² = 4

solving for x

we find the square root of both sides

√x² = √4

x= ±2

It is ± because square root value as two possible values of either both positive or both negative.

Therefore the value of x is ±2

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The expressions for the number of sweets that Tony and Sue now have are:

Given:
Sue has 18 sweets

Sue = 18

Tony also has 18 sweets, that is:

Toney = 18

Sue gives Tony × sweets; that is

Sue = 18 - x; and

Tony = 18 + x

Sue then eats 5 of her sweets, Tony then eats half of his ⇒ Sweets:

that is ⇒

Sue = 18 - x - 5

Tony = (18 + x) / 2

Thus, simplifying the above, we have:

Sue = 13 - x

Tony = (18 + x) / 2

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All x-values that are within the scope of both f and g make up the domain of the (f g)(x). In this instance, f has a domain of {"x | x ≥ 0"} and g has a domain of "all real numbers"; as a result, (f - g)(x) has a domain of {"x | x ≥ 0"} as these values of x fall inside both f and g's domains.

A function's domain is the collection of all potential inputs. All x-values, or inputs, and all y-values, or outputs, make up a function's domain and range, respectively. When viewing a graph, the domain consists of all of the graph's values from left to right. The graph's whole range, from the bottom to the top, is the range.

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Answer:

[tex]y = \frac{2}{5}x[/tex]

Step-by-step explanation:

⭐Perpendicular bisector of a segment

⭐Midpoint formula

⭐Point-slope form

⭐Slope

⭐Slope-intercept form

1. Find the midpoint of the given segment

[tex]midpoint = (\frac{(x_1+x+2)}{2}, \frac{(y_1+y_2)}{2})[/tex]

[tex](x_1,y_1)[/tex] = (3,7)

[tex](x_2,y_2)[/tex] = (7,-3)

∴ midpoint  [tex](\frac{3+7}{2}, \frac{7+(-3)}{2})\\= (\frac{10}{2}, \frac{4}{2})\\= (5,2)[/tex]

2. Find the slope of the given segment

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex](x_1,y_1)[/tex]  = (3,7)

[tex](x_2,y_2)[/tex] = (7,-3)

∴ slope [tex]m = \frac{-3-7}{7-3}\\= \frac{-10}{4}\\= \frac{-5}{2}[/tex]

3. Write the equation of the bisector equation in point-slope form

[tex]y - y_1 = m(x-x_1)[/tex]

4. Substitute the opposite-reciprocal of the given segment's slope into the bisector equation

The slope of the given segment is -5/2.

Therefore, the opposite-reciprocal of the given segment's slope is 2/5.

[tex]y - y_1 = \frac{2}{5}(x-x_1)[/tex]

5. Substitute the midpoint of the given segment into the bisector equation

midpoint = (5, 2)

[tex]y -2 = \frac{2}{5}(x-5)[/tex]

6. Expand & simplify the bisector equation to convert it into slope-intercept form

We need to convert  [tex]y -2 = \frac{2}{5}(x-5)[/tex] into [tex]y = mx + b[/tex] form.

[tex]y -2 = \frac{2}{5}x - \frac{2 * -5}{5}[/tex] . . . . . . . distribute the 2/5 into the parentheses

[tex]y -2 = \frac{2}{5}x - 2[/tex]      . . . . . . . compute

[tex]y = \frac{2}{5}x[/tex]                  . .  . . . .  add 2 to the LHS and RHS to isolate y

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Answer:

288

Step-by-step explanation:

32 x 9=288

The 10 represent in the function f(x) = 10(1. 015)* shows the balance in a savings account as time increases is the starting balance of the savings account.

Therefore the answer is D) The starting balance of the savings account.

The compound interest formula is used to calculate the total interest earned on a principal amount over a period of time, where the interest is compounded at regular intervals. The formula is:

A = P(1 + r)^(t)

Where:

A is the final amount (principal + interest)

P is the principal (initial) amount

r is the annual interest rate (expressed as a decimal)

t is the number of years the money is invested or borrowed

The function f(x) = 10(1. 015)* shows the balance in a savings account as time increases.

So 10 represents the principal (initial) amount

0.014 represents the annual interest rate (expressed as a decimal)

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Using the formula for the volume of cuboid that is the product of length, breadth and height, The answer is 7cm.

A cuboid is a three-dimensional shape with six rectangular faces, three of which are pairs of congruent squares and the other three are rectangles. It is also known as a rectangular prism. The opposite sides of a cuboid are parallel and equal in area. The length, width, and height of a cuboid are three of its measures of size.

The volume of a three-dimensional object is a measure of the amount of space it occupies. It is typically measured in units of cubic units, such as cubic centimeters (cm^3) or cubic meters (m^3). The formula for the volume of a cuboid is length x width x height. For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, its volume would be 5 x 3 x 2 = 30 cubic centimeters. In general, the volume of a three-dimensional object can be found by multiplying the area of its base by its height.

length = 2cm

breadth =3cm

volume = 42 cm³

volume = l*b*h

42 = 2*3*h

h= 42/6 =7cm

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