2.Find the GCF(224,264) using Euclid division algorithm. ​

The equation -x² + 3x - 3 = 0 has the sum of the roots as 3. Given that a quadratic equation's roots add up to three.

A quadratic polynomial in terms of the zeroes (α,β) is given by

x2 - (sum of the zeroes) x + (product of the zeroes)

f(x) = x2 -(α +β) x +αβ

From the options,

A) 2x² - 3x + 6 = 0

Dividing by 2,

x² - 3/2x + 3 = 0 ------------------ (2)

Comparing (1) and (2),

α + β = 3/2

Therefore, the sum of the roots of the equation is 3/2.

B) -x² + 3x - 3 = 0

The equation can be written as x² - 3x + 3 = 0 ------------- (3)

By comparing (1) and (3),

α + β = 3

Therefore, the sum of the roots of the equation is 3.

C) √2x² - 3/√2x + 1 = 0

Dividing by √2,

x² - 3/2x + 1/√2 = 0 ------------ (4)

By comparing (1) and (4),

α + β = 3/2

Therefore, the sum of the roots of the equation is 3/2.

D) 3x² - 3x + 3 = 0

Dividing by 3,

x² - x + 1 = 0 -------------------------- (5)

By comparing (1) and (5),

α + β = 1

The equation's roots are added together, and the result is 1.

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Answer:

(x - 5)² + (y + 3)² = 9

Step-by-step explanation:

The standard equation of a circle with center (a, b) and radius r is given by

(x - a)² + (y-b)² = r²

Here the center is (5, -3) and r = 3

Substituting values for a = 5, b = -3 and r = 3

(x - 5)² + (y-(-3))² = 3²

(x - 5)² + (y + 3)² = 9

It is OK to leave it in this form without expanding

After solving, the remainder when [tex]-x+3x^2-1[/tex]  is divided by x + 1 is 3.

In the given question, we have to find the remainder when [tex]-x+3x^2-1[/tex]  is divided by x + 1.

The given polynomial is [tex]-x+3x^2-1[/tex].

We have to find the remainder of the polynomial when we divide this polynomial x + 1.

To find the polynomial we equate x+1 equal to zero to find the value of x.

x + 1 = 0

x = -1

Now putting x = -1 in the given equation [tex]-x+3x^2-1[/tex].

P(x) = [tex]-(-1)+3(-1)^2-1[/tex]

P(x) = 1 + 3×1 - 1

P(x) = 1 + 3 - 1

P(x) = 3

Hence, the remainder when [tex]-x+3x^2-1[/tex]  is divided by x + 1 is 3.

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The complete question is:

When [tex]-x+3x^2-1[/tex]  is divided by x + 1 then remainder will be?

Answer:

I believe the first one

Step-by-step explanation:

The vertex, zeros, and y-intercept for the given quadratic equation f(x)=       -x² - 4x+5 are respectively,

Vertex- (2, 1)

Zeros-  (2 + i)

Y-intercept- 5

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

f(x) = y =  -x² - 4x+5

y = -x² - 4x+5

For making it perfect square, we can add and subtract square value of half of coefficient of x

So,  adding and subtracting +4 and -4 in the given equation

y = -x² - 4x+5+4-4

  = -x² - 4x+4+5-4

  = (-x +2)² +1

y-1 = (-x +2)²

So, for vertex

-x +2 = 0

x = 2

y-1 = 0

y = 1

For Zeros, y = 0

y-1 = (-x +2)²

(-x +2)² = -1

x = 2 + i,   -2-i

the zeros are imaginary

For y intercept, x = 0

y-1 = (-x +2)²

y   = 1 + (2)²

y   = 5

Hence,  vertex, zeros, and y-int. are respectively (2, 1), (2 + i), 5

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A discounted surfing lesson costs $50, and a discounted parasailing trip costs $80.

Let x represent the discounted cost per person for a surfing class.

Let y represent the reduced cost per person for surfing instruction.

The cost of taking a surfing lesson and going parasailing is $130

x + y = 130--------------(i)

25 people take

Surfing lessons and 30 people go parasailing and a total of $3,650 is collected

25x + 30y = 3650--------------(ii)

We solve for y using equ (i):

y = 130 - x ------------(iii)

Substitute equ (iii) to equ (ii) and solve for x

25x + 30(130 - x) = 3650

25x + 390 - 30x = 3650

-5x = -250

-x = 50

We solve for y using equ (iii):

y = 130 - x

y = 130 - 50

y = 80

Thus, a discounted surfing lesson costs $50, and a discounted parasailing trip costs $80.

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According to the information, the correct option is C. . 4x^2 − 13x + 9, since the expression is a polynomial.

To add the expressions we must add each of its components (those that are similar) to form a single expression. Below is the procedure:

Now we must reassemble the expression that would look like this.

4x^2 - 13 + 9. Additionally, we know that it is a polynomial because none of the terms related to x are affected by a square or fractional root.

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The total caps does Sid have is 55% of x = 33

x = (33 * 100)/55

x = 60

In programming, a collection is a class used to represent a set of similar data type items as a single unit. These unit classes are used for grouping and managing related objects.A collection has an underlying data structure that is used for efficient data manipulation and storage. Code readability and maintenance improves when collections are used in logical constructs.

Collections are designed to group certain objects with a logical connection. For example, a StudentCollection object may be used to maintain university student details. Details may include the total number of students or offer a student search facility based on attributes, such as name, class or grade.

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Jesse's train is faster than Khalid's since 150 is greater than (>) 140 and she is traveling at 150 mph as opposed to 140 mph.

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.

According to the graph, the climb is 140 and the run is 1.

Since 140/1 equals 140, Khalid's slope is 140.

The slope is 150 according to the equation (y = 150x; y = mx).

Jesse's train is faster than Khalid's since 150 is greater than (>) 140 and she is traveling at 150 mph as opposed to 140 mph.

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Complete Question -

Answer: Two equivalent ratios are, 16:28 and 24:42

Step-by-step explanation:

Answer:

17.6

Step-by-step explanation:

The circumcenter of the triangle is at the point (22, 36). This is the point where the three thin strips of wood cross and where Mike attached the kite's string.

The point of concurrency of the lines perpendicular to the sides of a triangle is known as the circumcenter of the triangle. To find the circumcenter of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), you can use the following formula:

x = (x1 + x2 + x3) / 3

y = (y1 + y2 + y3) / 3

Plugging in the coordinates of the three vertices, we get:

x = (0 + 44 + 0) / 3 = 22

y = (58 + 36 + 0) / 3 = 36

So the circumcenter of the triangle is at the point (22, 36).

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The product between functions f(x) and g(x) is:

(fg)(x) = x^3 - 4x^2 - 16x + 4

Here we have two functions:

f(x) = x - 4

g(x)  = x^2 - 16

We want to find the product:

(f times g)(x)

So we just need to take the product between the two functions:

(x - 4)*(x^2 - 16)

x^3 - 4x^2 - 16x + 4

Then the product of the functions is:

(f times g)(x) = x^3 - 4x^2 - 16x + 4

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The probability that both cards are sevens is 0.0044
What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

There are 52 cards, 4  are sevens.  

So the probability of picking the first 7 is 4/52.  

If you don't replace the card, then there are only 51 cards left, 3 of which are sevens.

So the probability of picking a seven on the second draw is 3/51.  

The probability of picking sevens on both draws is:

P(picking two sevens) = (4/52)·(3/51) =0.076*0.058=0.0044

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The value of x is -3 for the given equation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 4 *3 + 4*x = 0

Simplify the equation using PEMDAS

=> 4*3 + 4*x = 0

=> 12 + 4x = 0

=> 4x = -12

=> x = -3

Therefore, the simplified value of the Given equation is x = -3.

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Answer:

x > 10.4

Step-by-step explanation:

Isolate X by adding 3.5 to each side of the inequality

That leaves you with x > 6.9 + 3.5

Answer: A or C i would go with C but ur instict

Step-by-step explanation:

Answer:

A or C

Step-by-step explanation:

Good Luck!

Gradient of given equation x-intercept: a=−32 y-intercept: b=3

The gradient of a function is defined to be a vector field. Generally, the gradient of a function can be found by applying the vector operator to the scalar function. (∇f (x, y))

The given equation of line:

y=2x+3

Comparing above equation with the standard slope-intercept form

y=mx+ c,

we get

Slope:

m=2

Now, given equation can be re-written as

2x−y=−3

x−32+y3=1

Comparing above equation with intercept form:

x a + y b =1,

we get

x-intercept:

a=−32

y-intercept:

b=3

Now, the given straight line intersects the coordinate axes at

(−32,0) & (0,3)

Specify these points on XY-plane & join them by a straight line to get plot.

Gradient of given equation x-intercept: a=−32 y-intercept: b=3

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Answer:150

Step-by-step explanation:

suppose he asks 300 and only 1/2 say yes,

There are a lot of linear solutions to problems. In fact, there are an infinite number of them.

Linear solutions are the most common type of solution. They're also the easiest to solve. These solutions are used in algebra and geometry. There are six different types of equations in which a linear solution exists. These are:

1) One variable equals zero

2) Two variables are equal

3) Three variables are equal

4) Any equation with one constant and one other variable

5) Two variables have an equal ratio to another variable

6) Two variables are equal to a certain number One solution that's linear is a quadratic equation with two variables. It has the form x2 + bx + c = 0 To solve this equation, you can use basic algebraic skills like factorization, substitution, and addition.

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Answer:

9

Step-by-step explanation:

x/6=12/8

x=12*6/8

x=72/8

x=9

Equivalence relations are important in maths because of the following parts,

A relation R on a set A is called an equivalence relation if and only if the relation R is recursive, symmetric, and transitive. An equivalence relation is a relation on sets, and is generally represented by the symbol “~”. For example: "Equal to (=)" is the equivalence relation on any set of numbers A for all elements a, b, c ∈ A,

Reflexive: a = a ,

Symmetric: a = b ⇒ b = a and

Transitive: a = b, b = c ⇒ a = c.

This means that (=) is recursive, symmetric, and transitive. Equivalence relations are used in several areas of mathematics.

does not satisfy || f || = 0 <=> f=0.

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Complete question:

Why is equivalence relation important in maths?.

Answer:

the answer is A because you can know

The number of hats Sara bought is 7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Sarah went shopping at a store and bought some hats that cost $6 each and 2 necklaces that cost $12 each.

The number of hats will be calculated as,

12N + 2H = 66

12 x 2 + 2 H = 66

2H = 66 - 24

2H = 42

H = 42 / 2

H = 21

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From the situation described in the problem: all the required values are given below.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Given:

The dot plots show the distribution of the length, in centimeters, of 25 shark teeth for an extinct species of shark and the length, in centimeters, of 25 shark teeth for a closely related shark species that is still living.

The shape of the distribution:

For living species - Left-skewed distribution

For extinct species - The symmetric distribution.

Measures of the center:

For living species - mean = 2.32

For extinct species - mean = 3.02

The measures of variability:

For living species - 0.13

For extinct species - 0.55

Therefore, all the required values given above.

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-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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A polynomial of degree 3 is called a cubic polynomial.

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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The solution is, 1) f+g =3x^3+x^2+2x-9 and, 2)  f+g = x^2-6x +2√(x-2)+17

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

given that,

            g(x) = x^2+8x-9

so, f+g

=3x^3+x^2+2x-9

and,

             g(x)=2√(x-2)+10

so, f+g

= x^2-6x +2√(x-2)+17

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