A scientist is working with 11 meters of gold wire. How long is the wire in millimeters?

Answer: f(x)=-3x+2

Step-by-step explanation:

Answer:

i d k

Step-by-step explanation:

The factored form of the given equation as found by calculating is known to be,  (12x + 4)(x - 1) .

The given equation is 12x² - 8x - 4 , now in order to get the factors we will factorize the expression.

  12x² - 8x - 4

= 12x²  -12x + 4x -4

= 12x( x - 1) +4( x - 1 )

= (12x + 4)(x - 1)

Therefore, the factors of the given equation is found to be as ,

x = 1 or -4 / 12.

Factorizing is a process by which we find the factors of a given number. The factor of a number is made up of prime numbers . Prime numbers are the numbers which are only divisible by 1 or by the  number itself.

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A function to represent the number of pizzas Antonio’s pizza shop can make in x hours using function notation is y = 13x + 5.

A reasonable domain and range for the number of pizzas Antonio’s can make include the following:

In order to write a function to represent the number of pizzas Antonio’s pizza shop can make in x hours using function notation, we would have to determine the slope and y-intercept by using the point-slope form equation;

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

The table representing the number of pizzas Antonio’s pizza shop can make in x hours should be completed as follows;

Hours, x           1      2      3      4     5

# of pizzas, y  18     31    49    67   85

Next, we would determine the linear equation representing the line which passes through the points (1, 18) and (2, 31) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 18 = (31 - 18)/(2 - 1)(x - 1)

y - 18 = 13/1(x - 1)

y = 13x - 13 + 18

y = 13x + 5

Therefore, a reasonable domain and range for y = 13x + 5 is given by:

Domain = 1 ≤ x ≤ 5 or [1, 5]

Range = 18 ≤ y ≤ 85 or [18, 85]

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Answer:

-x+8

Step-by-step explanation:

8-4(x-6)=8-4x+24=-4x+32

(-4x+32)/4=-x+8

The perimeter of the rectangle is given by 4x+2.

The area of a rectangle is given by the formula A=l*w where l is the length and w is the width. In this case, the area is given by the equation x^2 + x - 6. To find the perimeter of the rectangle, we need to know the length and width. However, since the area is represented by an equation, we do not have a specific value for the length and width. The given equation x^2 + x - 6 is a quadratic equation which can be factorised as (x-2)(x+3). So, we can't find the length and width without the value of x. To find the perimeter of a rectangle we use the formula P=2(l+w). If we know the value of x, we can find the perimeter of rectangle. But, as we don't have the value of x, we can't find the perimeter of the rectangle

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Complete question:

Given a rectangle If its area is x² + x – 6, what is the perimeter of the rectangle .

The correct answer for the given questions is 26.82 km and 780.372 km respectively.

4. To find the distance between the ship and the buoy at the time of each sighting, we can use the principle of non-collinearity of the ship, buoy, and observer.

Let x be the distance between the ship and the buoy at the time of the first sighting and y be the distance between the ship and the buoy at the time of the second sighting.

The angle of bearing from the ship to the buoy is S46°E, which is equivalent to (180 - 46) = 134° from the North.

The angle of bearing from the ship to the buoy at the second sighting is S12°E, which is equivalent to (180 - 12) = 168° from the North.

Therefore, the angle between the two lines of bearing is 168 - 134 = 34°.

Thus, 15/x= tan 34°

=> x= 15/tan 34°

=>x= 22.28 m

And, 15/y= sin 34°

=> y= 15/sin 34°

=> y= 26.82 km

5. To find the direct distance from the helicopter to the landing port, we can use the tangent function.

Let d be the direct distance from the helicopter to the landing port.

The angle of depression is 64°, and the altitude of the helicopter is 1600 meters.

tan(64) = 1600/d

d = 1600 / tan(64) = 780.372 km

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To prove that 4π is irrational, assume the product is rational and set it equal to ​a/b​, where b is not equal to 0: 4π = a/b. Isolating π gives π=a/4b.

The right side of the equation is rational.

Because the left side of the equation is irrational, this is a contradiction.

Therefore, the assumption is wrong, and the number 4π is irrational.

Rational numbers refers to a numbers that can be represented as a fraction say a/b where a and b are integers

Irrational numbers refers to numbers that cannot be represented as a fraction

π is an irrational number often used 3.142, the number cannot be accurately represented as a fraction.

In the proof, a/b and a/4b are rational and this is contradictory to π which is irrational. The contradiction completes the proof as required.

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The solutions to the given absolute value equation as required in the task content are; x = 3 and x = -8.

It follows from the task content that the given absolute value equation which is to be solved for the value of x as required is; | 2x + 5 | = 11.

Hence, the equation can be solved as;

2x + 5 = 11

2x = 11 - 5; 2x = 6

x = 3

OR

2x + 5 = -11

2x = -11 - 5

2x = -16

x = -8.

Ultimately, the possible values of x which represents the solution to the absolute value equation are; x = 3 and x = -8.

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The expanded form for given expression y(3.05x−3.75​)−2.25y will be in form of a linear equation = 3.05yx - 6y.

What is linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now

By Solving y(3.05x−3.75​)−2.25y

=3.05yx -3.75y - 2.25y

=3.05yx - 6y

Hence,

            expanded form will be in form of a linear equation = 3.05yx - 6y.

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The probability of selecting 100 randomly selected people with an average MCAT score of more than 510 is essentially zero. The maximum MCAT score is 528, so it is impossible for the mean of 100 randomly selected people to exceed 510.

Furthermore, the average MCAT score nationally is 500, meaning that it is highly unlikely that the mean of 100 randomly selected people would be more than 510.  

To determine the probability of selecting 100 randomly selected people with an average MCAT score of more than 510, we would need to know the distribution of MCAT scores among the population. For example, if we knew that the population had a normal distribution with a mean of 510, we could calculate the probability of selecting 100 people with a mean of more than 510. However, without this information, it is impossible to calculate the probability.  

Overall, it is highly unlikely that the mean of 100 randomly selected people will be more than 510, and the mean can't be higher than the maximum MCAT score. Therefore, the probability of selecting 100 randomly selected people with an average MCAT score of more than 510 is essentially zero.

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The values of A and B are 1 , 5 from the given equation y=2x+1.

What is linear Equation ?

linear equation can be defined as the equation in which the highest degree is one .

Given Equation ,

y = 2x+1

The values of x are -1,0,1,2,3

The values of y are -1,A,3,B,7.

put x= 0 and y = A in the equation

we get,

A = 2*0 + 1

A =1

put x = 2 and y = B

we get,

B = 2*2 +1

B = 4+1

B = 5

Hence, The values of A and B are 1 , 5 from the given equation y=2x+1.

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A term is a constant, a variable, or a number-variable product.

In algebra, a symbol (usually a letter) used to indicate an unknown numerical value in an equation or algebraic statement. A variable is a quantity that is changeable rather than fixed. In mathematics, a variable is an alphabet or phrase that represents an unknown amount, unknown value, or unknown number. Variables are very useful in algebraic expressions or algebra. As an example, the variables x and 9 are constants in the linear equation x+9=4.

A term can be a number, a constant, a variable, or the product of a number and a variable in this context.

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Answer:

x = 144

Step-by-step explanation:

300 = x + [tex]\frac{1}{2}[/tex]x + [tex]\frac{1}{3}[/tex]x + [tex]\frac{1}{4}[/tex]x

300 = [tex]\frac{12}{12}x+\frac{6}{12}x+\frac{4}{12}x+\frac{3}{12}x[/tex]

300 = [tex]\frac{25}{12} x[/tex]

[tex]x=(300)(\frac{12}{25} )[/tex]

x = 144

To check if the answer is right:

300 = 144 + [tex]\frac{1}{2}[/tex](144) + [tex]\frac{1}{3}[/tex](144) + [tex]\frac{1}{4}[/tex](144)

300 = 144 + 72 + 48 + 36

300 = 216 + 84

300 = 300

The angles R and U of the two triangles are equal, the ratio of the sides is RS/UW = RT/UV.

A triangle is a three-sided polygon which is one of the basic shapes in geometry. It is a closed figure formed by three line segments which are connected end-to-end. Each side of a triangle is called an edge, and each corner is called a vertex. The angles of a triangle are the interior angles which are formed by the intersection of two edges. Triangles come in many different types depending on the length of the sides and the size of the angles. The three most common types of triangles are equilateral, isosceles, and scalene.

Proof:
The two triangles, RST and UWV, are similar triangles because the angles R and U are equal. According to the similarity theorems, if two angles of one triangle are equal to two angles of a second triangle, then the two triangles are similar.

Since the two triangles are similar, their sides are proportional. The proportionality can be expressed as:

RS/UW = RT/UV

The proof is completed by applying the Angle-Angle Similarity Postulate which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

This implies that the proportionality of the sides of the two triangles can be expressed as a ratio of the sides. Since the angles R and U of the two triangles are equal, the ratio of the sides is RS/UW = RT/UV.

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What are the term associated with set?

Now, According to the question:

Let's know:

What are Sets?

A set is a well-defined collection of objects. Sets are named and represented using a capital letter. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.

Any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.

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The probability of 5 people of different ages are sitting in age order is 1/12.

Let the youngest individual take a seat first. If the seats are not designated, this person may occupy any of the five available seats, and each one is equally valuable.

The next senior citizen must then be placed. For this reason, there are two possible placements for the second person: either to the left of the first person or to the first person's right. The two options, ascending order and descending order, are matched by this.

We are unable to place the additional individuals after the second person is set because there is only one spot available adjacent to the first person.

There are only two methods to arrange five persons of different ages sitting at a round table in ascending or descending order.

The number of ways in which we can arrange are 5 people at a round table without any restriction is  4!.

Probability of 5 people in  around table is 2/4! = 1/12.

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Real-world instances of parallel lines:

1. Tracks for a railroad.

2. Walls that are in direct opposition.

Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Both of them have the same slope and are equally spaced apart.

No matter how far we extend them, parallel lines are straight lines that never intersect. Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal).

Real-world instances of parallel lines:

1. Tracks for a railroad.

2. Walls that are in direct opposition.

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A positive line is a line that has a positive slope, meaning it rises from left to right. A negative line is a line that has a negative slope, meaning it falls from left to right.

The formula for a positive line is y = mx + b, where m is the slope, x is the x-intercept, and b is the y-intercept. The calculation for a positive line is the slope multiplied by the x-value, plus the y-intercept. For example, if the slope is 4 and the y-intercept is -2, the equation would be y = 4x - 2. If the x-value is 1, then the y-value would be 2 (4x – 2 = 4 * 1 – 2 = 2).

The formula for a negative line is y = mx + b, where m is the slope, x is the x-intercept, and b is the y-intercept. The calculation for a negative line is the slope multiplied by the x-value, minus the y-intercept. For example, if the slope is -4 and the y-intercept is -2, the equation would be y = -4x - 2. If the x-value is 1, then the y-value would be -6 (-4x – 2 = -4 * 1 – 2 = -6).

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The following are the most significant algebraic identities, or polynomial identities, in mathematics:

(a+b)2 = a2+b2+2ab

(a-b)2 = a2+b2-2ab

(a+b)(a-b) = a2-b2

(x+a)(x+b) = x2+ x(a+b)+ab

(a+b)3 = a3+3a2b+3ab2+b3

(a-b)3 = a3-3a2b+3ab2-b3

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

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

(a+b+c)2 = a2+b2+c2+2ab+2bc+2ca

An equation that makes it simple to solve expressions with greater exponents and integers is a polynomial identity. Typically, polynomial identities are employed to expand the equation by dividing it into smaller, more manageable components.

A polynomial identity is an equation that holds true regardless of the values of the variables. When factorizing or expanding a polynomial, we apply polynomial identities. It is crucial to grasp some of the significant polynomial identities that are listed in order to solve the polynomial equation quickly.

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The circumference of the circle is 40.84cm.

What is the circumference of the circle?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Here, we have

Given:  the diameter of a circle is 13 cm.

We have to find the circumference of the circle.

C = 2.π.r

where,

r is the radius of the circle.

r = diameter/2

r = 13/2

r = 6.5

then,

C = 2.π.6.5

C = 40.84cm

Hence, the circumference of the circle is 40.84cm.

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Answer: 180.

Step-by-step explanation:  x + 35 + 60 = 180.

The area of the lateral surface of the net Christine is using to create a triangular prism is about 42.8 cm²

A triangular prism is a polyhedron that has three rectangular faces, joined head to head together to form a closed loop, to which are attached two triangular faces on their sides.

The dimensions of the triangular prism are;

Dimensions of the lower right triangle; 7 cm, 2 cm

Width of the slant surface = 2 cm

Taking the length of the rectangular slant surface as the length of the hypotenuse side of the right triangle above, and using Pythagorean Theorem to find the length, we get;

The square of the length of the hypotenuse of the right triangle = 7² + 2² = 53

Length of the hypotenuse of the right triangle with side lengths of 2 cm and 7 cm = √(53) cm

Length of the side of the rectangular slant surface of the triangular prism = √(53) cm

Area of a rectangle = Length × Width

Area of the upper rectangular slant surface of the prism = √(53) × 2 ≈ 14.6

The lateral surface area, A, of the figure is therefore;

A = Area of the two right triangles + Area of the two rectangles

Area of a triangle = (1/2) × Base length × Height

A = (1/2) × √(53) × 2 + (1/2) × 7 × 2 + √(53) × 2 + 7 × 2 ≈ 48.8

The area of the lateral surface of the triangular prism is about 42.8 cm²

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From the given triangle, The value of angle ∠VWU = 74.

No matter what kind of triangle it is, all triangles have internal angles that sum to 180°. Two of the angles in an isosceles triangle will be of equal size. All angles in an equilateral triangle will be 60 degrees. In a right-angled triangle, one of the angles will be 90°, making the sum of the other two angles also 90°.

A triangle's three inside angles will always add up to 180 degrees. Since the other two angles (180°+0°+0°) would not exist, a triangle cannot have a single angle of 180°. A triangle's three angles must add up to 180 degrees.

Sum of the angles of triangle = 180°

⇒ 3n + 8 + 37 + 69 = 180°

⇒ 3n + 114 = 180°

⇒ 3n = 180 - 114

⇒ 3n = 66

⇒ n = 22

The measure of ∠VWU = 3 × 22 + 8 = 74

Checking the results = 74 + 37 + 69 = 180°

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The two consecutive odd integers are 9 and 11. 1/8 plus 1/11 equals 12/35.

The sum of the reciprocals of two consecutive odd integers is 12/35.

1/x + 1/(x+2) = 12/35

(x+2)/(x*35) + (x/35) = 12/35

x + 2 + x = 12

2x = 10

x = 5

5 and 7 are the next two odd numbers.

The sum of the reciprocals of two consecutive odd integers is 12/35. To find the two integers, we need to solve for x. Since the two integers are consecutive and odd, the equation

1/x + 1/(x+2) = 12/35

can be used to find x. We can then multiply both sides of the equation by x*35 and simplify it to (x+2)/(x*35) + (x/35) = 12/35.

By subtracting x/35 from both sides and then adding 2 to both sides, we can get the equation

x + 2 + x = 12.

By solving the equation 2x = 10, we find that x = 5. This means that the two consecutive odd integers are 5 and 7. This can also be verified by checking that 1/5 + 1/7 is equal to 12/35.

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The variables on one side of the equation must be brought together, and the numbers on the other side must be brought together, in order to solve an equation with the same variable on both sides.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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Answer: 25;20

Step-by-step explanation:

40-25=20

It ask for ratio of boys TO girls. So you put amount of boys then girls.

The inverse of (- 2 . 3 ) is (1 / - 2.3 ).

In mathematics, the inverse of a number refers to the concept of taking its reciprocal; for instance (2 . w ) results in its reciprocal as ( 1/ 2. w ). When a number is multiplied by its inverse the result yields 1, meaning that the product of the number and its inverse, i.e. reciprocal always equals 1.

As per the given number which is (-2.3) and its inverse is ( 1 / -2.3 ), when these two numbers are multiplied together they result in 1. Such as:

(-2.3) x ( 1 / -2.3 ) = 1

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The value x = 3 is not a zero of polynomial f(x) = x³ + 3 · x² - x - 3. (Correct choice: C)

Let p(x) be a polynomial, a value x is a zero of polynomial p(x) when p(x) = 0. Now we need to determine a value x such that polynomial f(x) = x³ + 3 · x² - x - 3 ≠ 0. The procedure is shown below:

Case A: x = 1

f(1) = 1³ + 3 · 1² - 1 - 3

f(1) = 1 + 3 - 1 - 3

f(1) = 4 - 4

f(1) = 0

Case B: x = - 1

f(- 1) = (- 1)³ + 3 · (- 1)² - (- 1) - 3

f(- 1) = - 1 + 3 + 1 - 3

f(- 1) = 0

Case C: x = 3

f(3) = (3)³ + 3 · (3)² - (3) - 3

f(3) = 27 + 27 - 3 - 3

f(3) = 48

Case D: x = - 3

f(- 3) = (- 3)³ + 3 · (- 3)² - (- 3) - 3

f(- 3) = - 27 + 27 + 3 - 3

f(- 3) = 0

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The number of ways the questions can be answered is given by the equation A = 5⁵ ways = 3125 ways

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of ways the questions can be answered be A

Now , the equation will be

The total number of questions in the test = 5 questions

The total number of choices for each question = 5 choices

And , each choice of the question has been answered

So , the number of ways the questions can be answered  A = choices ^ questions

Substituting the values in the equation , we get

The number of ways the questions can be answered  A = 5⁵ ways

The number of ways the questions can be answered  A = 3,125 ways

Therefore , the value of A is 3,125 ways

Hence , the number of ways is 3,125 ways

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