Show that x(x - 1)(x + 1) = x³ - x

“3 more than 5” written as an algebraic expression is “3+5” which is equal to 8.

In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra. Similar to how a statement explains the link between certain words, algebraic equations describe the connection between unknown variables.

We are given a mathematical statement and have to convert it into an algebraic expression using the information above.

3 more than 5 is obtained after adding 5 to the given number which is 3.

So 3 more than 5 is equal to 3+5=8.

Hence “3 more than 5” written as an algebraic expression is “3+5” which is equal to 8.

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On solving the provided question, we can say that the value of x = 5√3

and value of y = 10.

How to find the value of x and y?

To find the values of x and y, you will need to use

According to the given question:

Using the table of trig values, we find that

sin30°=1/2

So, this gives us:

1/2 = sin 30° = 5/y

1/2 = 5/y

(1xy)/2 = 5

y= 2×5 =10

Next, using the Pythagorean Theorem, we find that

5²+x²=10²

x²=100−25=75

Solve for x:

x=√75=√3×25=5√3

Complete question:

How do you find the value of X and Y. Y is the hypotenuse, 5 is the adjacent side and X is the opposite side from Y, and in the triangle there is 30 degrees where X and Y lines meet?

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Thousands, hundreds and tens are three examples of values and there are many more.

Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.

The number 4 is in this case in the tens column. As a result, the place value of the number four is tens or tens.

Thousands, hundreds and tens are three examples of values and there are many more like ones etc. Moreover after solving any problem for unknown variable the resulting numerical solution can also be termed as value.

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Two or more shapes are said to be similar if they have common corresponding properties of sides and/ angles. Thus the error made is option D.

Similar shapes are two or more given shapes that have some common properties with respect to their corresponding sides or angles. So that if on comparing each corresponding sides or angles, and are related, then they are similar. Note that similarity does not imply congruency.

Comparing the sides and angles of the given triangles ΔLMN and ΔQRS, it can be seen that;

Angle Side Angle (ASA) similarity relation implies that the included side between two pairs of congruent angles are similar. Thus, the error made in the diagram is explained in option D.

Option D. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the included sides between the two pairs of congruent angles are not marked as congruent in both triangles.

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The perimeter of triangle def similar to triangle abc is 22 cm.

Perimeter is the total distance around a object.

Note: The ratio of the perimeters of two similar figures is equal to the ratio of their corresponding side lengths.

To calculate the perimeter of triangle def, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for P'

Hence, the perimeter of triangle def is 22 cm.

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Answer:

9% decrease

Step-by-step explanation:

Hope this helps!

Answer:

If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then triangle ABC is congruent to triangle DEF.

The system has no solution.

What is linear equations?

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y)

We know that

The solution of the system of two linear equations, is the intersection point both lines.

In this problem

The lines are parallel, the lines don't intersect

therefore

The system has no solution

Remember that, if two lines are parallel then their slope are equal

Verify that the slopes are the same

Blue line

take the points  (0,2) and (-2,0)

[tex]m=(0-2) /(-2-0)=1[/tex]

Red line

take the points  (0,-3) and (3,0)

[tex]m=(0+3) /(3-0)=1[/tex]

The slopes are equal

The lines are parallel

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0.03, 0.04, 0.38, and 1 are the figures that could represent an event's likelihood .Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible

Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible. Probability differs from odds in this regard. Calculating odds involves dividing the likelihood of a particular event by the likelihood that it won't occur.

The likelihood of success is a measure of probability. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.

6. P(7) = 1/10

7. P(less than 5) = 4/10 = 2/5

8. P(greater than 10) = 5/10 = 1/2

11. P(divisible by 2 or 3) = 6/10 = 3/5

12. P(moon) = 8/36 = 2/9

13. P(star) = 12/36 = 1/3

14. P(blue moon or planet) = (6+9)/36= 15/36= 5/9

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Answer:

Step-by-step explanation:

6. P(7) = 1/10

7. P(less than 5) = 4/10 = 2/5

8. P(greater than 10) = 5/10 = 1/2

11. P(divisible by 2 or 3) = 6/10 = 3/5

12. P(moon) = 8/36 = 2/9

13. P(star) = 12/36 = 1/3

14. P(blue moon or planet) = (6+9)/36= 15/36= 5/9

If Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. The amount that is closest to how much she will earn in hourly wages and commission for those two weeks is A $592.

Earnings can be defined as the money a person earn as wages or as salary.

First step is to find the amount that Sandy earns per hours

Earnings per hour = 9+ (0.15×9)

Earnings  = $10.35 per hour

Second step is to find her earnings

Earnings =73 × $10.35

Earnings = $755.55

Closest amount is $592.

Therefore  the correct option is A.

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The complete question is:

Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 73 hours over the last two weeks and had a total of $2,830 in sales before taxes.

Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?

A $592

B $890

C $386

D $298

Answer:

Step-by-step explanation:

138 cm² = (x + 2) × ( 2x + 3) x 1/2​

138 cm² = x + 2 ×  2x + ) x 1/2​

138 cm² = x + 4x + x * 0.5

0.5/138 cm² = 6x * 0.5 /0.5

6/69cm²  = 6x/6

x = 11.5

This might be wrong so just take the square root of 138.

Answer:

A. 4,500 + 50g = 6,000

Step-by-step explanation:

25(18) + 50(g) = 6000

4500 + 50g = 6000

The correct option is A.

Answer:

24 Square Units (B)

Step-by-step explanation:

⭐ The formula for the area of any triangle is: 1/2(bh), where b = base, and h = height.

⭐ The height of a triangle is the triangle's altitude, which can be denoted by a straight line with a right angle. In this problem, the height is given to you.

Let's substitute what we are given to find the area.

The last expression is equivalent to √5³.

What equation contains an expression?

The equal to sign (=) is the best indicator of whether a given problem is an equation or an expression because it indicates that the problem is an equation.

                    It is only an expression if there isn't an equal to (=) sign present. It contains data that is used to demonstrate value, such as numbers, variables, and operators.

                   [tex]= ( 5^{1/8} * 5^{3/8} )[/tex]

                   [tex]= ( 5^{1/8} * 5^{3/8} ) \\= 5^{(1/8 + 3/8)}[/tex]

                    [tex]= 5^{4/8}[/tex]

                    [tex]= 5^{(1/2)}[/tex]

                   [tex]= [5^{(1/2)}]^{3}[/tex]

    Because of the "Power of a power property"

                                    = [tex]5^{3/2}[/tex]

The last expression is equivalent to √5³.

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We can factor using the rational root theorem by a rational number, both the leading coefficient and the constant term must be divisible by the fraction's denominator.

The rational root theorem, also known as the rational root test, is an algebraic principle that states that for a polynomial equation with one variable and integer coefficients to have a solution (root) that is a rational number, both the leading coefficient and the constant term must be divisible by the fraction's denominator.

A particularly helpful theorem is the theorem of rational roots.

It explains how to get a list of potential solutions for a polynomial function with integer or whole number coefficients by ranking the factors of the constant, or last term, over the factors of the coefficient of the leading term.

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The AAA (angle-angle-angle) similarity theorem states that two triangles' corresponding angles are identical if and only if their corresponding sides are proportionate.

Knowing two angles, such as 32° and 64°, we may calculate the following angle, which is 84°, since 180-(32+64)=84. (This is commonly referred to as the AAA Postulate—which is valid in every way, although two angles are more than enough.) Working backwards will help you understand the proposition better.

The sides and angles of a set of triangles must be equal for them to be congruent. The sides of a triangle with all respective angles equal, i.e. AAA condition, may or may not be equal.

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Answer:

8(11x-13)

Step-by-step explanation:

[tex]13(5x-8)+23x\\65x-104+23x\\88x-104\\8(11x-13)[/tex]

The equation of the line that passes through the given points will be equal to  11x -9y + 101 = 0.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the data in the question,

Use the equation of the line passing through the point (x₁, y₁) with slope m will be:

y - y₁ = m(x - x₁)

Slope, m = 11/9

And, the points are (-1, 10)

Now,

y - 10 = 11/9(x + 1)

9y - 90 = 11x + 11

11x - 9y + 11 + 90 = 0

11x -9y + 101 = 0

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The 17th hole would be 255 yards long.

What are ratio and proportion?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

hole = c yards

1.5 / 40 = 8.5 /c

1.5 * c = 45 * 8.5

1.5 * c = 382.5

c = 255 yards

Hence, the 17th hole would be 255 yards long.

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An example expression is the following:

$100 + $50n

An algebraic expression is a set of letters and numbers, in which the letters are called variables and take on an unknown value, the numbers are coefficients or independent terms while the variables are dependent terms.

We will write an algebraic expression to exemplify what has just been defined, with a verbal example.

A person has a business, and he adds $100 to the box (and his sales are on average $50 per hour, with this we build the expression of total income:

$100 + $50n

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This is an arithmetic sequence. In this sequence, the common difference is 6 (12 - 3/6 = 6).

A sequence is an ordered arrangement of objects or events which follow one another in a specific order. This order can be based on a mathematical rule or pattern, such as a sequence of numbers, or it can be based on physical or temporal characteristics of the objects or events, such as the order in which they appear in a movie or story. Sequences are useful for representing and analyzing data, as well as for visualizing relationships between objects. They can also be used to model problems, such as predicting the future or solving a puzzle.

This is an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a constant, called the common difference, to the preceding term. In this sequence, the common difference is 6 (12 - 3/6 = 6).

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The answer is True. If two vertical angles are congruent, then two lines cut by a transversal will be parallel.

Vertical angles are angles that are opposite each other and share the same vertex. They are congruent angles, meaning that they have the same measure. When two angles are congruent, the sides of the angles are parallel. This means that the two lines cut by a transversal will also be parallel.

The formula for this is that if two angles are congruent, then the lines cut by a transversal are parallel. This is also known as the Angle-Angle-Angle (AAA) Postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. This means that the lines cut by a transversal are parallel.

In other words, if two angles of a triangle are congruent, then the two sides of the triangle that make those angles are parallel. This is because the two angles are congruent, meaning that they have the same measure. Therefore, if two vertical angles are congruent, then two lines cut by a transversal will be parallel.

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Answer:

There were 74 hot dogs and 117 sodas sold.

Step-by-step explanation:

The following equation describes the conditions of the question:

[tex]191=x+(x+43)\\191=2x+43\\[/tex]

where x is the number of hot dogs sold.

Solve for x:

[tex]191=2x+43\\(191)-43=(2x+43)-43\\148=2x\\\frac{148}{2}=\frac{2x}{2}\\74=x[/tex]

There were 74 hot dogs sold and (74+43) or 117 sodas sold.

The inverse of a 2x2 identity matrix is also a 2x2 identity matrix. This is because the identity matrix is its own inverse.

An identity matrix is a square matrix with all primary diagonal members set to one and all other elements set to zero. The letter "In" or just "I" is used to indicate it. Any matrix will produce a given matrix if it is multiplied by the identity matrix. . The components of the provided matrix stay the same.

The 2x2 identity matrix is a square matrix with 1s on the main diagonal and 0s everywhere else. It has the following form:

[1 0]

[0 1]

The inverse of this matrix is also a 2x2 identity matrix with the same form:

[1 0]

[0 1]

Therefore, the inverse of a 2x2 identity matrix is also a 2x2 identity matrix.

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The altitude of an isosceles triangle is sqrt (a^2 - b^2 / 4).

In the triangle ABC, sides AB and AC are equal (say a) and side BC = b. Let  us consider the triangle ADC which is the right triangle in the isosceles triangle ABC, and by Pythagoras' theorem,

we get that the altitude AD of the isosceles triangle can be obtained:

AD ^ 2 = AC ^ 2 - (BC / 2) ^2

AD ^ 2 =  (a ^ 2 - b ^ 2 / 4)

AD = sqrt (a ^ 2 - b ^ 2 / 4).

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43 in arithmetic stands for multiplying 4 by three. Suppose x =43; then, x+4*4*4.

If the power is positive, multiply the integer by itself that many times. If the power is negative, multiply the reciprocal of the integer by itself that many times. If the power is 0, the result is always 1.

No, 3:9 and 9:3 are not equivalent. 3^9=19683 and 9^3=729.

4^3=4*4*4\s =16*4\s =64

In the US and Canada, math is the word of choice. In the United Kingdom, Ireland, Australia, and other English-speaking countries, math is the preferred term. There isn't really a rational reason why math grew more popular in certain locations while maths was elsewhere.

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Therefore , the factors of the given equation are (x + 4), (x - 5) and (x + 1)

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

Here,

The first term, x2, has a coefficient of 1 and is the starting term.

The coefficient of the middle word, +5x, is 5, thus

"The constant," the final word, is +4.

Step 1: Multiply the first term's coefficient by the formula 1 + 4 = 4.

Step 2 is to identify two factors of 4 whose sum equals the middle term's coefficient, which is 5.

     -4    +    -1    =    -5

     -2    +    -2    =    -4

     -1    +    -4    =    -5

        4          +            1      =    5    

Step 3: Rewrite the polynomial by separating the middle term into the two parts 1 and 4 x2 + 1x + 4x + 4 discovered in Step 2 above.

Step-4 : adding the first two terms while excluding similar elements

                   x • (x+1)

             Adding the last two terms together and finding commonalities:

                   4 • (x+1)

Step-5 : In step 4, add up the four terms:

                   (x+4)  •  (x+1)

            Which is the desired factorization

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The relationship between the volume of pyramid and prism is that when a pyramid and prism have the same base and height, volume of prism is 1/3rd the volume of prism.

The volume of the cylinder is 1/3rd the volume of the cone.

The volume of the sphere is 2/3rd the volume of the cylinder with same radius and height equal to the diameter.

Pyramid is said to have a polygonal base and flat triangular faces, which are connected to a common point called apex.

Prism is a combination of flat faces, identical bases and cross-sections being equal.

Cylinder has two parallel bases joined by curved surface through a fixed distance.

Cone has a circular base and a curved surface tapering till the apex.

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