The sides of a triangle are 68, 61, and 46. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.

A. Triangle ABC is similar to triangle DEF.

B. The value of x is 21.

What are similar triangles?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are items that feature more than two figures that are the same shape but different sizes.

Here, we have

Given a triangle and we have to show both triangles are similar.

A. ABC will be similar to DEF if two sides along with their corresponding angle of ABC is equal to two sides and their corresponding angle of DEF. ABC will be similar to DEF if the corresponding ratios of all sides of both triangles are equal to each other.

Hence, triangle ABC is similar to triangle DEF.

B. By the property of similar triangles,

= AB/DE = AC/DF

= 14/x = 10/15

x = 21.

Hence, the value of x is 21.

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As per the given simple interest, the principal amount is $165.35.

The term simple interest in math is defined as  the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.

Here we have given that If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420.

Therefore, through the given question we have identified the value of

interest rate = 3.5%

time period = 44

sum amount = 420.

Then the principal amount is calculated by using the formula of simple interest as,

P = A / (1 + rt)

Here first we have to convert R percent to r a decimal, then we get

r = R/100 = 3.5%/100 = 0.035 per year.

Now, we have to apply the values on the equation and then we have to solve our equation, then we get

P = 420 / ( 1 + (0.035 × 44)) = 165.35433070866

P = $165.35

Therefore, the principal investment required to get a total amount, principal plus interest, of $420.00 from simple interest at a rate of 3.5% per year for 44 years is $165.35.

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If point P(2k, k) is equidistant from A(-2, 4) and B (7,-5), the numerical value of k is 3.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

The distance between P(2k, k) and A(-2, 4) is:

d = √((2k - (-2))² + (k - 4)²)

d = √((2k +2)² + (k - 4)²)

The distance between P(2k, k) and B(7, -5) is:

d = √((2k - 7)² + (k - (-5))²)

d = √((2k - 7)² + (k + 5)² )

Since the distances are equal, we can set the two equations for d equal to each other and solve for k.

√((2k +2)² + (k - 4)²) = √((2k - 7)² + (k + 5)² )

Square both sides

(2k +2)² + (k - 4)² = (2k - 7)² + (k + 5)²

(2k +2)² + (k - 4)² = 5k² - 18k + 74

5k² + 20 = 5k² - 18k + 74

Collect like terms

5k² - 5k² + 18k = 74 - 20

18k = 74 - 20

18k = 54

k = 54/18

k = 3

Therefore, the value of k is 3.

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The volume of the building block in terms of x is V = x⁶/1728

Volume is the amount of space a substance occupies.

Since building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as x²/12 centimeters, where x is the length of the packaging box.

Since the building blocks are in the shape of a cube, its volume is the volume of a cube.

The volume of a cube is given by V = L³ where L = length of side of cube.

To find the volume of the building block, since the length of the building block is L = x²/12, then we find the volume of the building block by substituting L into V.

So, V = L³

V = (x²/12)³

= x⁶/12³

= x⁶/1728

So, the volume of the building block is V = x⁶/1728

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Answer:

29000000000*140% = 40600000000

=40.6 billion

Step-by-step explanation:

right!!!

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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Answer: x= 1/7y + 19/7 (Standard form will be:7x−y=19)

Step-by-step explanation:

Step 1: Add -y to both sides.

−7x+y+−y=−19+−y

−7x=−y−19

Step 2: Divide both sides by -7.

−7x/−7

= −y−19/−7

x= 1/7y + 19/7

a=12,d=17-12=5

nth term =a+(n-1)d

36th term=12+(36-1)5

=12+(35×5)

12+175

36th term=187

Answer: 187

Step-by-step explanation: 17 - 12 = 5 and 22 - 17 = 5

aₙ = a₁ + (n - 1) d

where a₁ = 12, n = 36, d = 5

a₃₆ = 12 + (36 - 1) 5

a₃₆ = 12 + 35 × 5

a₃₆ = 12 + 175

a₃₆ = 187

187 is the 36th term

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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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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The terminal point of vector cu lies in quadrant III.

Option B is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

p = (0, 0) and Q = (9, 12)

u = PQ = (9 - 0, 12 - 0) = (9 , 12)

Now,

cu = (9c, 12c)

where c < 0

If c = -1

cu = (-9, -12)

The coordinates (-x, -y) lie in quadrant III.

(-9, -12) is in quadrant III.

Thus,

Vector cu lies in quadrant III.

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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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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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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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Yes, the sides with 5,12,13 make a triangle.

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude is called Pythagorean Triples.

Pythagorean triples describe the three integer side lengths of a right triangle.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

which contain three positive integers a, b, and c.

the original Pythagorean triplets, two of the numbers are prime, but one is even. If all three numbers are multiplied by a factor, the triplet is called a relatively prime.

The most well-known examples are (3,4,5) and (5,12,13)

consider c=13 a=12, b=5 substitute in above formula:

13²=12²+5²

⇒169=144+25

⇒169=169

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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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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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Answer:

Step-by-step explanation:

scale,= 1 : 5000000

it means 1 cm depicts 5000000cm

or 50000m else 50km

the distance between two towns in map = 7cm

so the distance between two towns = 7 *50

                                                      = 350km

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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Bag A as required by the task content has 31.25 percent fewer marbles than Bag B.

It follows from the task content that the percent fewer marbles which Bag A has relative to Bag B is to be determined.

As given in the task content; Bag A contains 110 marbles, while Bag B contains 160 marbles.

On this note, the difference between the number of marbles is; 160 - 110 = 50 marbles.

Hence, the percent of fewer marbles in Bag A relative to Bag B is;

= ( 50 / 160 ) × 100%

= 31.25%.

Therefore, Bag A has 31.25% fewer marbles than Bag B.

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The algebraic expression for the given sequence 1, 10, 19 as required to be determined is; a (n) = 1 + ( n - 1 ) 9.

As evident in the task content; it follows that the common difference of the given sequence is constant since; 19 - 10 = 10 - 1 = 9.

On this note, since the nth term of arithmetic sequences take the form;

a (n) = a (1) + ( n - 1 )d

Since the first term is; 1 and the common difference is; 9; the resulting algebraic expression is;

a (n) = 1 + (n - 1)9.

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l think it's answer is this .

You can use your calculator.

Therefore .as a result the supplied linear equation problem's solution is shown to be a linear equation with two variables.

Any model that meets the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both y and x are distinct factors, the preceding sentence is commonly referred as a "mathematical model with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations, all of which end in zero. If an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is classified as linear. The equation is written as Y=mx+b, where m denotes the slope and b

Here,

Assumed: 2x + 3Y = 0.

As a result, the following equation can be used to determine whether it is linear in two variables.

As x is the sole variable, as can be seen.

Therefore, it is a two-variable linear equation.

As a result, the supplied linear equation problem's solution is shown to be a linear equation with two variables.

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The __main__ is a constructor used in python which can be used to check the name of the top-level environment of the program.

It is contained inside the  __ main __ PY file package.

Example,  __name__ == '__main__' expression.

Python is a programming language which is high level in nature and is mainly used in the field of data science and artificial intelligence . Python is dynamically-typed and garbage-collected. It has a large community of developer and is an upcoming language.

It is easy to learn and evolving language and has a lot of packages and modules which makes it easy to work on it.

It is an interpreted language and a python file is saved using the extension .py .

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Answer:

Step-by-step explanation:

m∡IGH = ? m∡FGH = 141 degrees and m∡FGI = 72 degrees

therefore, m∡IGH = m∡FGH - m∡FGI = 141 - 72 =  69 degrees

A = 1, y = -2/3, The value of a for which the system of equations has a unique solution is a = -3.

1. Set the first equation equal to 0:

2x + ay = 2

2. Subtract 2x from both sides of the equation to get:

ay = -2

3. Divide both sides of the equation by a to get:

y = -2/a

4. Substitute this value of y into the second equation to get:

6x + 3(-2/a) = 3

5. Multiply both sides of the equation by a and simplify to get:

6ax - 6 = 3a

6. Add 6 to both sides of the equation to get:

6ax = 3a + 6

7. Divide both sides of the equation by 6 to get:

x = (3a + 6)/6

8. The value of a for which the system of equations has a unique solution is a = -3.

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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 measure of angle B is 82°

What is angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

∠A = 180° - 143°

     = 37°

∠A + ∠B + ∠C = 180°

37° + ∠B + 61° = 180

∠B = 180 - 61 - 37

     = 82°

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