What is the definition of the sine ratio in a right triangle?.

Answer:

a³(b-c) + b³(c-a) + c³(a-b) = (a-b)(b-c)(c-a) (a + b + c)(a² + b² + c² - ab - bc - ca)

This is a factorized form of the polynomial, as you can see it factorizes as a combination of difference of squares and difference of cubes.

here is one way to factorize the polynomial a³(b-c) + b³(c-a) + c³(a-b) step by step:

First, we can factor out a³ from the first term, b³ from the second term, and c³ from the third term:

a³(b-c) + b³(c-a) + c³(a-b) = a³(b-c) + b³(c-a) + c³(a-b)

Next, we can factor out (b-c) from the first and second terms, and (c-a) from the second and third terms:

a³(b-c) + b³(c-a) + c³(a-b) = (b-c)(a³ + b³) + (c-a)(b³ + c³)

We can factor out (a-b) from the first and third terms, and then we can use difference of cubes to factorise out:

(b-c)(a³ + b³) + (c-a)(b³ + c³) = (b-c)(a-b)(a² + ab + b²) + (c-a)(a-b)(b² + ab + c²)

Now we can combine like terms, and we get:

(b-c)(a-b)(a² + ab + b²) + (c-a)(a-b)(b² + ab + c²) = (a-b)(b-c)(c-a)(a + b + c)(a² + b² + c² - ab - bc - ca)

The factorized form of the polynomial is (a-b)(b-c)(c-a) (a + b + c)(a² + b² + c² - ab - bc - ca)

This is a general formula for the factorization of a polynomial of the form a³(b-c) + b³(c-a) + c³(a-b)

By using difference of cubes we can factorise the above polynomial, hope it helps.

Step-by-step explanation:

Firstly you have to open brackets

4b(5a - 2) = 2c

20ab - 8b = 2c

20ab = 2c + 8b

Divide both sides by 20b(coefficient of a)

a = (2c + 8b)/20b

Answer:

[tex]a = \dfrac{2}{5} + \dfrac{c}{10b}[/tex]

Step-by-step explanation:

Expand 4b(5a-2) on the left side

4b(5a-2)  = 4b · 5a -4b · (-2)

= 20ab -8b

Therefore we get

20ab -8b = 2c

Add 8b on both sides to get rid of the -8b on the left

20ab - 8b + 8b = 2c + 8b

20ab = 8b + 2c

Divide by 20 both sides:
20ab/20 = 8b/20 + 2c/20

ab = (2/5)b + c/10

Divide by b both sides

==> ab/b = (2/5)b/b + c/10b

==> a = 2/5 + c/10b

The concept is Binomial distribution, an integer that can be obtained by evaluating a polynomial containing two terms The answer is, a linear equation in two variables.

In probability theory and statistics, a binomial distribution with parameters n and p is a discrete probability distribution of the number of successes in a sequence of n independent experiments, each of which asks a yes-no question and each has its own assessment of the Boolean result: passed or failed.

Data:

A polynomial of form 2x + 3y

The polynomial above is the sum of 2x and 3y.

In the expression, the polynomial is the sum of two terms, each of which is a monomial

Again, we know that a binomial is a polynomial that is the sum of two terms, each of which is a monomial, so the given polynomial is a binomial

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Answer:

3, 7

Step-by-step explanation:

-5 - (-9) = 4

The common difference is 4.

Add 4 to a term to find the next term.

-1 + 4 = 3

3 + 4 = 7

Answer: 3, 7

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

Area = (1/2) * base * height

In this case, the base of the triangle is 48cm and the hypotenuse is 50cm. Since this is a right triangle, we can use the Pythagorean theorem to find the length of the height. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So,

c^2 = a^2 + b^2

50^2 = 48^2 + b^2

2500 = 2304 + b^2

b^2 = 2500 - 2304

b = √(2500 - 2304)

b = √(196)

b = 14

So, the height of the triangle is 14cm.

Area = (1/2) * 48 * 14 = 336cm^2

The point of intersection of the perpendicular bisectors of the sides of a triangle is called circumcenter

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The sum of the polynomials (m + n + 3) + (m + n + 4) is 2m+2n+7

Sum of given polynomials (m+n+3) +(m+n+4)

Firstly, open the parenthesis we will get  m+n+3+m+n+4  

After simplification, we will get  2m+2n+7

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

What is the sum of the polynomials (m + n + 3) + (m + n + 4)?

The value of quadratic function is,

⇒ y = 9x² + 54x - 63

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ y = 9 (x - 1) (x + 7)

Now, We can find the quadratic equation as;

⇒ y = 9 (x - 1) (x + 7)

⇒ y = 9 (x² + 7x - x - 7)

⇒ y = 9 (x² + 6x - 7)

⇒ y = 9x² + 54x - 63

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The multiplicative inverse of -7/9 is -9/7

The multiplicative inverse of a number is basically the reciprocal of the number Multiplicative inverse of a  is  1/a    where a≠ 0

The standard form to represent the multiplicative inverse is as follows:

a * (1/a)  =  1

when a number is multiplied by its multiplicative inverse then the result is 1.

The multiplicative inverse is the Reciprocal of a fractional number where the number and denominator are simply interchanged.

Hence multiplicative inverse of 7/9 is

1/(7/-9)  = -9/7

The multiplicative inverse of -7/9 is- 9/7.

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Answer:

5 maybe????????

Step-by-step explanation:

Um, I'm guessing because 10/2=5, and yeah?????

The radius of the tank is 28.3 feet (rounded to one decimal place).

Radius is a term used to describe the distance from the center of a circle to any point on the circumference. It is a line segment that runs from the center of the circle outwards, perpendicular to the circumference. The radius of a circle is the same for all points on the circumference, and it is always half of the diameter.

The radius of the tank can be determined using the Pythagorean Theorem. Since we are given the distances from the center of the tank (O) to points A and B, we can use the following formula to calculate the radius:

R = √(OA² + OB²).

Plugging in the given values, we get:

R = √(21² + 19²) = √(441 + 361) = √802 = 28.29

Therefore, the radius of the tank is 28.3 feet (rounded to one decimal place).

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Answer:

f(5) = 31/11

f'(5) = 4/11

Step-by-step explanation:

y = 4/11x + 1

f(x) = 4x/11 + 1  ==> y = f(x)

f(5) = 4(5)/11 + 1  ==> substitute 5 for x

f(5) = 20/11 + 1  ==> simplify

f(5) = 20/11 + 11/11  ==> make common denominators to simplify easier

f(5) = (20+11)/11

f(5) = 31/11

f'(x) = 4/11

Hence, f'(5) = 4/11 since every value of x will make the derivative 4/11.

Answer:

m = [tex]\frac{1}{5}[/tex] , c = - 4

Step-by-step explanation:

m is the slope of the line and is calculated using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (1, 1) ← 2 points on the line

m = [tex]\frac{1-0}{1-(-4)}[/tex] = [tex]\frac{1}{1+4}[/tex] = [tex]\frac{1}{5}[/tex]

c is the value of the y- intercept , where the line crosses the y- axis

the line crosses the y- axis at - 4, then c = - 4

The value of tan A is 5/12.

To find the value of tan A, we use the trigonometric function tangent, which is defined as the ratio of the length of the side opposite angle A to the length of the side adjacent to angle A. In a right triangle, these sides are labeled as x and y, respectively. Therefore, to find the value of tan A, we divide the length of the side opposite angle A (x) by the length of the side adjacent angle A (y).

tan A = x/y

Here,

tan A = 5/12

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The complete question is:

Given a right triangle with one angle measuring A, and the lengths of the side opposite angle A and the side adjacent angle A as 5 and 12 respectively, find the value of tan A.

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The solution set for the system of equations is (x, y) = (-2.44, 10.11)

To find the solution set for the system of equations, we can use several methods such as substitution, elimination, or matrix method.

In the elimination method, we try to eliminate one of the variables by adding or subtracting the equations.

One method is to use elimination method:

9x + 5y = 28

5x + 9y = 56

We can eliminate one of the variables by multiplying the first equation by -5 and the second equation by 9:

-45x - 25y = -140

45x + 81y = 504

Adding these two equations together we get:

36y = 364

Solving for y, we get:

y = 364/36 = 10.11

We can then substitute this value back into one of the original equations, for example, the first equation:

9x + 5(10) = 28

9x + 50 = 28

9x = -22

x = -2.44

So, the solution set for the system of equations is (x, y) = (-2.44, 10.11)

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Leticia babysat 5 hours on Saturday.

First, we have to look at the equation that models this situation. We learn that the price per hour of babysitting is $8. On Friday, Leticia babysat for 4 hours, and on Saturday, she babysat an unknown amount of time. Leticia watched the children for four hours on Friday and for an undetermined period of time on Saturday.

earned $72, Therefore:

8 ( 4 + x ) = 72

( 4 + x ) = 72 / 8

4 + x = 9

x = 9 - 4

x = 5

Leticia babysat 5 hours on Saturday

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This figure and the given statements are important for understanding basic principles of geometry.

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The length of CD is 7 units.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

From the figure it is given that C is between A and D.

B is the midpoint of AC

BC=3 and AD=13, we have to find CD.

As B is the midpoint of AC, then BC=AB

BC=AB=3

AC=AB+BC=6

Now to find CD=AD-AC

CD=13-6

CD=7

Hence, the length of CD is 7 units.

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The height of Andre, given the height of Elena is 63 inches tall.

The height of Lin is 65 .5 inches tall.

The height of Noah is 59 + d inchs tall.

The height of the other people given which include Andre, Lin, and Noah, are all dependent on the height of Elena.

Andre is 4 inches taller than Elena so the height is:

= 59 + 4

= 63 inches

The height of Lin is:

= 59 + 6 .5

= 65 .5 inches

The height of Noah is:

= 59 + d  inches

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Answer:

0.22  <  

1

4

 <  

26

100

 <  

272

10

Step-by-step explanation:

Answer:

Sample 1

ATTCGACGTC

k to add speaker notes

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acer

Sample 2

GATAGCTAGG

?--?

A group of numbers in a particular order are called a sequence. For instance: a1, a2, a3, a4,..., an,... The first term is designated as a1, the second term as a2, and the nth term as an.

The sequence's first term is a1 = 1, making it the first term. I = 2 and a2 = 2 if I = 2. I = 3, hence a3 = 3 if I = 3.

The definition of an arithmetic sequence's nth term is: The equation a = a1 + (n - 1)d determines the nth term of an arithmetic sequence with a1 as its first term and d as its common difference.

A group of numbers in a particular order are called a sequence. For instance: a1, a2, a3, a4,..., an,... The first term is designated as a1, the second term as a2, and the nth term as an.

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Answer:

-4w^6

Step-by-step explanation:

12/-3 = -4

w^9/w^3 = w^6

y^3/y^3 = 1

Answer: -4w^6

Answer:

option 1 = - 4w⁶

Step-by-step explanation:

attached the solution, hope that helps...

Answer:

Step-by-step explanation:523x2 1323

Answer:

Answer is in the attached photo.

Step-by-step explanation:

Solution is in the attached photo, do take note when you square a square root, you will get the original expression. (Power 2 x Power Half = Power 1).

Answer:

This meant to be a question?

Step-by-step explanation:

Answer:

There are 7 ounces of applesauce in each of Newton's containers.

Step-by-step explanation:

72.5/2.5= 29

29-8=21

21/3=7

Answer: it is 7 in each container .

Step-by-step explanation: becuase if she has 2.5 times more than her what you want to do is divide 72.5 by 2.5 and get 29 the he ate 8 ounces now take away 8 from 29 and you will get 21 and then divide 21 by 3 and you will get 7....    Easy math hope this helps

The ratios of the sides of a 45-45-90 triangle are 1:1:[tex]\sqrt{2}[/tex].

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The height that represents the 85th percentile is 66.8 inches.

The height that represents the first quartile is 62.4 inches.

Generally, To find the height that represents the 85th percentile, you would need to use a z-score table or calculator.

The z-score represents the number of standard deviations away from the mean of a particular value.

For the 85th percentile, the z-score would be 1.04. To find the height, you would use the formula:

(z-score) * (standard deviation) + mean

So, in this case:

1.04 * 2.8 + 63.7 = 66.612 inches

b) To find the height that represents the first quartile (25th percentile), you would use the same process but with a z-score of -0.67.

-0.67 * 2.8 + 63.7 = 61.824

This means that the height that represents the first quartile is 62.4 inches.

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