if[ tex]x-\frac{1}{x} =1[/tex] then what is [tex]\frac{x}{x^{2}+3x-1 } =\frac{1}{4}[/tex]

let the missing length = x

[tex] \frac{ x }{27} = \frac{8}{8 + 10} \\ [/tex]

Corresponding side of congruent triangle are similar...

[tex] \frac{x}{27} = \frac{8}{18} \\ [/tex]

[tex]18x = 216[/tex]

[tex]x = \frac{216}{18} \\ [/tex]

[tex]x = 12[/tex]

hence the missing length is 12...

Answer:

43. 2 in. 2

Step-by-step explanation:

]43. 2 in. 2, 103. 68 in. 2

bottom was cut off a bit its 4=b

The exact area of the circle is 4π [tex]units^2[/tex].

The center of the circle is at the origin (0,0)

The diameter of the circle = 4 units.

So, the radius of the circle = 2 units.

The circle passes through points (2,0) and (-2,0). The given points are on the x-axis and they are exactly 2 units away from the origin

The area of a circle  A = π [tex]r^2[/tex],

where A is the area, π is approximately 3.14 and r is the radius of the circle.

So, the area of the circle with a radius of 2 units is A = π [tex]r^2[/tex] = π([tex]2^2[/tex]) = 4π [tex]units^2[/tex]

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Answer:2 = x

The missing step is:

Take the square root of both sides of the equation to get the value of x, which is:

x = 2 ± √(19/6)

Now we have our solutions, x = 2 + √(19/6) and x = 2 - √(19/6) which are the solutions of the quadratic equation.

Step-by-step explanation:

Answer: 1) Add 4   2) Subtract 24 from 5   3) 2

Correct on Edge 2023 :)

One example of a function that is its own inverse is the square root function. The square root function takes a number and returns its inverse, which is always negative.

For example, the square root of 4 is equal to -2, and the square root of -3 is equal to 3. This means that you can multiply a number by -1 and then take the square root to get the same number as the original number. This proves that the inverse of a number is always a negative number. The opposite of a square is known as a rectangle. This shows that the square functions as its inverse. Another example of a function that is its own inverse is the exponential function. The exponential function takes two numbers and returns the reciprocal of their product. This means that the exponential function is also its own inverse because the reciprocal of a product is equal to the product of the reciprocals.

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A linear graph depicts a direct relationship between two variables when it follows a straight line.

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Answer:

255

Step-by-step explanation:

51 x 100/20

After factorising 2+ k/3 = 5, the value of k is 9.

Finding the value of f(x) =   or y =   that corresponds to a given value of x is the definition of function evaluation.

Simply swap out all instances of x with the value that has been allocated to x to do this. For instance, if f(4) is to be evaluated, then x has been given the value of 4.

Fully factorizing an equation entails putting it in brackets by eliminating the factors with the highest common denominator.

The easiest method of factoring is: Find the terms in the phrase that have the highest common factor. Any bracket should have the highest common factor (HCF) in front of it.

In this question,

2+ k/3 = 5

Take L.C.M. of 1 and 3.

(6 + k)/3 = 5

6 + k = 15

k = 15 - 6

k = 9

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Answer: The formula for compound interest is A = P(1 + r/n)^(nt) where A is the amount, P is the principal (initial deposit), r is the interest rate, t is the time in years, and n is the number of times compounded per year.

To find out how many years it will take for the money to grow to 500 naira, we can set A equal to 500, P equal to 400, r equal to 5% (or 0.05), and n equal to 1 (since the interest is compounded annually).

Plugging these values into the formula, we get:

500 = 400(1 + 0.05)^t

By solving this equation, t = 3.32 years.

So, it will take 3.32 years for the money in the savings account to grow to 500 naira.

Step-by-step explanation:

Answer:

3, 6,  11, 18, 27

Step-by-step explanation:

[tex]1^{2}[/tex] + 2 = 3

[tex]2^{2}[/tex] + 2 = 6

[tex]3^{2}[/tex] + 2 = 11

[tex]4^{2}[/tex] + 2 = 18

[tex]5^{2}[/tex] + 2 = 27

Answer:

The sequence = [tex]a_{n} = 5n-5[/tex]

Step-by-step explanation:

To find the sequence use the formula [tex]a_{n} = a_{1} +d(n-1)[/tex] to identify the arithmetic sequence,  [tex]a_{n} = 5_{n} - 5[/tex].

The answer is Option 3: log 28.

Logarithm is a mathematical function that is used to determine the exponent of a given number. For example, the logarithm of 8 is equal to 3, since 2 to the power of 3 is equal to 8. Logarithm is also known as log and is commonly used in scientific calculations to simplify complex equations.


This can be derived by using the logarithmic rule of multiplication and addition: log(ab) = log(a) + log(b). In this case, log 4 + log 7 - log 2 = log(4*7) - log 2 = log 28.

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Answer:

d

Step-by-step explanation:

The multiplication functions are given as follows:

7) (f x g)(x) = 2x³ - 3x² - 21x - 18.

8) (f x g)(x) = (4)^x(2x + 8) - 10^x + 8.

The functions are multiplied first applying the associative property, multiplying all the terms among themselves, and then combining the like terms.

For item 7, the multiplication of the terms is given as follows:

(2x + 3)(x² - 3x - 6) = 2x³ - 6x² - 12x + 3x² - 9x - 18

Combining the like terms, the product is given as follows:

(2x + 3)(x² - 3x - 6) = 2x³ - 3x² - 21x - 18.

For item 8, the multiplication of the terms is given as follows:

(4^x - 5)(2x + 8) = 2x(4)^x + 8(4)^x - 10x + 8

Combining the like terms, the product is given as follows:

(4^x - 5)(2x + 8) = (4)^x(2x + 8) - 10^x + 8.

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42 is the answer to x3 y3 z3 K in sum of cubes problem.

In mathematics, completely by accident, there is a polynomial equation whose solution, 42, has similarly baffled mathematicians for decades. The "sum of cubes problem" refers to the equation x3+y3+z3=k.

The "sum of cubes problem" refers to the equation x3+y3+z3=k. The most brilliant mathematicians in the world have been baffled by a mathematical problem for decades. A Diophantine equation known as "summing of three cubes" is x3+y3+z3=k, where k is the sum of all the numbers between one and 100. ∴ 3xyz will be the necessary outcome.

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To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator. To find the conjugate, just change the sign in the denominator.

Now, According to the question:

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.

Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator. To find the conjugate, just change the sign in the denominator.

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The jam recipe that has more strawberry flavour would be recipe A with 1 cup of sugar to 6 cups of strawberries.

A recipe is defined as the a structured list that contains all the substances that are used for the preparation of a meal.

Strawberries = 3 cups

sugar = 1/2

Therefore 1 cup of sugar = 6 cups of strawberries

Strawberries = 5 cups

sugar = 1

Therefore 1 cup of sugar = 5 cups of strawberries

It can be concluded that jam recipe that has more strawberry flavour would be recipe A with 1 cup of sugar to 6 cups of strawberries.

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No, it is not possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(4.5cm + 5.5cm) =10.0cm

10.0cm = 10.0cm

LHS = RHS

A triangle is not possible.

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 distance between the points (2, 0) and (-3, 2) = 5.4 units.

As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given points (2, 0) and (-3, 2)

Let us assume that  (x₁, y₁) = (2, 0)

and (x₂, y₂) = (-3, 2)

Let d represents the distance between points (2, 0) and (-3, 2)

Using above distance formula the distance d between given points would be,

[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-3 - 2)^2 + (2 - 0)^2]}\\\\\Rightarrow d = \sqrt{[(-5)^2 + (2)^2]}\\\\\Rightarrow d = \sqrt{25+4}\\\\\Rightarrow d = \sqrt{29}\\\\\Rightarrow d = 5.4~units[/tex]

Therefore, the distance is 5.4 units.

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The complete question is:

What is the distance between the points (2, 0) and (- 3, 2)?.

The probability that both people have their ears pierced is calculated by dividing the number of people with pierced ears by the total number of people in the sample. This can be expressed as a fraction, with 430/2000 = 0.215, or 21.5%.

Probability is a measure of how likely an event is to occur. It is stated as a number between 0 and 1, with 0 indicating that the occurrence is impossible and 1 indicating that the event is unavoidable.

In this question, by dividing the number of persons with pierced ears by the total number of participants in the sample to find the chance that both people have their ears pierced. In this situation, the answer is 430/2000 = 0.215.

This may be read as follows: 430 persons out of every 2000 get their ears pierced. Therefore the chance of picking two persons at random from this sample who both had their ears pierced is 0.215, or 21.5%.

This may also be stated as a fraction, with the numerator being the number of persons with pierced ears (430) and the denominator representing the total number of participants in the sample (2000). As a result, the likelihood is 430/2000, or 0.215.

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The statements that are true about the reflectional symmetry of a regular heptagon are:

A heptagon is a type of shape.

A two-dimensional shape having seven sides and seven angles is called a heptagon. It is a member of the two-dimensional geometry polygon class. Polygons are closed geometric shapes with only straight edges. In Greek, "hepta" denotes seven, while "gonia" denotes an angle.

A line of symmetry will connect a vertex and a midpoint of an opposite side.

It has 7-fold symmetry.

A regular heptagon has 7-fold symmetry, which means that it can be divided into 7 identical parts by rotating it by 360/7 = 51.43 degrees. Since it has 7 sides, a line of symmetry will connect a vertex and a midpoint of an opposite side.

It has only 1 line of symmetry, and a line of symmetry will not connect 2 vertices or the midpoints of 2 opposite sides.

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If the bisector of one of the angles of a rectangle also bisects the side of a rectangle. The perimeter of the rectangle if you know that the shorter side of the rectangle is equal to 10 cm is 60cm.

If we look at triangle BCE, we will see that triangle BCE   is isosceles based on the fact that both angles are equal to 45 degrees.

Hence,

BC = CE =10 cm

Lengths of the base and height = 20 and 10

Now let find the  perimeter of the rectangle

Perimeter of the rectangle  = 20 + 10+20+10

Perimeter of the rectangle = 60cm

Therefore the  perimeter of the rectangle is 60cm.

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Answer: x= 12.4

Step-by-step explanation:

you should use trigonometry for this question, and you will have to follow tan to find the opposite side of the right-angled triangle.

tanθ = [tex]\frac{O}{A}[/tex]

tan(54°)= [tex]\frac{x}{9}[/tex]

tan(54)°x 9 = x (you should cross multiply)

x= 12.39

x= 12.4

One can solve basic algebraic expressions by following these steps.

In grade 6, students typically learn to solve basic algebraic expressions by following these steps:

Identify the variable and the coefficient (number in front of the variable) in the expression.

Use the order of operations (PEMDAS) to simplify any arithmetic within the expression.

Use the distributive property to combine like terms.

Isolate the variable on one side of the equation by using inverse operations (such as adding or subtracting the same value from both sides, or dividing or multiplying both sides by the same non-zero value).

Substitute in a value for the variable to find the numerical value of the expression.

It's good to practice with a lot of examples and check the solutions and ask for help if needed.

Example:

Solve for x: 3x + 2 = 12

variable is x, coefficient is 3

nothing to simplify

nothing to combine

subtract 2 from both sides: 3x = 10

divide both sides by 3: x = 10/3 or 3.3333

x = 3.3333

It's important to note that solving algebraic expressions can become more complex as the student progresses, but the basic steps remain the same.

Thus, One can solve basic algebraic expressions by following these steps.

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As a result, the square root function has a range of [0,]. Any x value for which the radicand (the value below the radical sign) is not negative is the domain of a radical function.

This indicates that x  5 equals 0. due to the fact that the square root must always be positive or 0

All of a function's possible x-values, or inputs, are included in its domain. Both positive and negative numbers are included in this.

The fact that the square root of any real number x cannot be negative creates this problem. As a result, the system of real numbers does not contain the square root of a negative number.

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A scatter plot is a form of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a collection of data.

It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram. A plot is a visual representation of a data collection, typically in the form of a graph illustrating between two or more variables.

But you may also do this with data that is offered in tabular form. Graphs may also be used to count off the value of an unknowing variable plotted as a function of a known variable if a scale or ruler is available.

Graphs and charts are useful visual aids because they make information accessible and quick to understand.  When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.

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The linear equation that gives the rule for this table is y = 19x - 12.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The standard linear equation can be represented as:

y = mx + b

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

From the table we can see the two points through which the point passes is:

(x1, y1) = (2, 26)

(x2, y2) = (3, 45)

The slope of the line is given by:

m = (y2 - y1) / (x2 - x1)

m = (45 - 26) / (3 - 2)

m = 19 / 1 = 19

The slope m = 19.

The point-slope form of the line can be written as:

y - y1 = m (x - x1)

y - 26 = 19 (x - 2)

y - 26 = 19x - 38

y = 19x - 38 + 26

y = 19x - 12

Hence, the linear equation that gives the rule for this table is y = 19x - 12.

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We can use zero product property in a series of steps to find the quadratic equation by factoring.

In mathematics, the zero product property states that if A and B are mathematical expressions, and AB = 0, then A = 0 or B = 0.

The steps that we use to solve a quadratic equation by factoring are as follows:

1- Put the equation in the form ax² + bx + c = 0, where a, b, and c are constants.

2- Factor ax² + bx + c.

3- Use the zero product property to set each factor equal to 0.

4- Solve each of the resulting equations for x.

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