What is complex rational algebraic expression *?.

Answer:

n = 28

Step-by-step explanation:

2^2 is equal to 4, so we can plug in 2^2 as 4. Then, 4 * 7 = 28, so n = 28.

The complete table would look like this:

Number of loaves    Number of Bananas

1                                    2 1/2

2                                   5                            

4                                    10

What is a number line?

A number line is a visual representation of a continuous range of numbers, usually represented as a straight line. Numbers are represented by points along the line, and the distance between two numbers corresponds to the difference between their numerical values. The numbers are usually represented by evenly spaced marks or tick marks on the line, and they can be positive or negative numbers, integers or fractions, or real numbers. The number line is used to represent various mathematical concepts such as inequalities, absolute values, and intervals. It is also used to help students understand concepts such as addition, subtraction, and ordering of numbers.

So the first one was easy because it already said it in the number line.

For the second one you simply multiply 2x 2 1/2

For the third one, you multiply 4x 2 1/2.

Hence, The complete table would look like this:

Number of loaves    Number of Bananas

1                                    2 1/2

2                                   5                            

4                                    10

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A 30-degree angle is a measure of an angle, which is one-sixth of a full rotation or circle.

The measure of an angle is the amount of rotation between the two rays that form the angle, measured in degrees. The full rotation of a circle is 360 degrees, so one-sixth of a full rotation is 360 degrees divided by 6, which equals 60 degrees. However, a 30-degree angle is half of a 60-degree angle, so it is half of one-sixth of a full rotation, which is 30 degrees. It's also a right angle's complement angle, meaning that the sum of the 30 and 60 degrees angles is 90 degrees, a right angle. In geometry, 30-degree angles are often used in various calculations and constructions, such as finding the measure of complementary and supplementary angles, solving trigonometric problems, and drawing geometric figures.

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Its value is expressed as f(x). The line has a slope of m.In the coordinate plane, the point where the line crosses the y-axis is where the function's value, or b, is determined when x is equal to zero.The coordinate's value, x, is given. The f(x) is 1.2x.

Its value is expressed as f(x). The line has a slope of m.In the coordinate plane, the point where the line crosses the y-axis is where the function's value, or b, is determined when x is equal to zero.The coordinate's value, x, is given.

Detailed explanation:

Given:

f(x - 5) = 1.2x - 6

Required:Find f (x) In order to solve f(x), we must translate f(x - 5) into terms of f. (x). The procedure is as follows.

f(x - 5) = 1.2x - 6

The expression to the right should be factored.

f(x - 5) = 1.2(x - 5) (x - 5)

Now that we have changed x for x - 5 in the previous formula, we may solve for f(x) (on the right hand side and the left hand side).

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An intuitive definition: a function ݂f is said to be convex at an interval I if, for all pairs of points on the ݂f(x) graph, the line segment that connects these two points passes above the ݂f(x) curve.

A function ݂ is said to be concave at an interval I if, for all pairs of points on the graph f(x), the line segment that joins these two points passes below the ݂f(x) curve.

A convex function has a regularly increasing first derivative, making it appear to bend upwards.

Contrarily, a concave function has a regular decreasing first derivative making it bend downwards. It is very important to know the distinction between the first derivative, that tells us of the slope of the tangent of a function, and the second derivative, which shows us how it is curved.

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According to the given statement, If the principal was invested at 2.45% compounded weekly for 78 months, then The principal is 9521.

When you first take out a home loan, you borrow a certain amount of money, which is known as the principal. Simply deduct your deposit for a house from the final selling price of your home to determine your mortgage principal.The principal amount means the amount you owe at any point in time.

The formula is =

11139.58 = x (1 + 0.0245) ^6.5

11139.58 = x (1.0245) ^ 6.5

11139.58 = 1.17x

x = 11139.58/ 1.17

x = 9521 (approx)

Hence, the principal is 9521.

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If the historical data says that the number of road bikes sold is 9 and the number of stationary bikes sold is 3, out of a total of 60 bikes, then  the probability that the next customer purchase a stationary bike is 1/20.

A probability based on historical data is referred to as empirical probability or experimental probability. In other words, empirical probability depicts the probability of an occurrence occurring based on past data.

Empirical probability is also known as the relative frequency.

Formula for the empirical probability is:

Empirical probability = times of event A occurs / total number of trials

In the problem, there are two kinds of bike: road bike and stationary bike.

The historical data:

sales of road bike = 9

sales of stationary bike = 3

total bikes = 60

Hence, the probability that the next customer will buy a stationary bike is:

P(stationary) = sales of stationary bike / total bikes

P(stationary) = 3/ 60 = 1/20

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The transformed equation is y = -1/(x + 2) - 3

From the question, we have the following parameters that can be used in our computation:

y = -1/x

We have the transformation to be

(2, -3)

This implies that we transform the function be (x + 2, y - 3)

using the above as a guide, we have the following:

y = -1/(x + 2) - 3

The above represents the new equation when the previous is transformed

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The value of x as shown in the straight line is 32

An equation is an expression showing the relationship between numbers and variables.

An angle is formed when two lines intersect at a point. The sum of angles in a straight line is 180 degrees.

From the diagram:

(3x - 4) + (3x - 8) = 180° (sum of angle in a straight line)

3x + 3x - 4 - 8 = 180

6x - 12 = 180

6x = 192

x = 32

The value of x is 32

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y = (1/3)x - 2 is an equation of a line where the slope of the line is 1/3 and the y-intercept of the line is -2.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = (1/3)x - 2

This is in the form of y = m + c

So,

This is an equation of a line.

The slope of the line = 1/3

The y-intercept of the line is -2.

Thus,

y = (1/3)x - 2 is an equation of a line.

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The roots of the quadratic equation 6x²-2x=8 are x=4/3 and x=-1.

Given that,

The equation is 6x²-2x=8

To find : The roots of the quadratic equation 6x²-2x=8

Any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known values, where a 0, is referred to as a quadratic equation in algebra (from Latin quadratus, "square"). The equation is linear, not quadratic, if a = 0 and b 0. The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.

We know that,

The solutions are x1 and x2  = -b±√b²-4ac/2a

Here b = -2 ,a = 6 and c= -8

No substitute those values in the formula,

= -b±√b²-4ac/2a

= -(-2) ± √(-2²)-4(6)(-8) / 2(6)

x = 4/3 and x =-1

So, The roots of the quadratic equation 6x²-2x=8 are 4/3 and -1

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The two chickens and a dog three animals won.

The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.

Given that There are 1 hamster 4 dogs running at 5mph and 2 chickens running at 3mph.

One dog speeds up 5mph and the chickens speeds up 10mph.

Then the dogs quit and the chickens keep going and speed up at 3 mph.

We have to find the winner.

The chicken win the race.

Hence, the two chickens and a dog three animals won.

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Antionette can purchase a maximum of 56 adult-sized t-shirts.

What is algebraic ?

Algebraic refers to anything that pertains to algebra, which is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Algebraic concepts include using variables (such as x or y) to represent unknown values, using operations such as addition, subtraction, multiplication and division.

Let x be the number of adult-sized t-shirts that Antionette purchases.

We know that ,

The cost of each adult-sized t-shirt is $6.25

The cost of each youth-sized t-shirt is $4.50

Antionette has $550 to purchase both adult-sized and youth-sized t-shirts

Antionette purchases 45 youth-sized t-shirts

We can set up the equation to represent the total cost of all the t-shirts and the money Antionette has ,

(x6.25) + (454.50) = 550

To solve for x, we can simplify the equation by multiplying the number of adult-sized t-shirts by the cost per t-shirt and the number of youth-sized t-shirts by the cost per t-shirt, and then set it equal to the total money Antionette has ,

x*6.25 + 202.5 = 550

then we can subtract 202.5 from both sides , x*6.25 = 347.5

then divide both sides by 6.25 to get ,  x = 56

So, Antionette can purchase a maximum of 56 adult-sized t-shirts.

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The cost of each adult-sized t-shirt is $6.25

The cost of each youth-sized t-shirt is $4.50

Antionette has $550 to purchase both adult-sized and youth-sized t-shirts

Antionette purchases 45 youth-sized t-shirts

(x*6.25) + (454.50) = 550

x*6.25 + 202.5 = 550

then we can subtract 202.5 from both sides , x*6.25 = 347.5

then divide both sides by 6.25 to get ,  x = 56

So, Antionette can purchase a maximum of 56 adult-sized t-shirts.

The radius of the circle created by the ice skater is 1 yard.

What is circle ?

A circle is a two-dimensional geometric shape that is defined by a set of points that are all the same distance from a central point called the center. The distance from the center to any point on the circle is called the radius. The distance across the circle, passing through the center, is called the diameter.

The radius of a circle is half of its diameter, so the radius of a circle with a diameter of 2 yards is 1 yard.

Radius = Diameter/2

Radius = 2/2 = 1 yard

So, the radius of the circle created by the ice skater is 1 yard.

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The radius of a circle is half of its diameter, so the radius of a circle with a diameter of 2 yards is 1 yard.

Radius = Diameter/2

Radius = 2/2 = 1 yard

So, the radius of the circle created by the ice skater is 1 yard.

The lines which are parallel among the given answer choices are; line 1; y = 1/2x - 6 and line 2; x - 2y = -1.

Recall that parallel lines are described by the feature such that; they have equal slopes but different y-intercepts.

Hence, by representing the equations in slope-intercept form; we have;

line 1; y = 1/2x - 6

line 2; x - 2y = -1;. y = 1/2x + 1

line 3; y = 4x + 6

line 4; y + 3 = 1/4 (x-6);. y = 1/4x - 9/2.

By comparison with the slope-intercept form equation; it follows that the lines which have equal slopes but different y-intercepts is the pair; line 1 and 2.

Hence, the parallel lines are; lines 1 and 2.

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The process of dividing the two digit numbers without a calculator is solved by using the dividend, divisor, quotient and remainder.

Division in math is defined as the process to distribute the whole thing to a group in equal parts or make equal parts.

Here we need to find he way to divide two digit numbers without a calculator.

As per the definition of division, here we have to divide the first number of the dividend or the two first numbers if the previous step took another digit by the first digit of the divisor.

And then we have to write the result of this division in the space of the quotient.

Finally we have to multiply the digit of the quotient by the divisor, then write the result beneath the dividend and subtract it.

This process is repeated until we get zero as remainder.

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Answer:

2.964

Step-by-step explanation:

4-1.036=2.964

Answer:

2.964

Step-by-step explanation:

4 - 1.036 = 2.964

The square root of negative number can be negative imaginary number (complex number)

As we know the square root of a number is nothing but the factor/value that we can multiply by itself to get that number.

Finding a square root of number is an inverse method of squaring a number.

A radical symbol '√' used to represent the square root of number.

If m is the square root of n, then it is represented as m = [tex]\sqrt{n}[/tex],

We can write above relation as, m² = n

We know that square of any real number is positive.

For example, 3² = (3 × 3) = 9

(-3)² = (-3) × (-3) = 9

i.e., the square root of 9 is 3 and -3

Thus the square root of a negative number is undefined among the set of Real Numbers.

As we know the set of real numbers is subset of complex numbers.

In complex numbers, the imaginary number 'i' is the square root of negative 1.

When an imaginary number is squared, the result is negative number.

Consider example,

[tex]\sqrt{-16}\\\\ =\sqrt{16} \times \sqrt{-1}\\\\ =(\pm 4)\times i\\\\=\pm4i[/tex]

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In the given arithmetic sequence, the First term is -74, 2nd term is -81 3rd term is -88 and 4th term is -95.

There are two ways to define an arithmetic sequence. It is a "sequence where the differences between every two successive terms are the same" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term." The following is an arithmetic sequence where each term is obtained by adding 4 to the term before it.

We know that arithmetic sequence is:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

Given

a = -74, d = -7

[tex]a_{1} = -74 + (1 - 1)(-7)[/tex]

[tex]a_{1} = -74 + (0)(-7)[/tex]

[tex]a_{1} = -74[/tex]  (First term)

[tex]a_{2} = -74 + (2 - 1)(-7)[/tex]

[tex]a_{2} = -74 + (1)(-7)[/tex]

[tex]a_{2} = -81[/tex] (2nd term)

[tex]a_{3} = -74 + (3- 1)(-7)[/tex]

[tex]a_{3} = -74 + (2)(-7)[/tex]

[tex]a_3 = -88[/tex] (3rd term)

[tex]a_{4} = -74 + (4- 1)(-7)[/tex]

[tex]a_{4} = -74 + (3)(-7)[/tex]

[tex]a_3 =-95[/tex] (4th term)

Thus, In the given arithmetic sequence, the  First term is -74, 2nd term is -81 3rd term is -88 and 4th term is -95.

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The evaluation of the simultaneous equation is as follows;

a) The simultaneous equations, indicates by plugging in the value of the variable x in the first equation, that the first equation is; 7·x² + 5·y + 3 = 0

b) The equation has no real solutions

Simultaneous equations are set two or more equations that have common solution.

The simultaneous equations are;

y² + x·y + 3 = 0...(1)

x = 6·y + 5...(1)

Plugging in x = 6·y + 5, in equation (1) we get;

y² + x·y + 3 = y² + y × (6·y + 5) + 3 = 0

y² + 6·y² + 5·y + 3 = 0

b) The number of solutions the simultaneous equation has can be obtained by solving the equation, obtained in part (a), 7·y² + 5·y + 3 = 0, as follows;

7·y² + 5·y + 3 = 0

The quadratic formula for finding the solution of the equation; a·x² + b·x  + c = 0, is; -b±√(b² - 4·a·c)/(2·a)

Where the discriminant is; b² - 4·a·c

Comparing the equations, we get;

a = 7, b = 5, and c = 3

b² - 4·a·c is therefore; 5² - 4 × 7 × 3 = -59

The discriminant is less than 0, therefore, there are no real solutions to the equation, but there are to imaginary solutions

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Answer:

These two equations are equivalent to each other because they both represent the same mathematical operation and they both yield the same result.

The first equation, 88 + 32, is adding 88 to 32, which results in the sum of 120.

The second equation, 90 + 30, is adding 90 to 30, which also results in the sum of 120.

In other words, both equations represent the same mathematical operation (addition) of two numbers (88 and 32 or 90 and 30) and both yield the same result (120).

Step-by-step explanation:

a brainliest pls

The amount of natural numbers from m to k that Jane wrote is given as follows:

k - m + 1.

The natural numbers are the numbers that represent countable amounts, hence they are non-decimal and non-negative amounts.

The set of natural numbers can be represented as follows:

{0, 1, 2, 3, ...}

The number of natural numbers between 0 and 1 is given as follows:

2, which are 0 and 1.

2 = 1 - 0 + 1.

Hence the number of natural numbers between m and k is given as follows:

k - m + 1.

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The player's chances of scoring a goal on their next shot are 0.205, or 20.5%.

This is calculated by dividing the number of goals they scored (16) by the number of shots they took (78).

The formula for finding the probability:

P(A) = number of favorable outcomes / total number of possible outcomes

16 / 78 = 0.205

Probability is a mathematical concept that quantifies the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is unavoidable.

A probability of 0.5 (or 50%) means that the event is equally likely to occur or not occur.

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Answer:

no its incorrect

Step-by-step explanation:

-2(8m+8)=-16 is worng its m=0

The problem is incorrect.

The correct solution for the given equation is:

-2(8m +8) = -2(8m) -2(8) = -16m -16

You cannot simplify it to -16 as the equation is not a true equation.

Please let me know if there is something more I can assist you with.

A quadratic function has no real roots and does not intersect the x-axis if the discriminant of the function is less than zero.

How many roots f(x) has is shown by the discriminant's value: - The quadratic function has two unique real roots if b2 - 4ac > 0 A repeated real root exists in the quadratic function if b2 - 4ac = 0. The quadratic function doesn't have any real roots if b2 - 4ac is less than 0.

Formula for the quadratic 4x2-8x9=0

4x2−8x−9=0

The answers can be found using the quadratic formula.

−b±√b2−4(ac)/2a

Replace the values

a=4

, b=−8

, and

c=−9

Then enter it into the quadratic formula to find

x.8±√(−8)2−4⋅(4⋅−9)/2⋅4

Simplify.

To continue, tap...

x=2±√13/2

There are various ways to display the outcome.

precise form:

x=2±√13/2

Number Form:

x=2.80277563…,−0.80277563…

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Full Question = What is the nature the roots of quadratic equation 4x²-8x+9=0?​

The area of the rectangle is 20. The length of the base and the height are 2√10 and √10.

From the case, we know that each point's locations are:

A = (-7, 4)

B = (-1, 6)

C = (0, 3)

D = (-6, 1)

Since the graph is a rectangle then it has 2 kind of sides, the height and the weight. Based on the given graph, we can categorize each side as:

Height = BC = DA

Base = AB = CD

We can find the length of each sides by using the coordinates of each point.

Length of a side = √[(x2 - x1)² + (y2 - y1)²]

Lenght of AB = √[(xB - xA)² + (yB - yA)²]

Length of AB = √[(-1 - (-7))² + (6 - 4)²]

Length of AB = √[6² + 2²]

Length of AB = √(36 + 4)

Length of AB = √40

Length of AB = 2√10 --> Length of the base

Length of BC = √[(xC - xB)² + (yC- - yB)²]

Length of BC = √[(0 - (-1))² + (3 - 6)²]

Length of BC = √(1² + (-3)²)

Length of BC = √(1 + 9)

Length of BC = √10 --> Length of the height

The area of the rectagle would be:

Area = base x height

Area = 2√10 × √10

Area = 20

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