There are integers b, c for which both roots of the polynomial x^2-x-1 are also roots of the polynomial x^5-bx-c. Determine the product bc.

The simplified form of the expression  (2x⁵ + 3y⁴)(- 4x² + 9y⁴)

is 36y⁸ - 8x⁷ + 18x⁵y⁴ - 12x²y⁴.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, A multiplication of two polynomials (2x⁵ + 3y⁴)(- 4x² + 9y⁴).

= 2x⁵(- 4x² + 9y⁴) + 3y⁴(- 4x² + 9y⁴).

= - 8x⁷ + 18x⁵y⁴ - 12x²y⁴ + 36y⁸.  (multiplication of the same base is the

                                                                                addition of exponents)                                                                                                              

= 36y⁸ - 8x⁷ + 18x⁵y⁴ - 12x²y⁴.

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Answer:

13/20

Step-by-step explanation:

Answer:

65/100

Step-by-step explanation:

65/100 because if you try to divide it by 2 u get 32.5

The value of the equation is b = 30 , which is greater than 25

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 equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

b x ( 5/6 ) = 25   be equation (1)

On simplifying the equation , we get

Multiply by 6 on both sides of the equation , we get

5b = 25 x 6

5b = 150

Divide by 5 on both sides of the equation , we get

b = 150 / 5

b = 30

So , the value of b is 30 and is greater than 25

b > 25

Hence , the equation is b = 30

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Based on a system of equations, the investment at each rate is as follows:

A system of equations, also known as simultaneous equations, yields the solutions to two or more equations solved concurrently or simultaneously.

We use the let statements to state the variables of simultaneous equations.

The total investment = $6,000

The total interest earned = $460

Interest rates:

A = 7%

B = 11%

Let investment A = a and investment B = b

0.07a + 0.11b = 460 ... Equation 1

a + b = 6,000 ... Equation 2

Multiply Equation 2 by 0.07:

Equation 3: 0.07a + 0.07b = 420

Subtract Equation 3 from Equation 1:

0.07a + 0.11b = 460

-

0.07a + 0.07b = 420

0.04b = 40

b = 1,000

= $1,000

From Equation 2:

a + b = 6,000

a + 1,000 = 6,000

a = 5,000

= $5,000

Thus, whereas $5,000 is invested at 7%, $1,000 is invested at 11%.

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All, 25%, and 5 are all valid options that can be selected in the Top Values list for a query.

All will display all the values in the query, 25% will display the top 25% of the values, and 5 will display the top 5 values.

To calculate 25%, we can use the formula (value/total)*100. For example, if the total number of values is 20, then 25% would be (20/20)*100 = 100. This would display all 20 values in the query. Similarly, if the total number of values is 50, then 25% would be (50/50)*100 = 100, which would also display all 50 values.

To calculate 5, we can use the same formula (value/total)*100. For example, if the total number of values is 20, then 5 would be (5/20)*100 = 25. This would display the top 5 values in the query. Similarly, if the total number of values is 50, then 5 would be (5/50)*100 = 10, which would also display the top 5 values.

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The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.

Alice always takes the first turn. Bob can either take the leftmost card or the rightmost card. If Alice takes the leftmost card and Bob takes the rightmost card, then Alice will have the advantage of being able to make the last move. If Bob takes the leftmost card and Alice takes the rightmost card, then Bob will have the advantage of being able to make the last move.

The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.

Alice should also be aware of Bob's strategy and try to anticipate what card he will take. If Alice can guess correctly, she can adjust her strategy to ensure she takes the card with the highest point value. If she guesses incorrectly, she should still attempt to take the card with the highest point value.

Alice should take the card with the highest point value and Bob should take the card with the lowest point value. Alice should also anticipate Bob's strategy and adjust accordingly to ensure she takes the card with the highest point value.

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The value of expression is 1 of the equation -8b+15b+14=21b

Two or more expressions with an Equal sign is called as Equation.

The given expression is -8b+15b+14=21b

Minus eight times of b plus fifteen b plus forteen equal to twenty one.

In the given expression b is the variable and minus and plus are the operators.

-8b+15b+14=21b

Take the variable terms on one side and constant on other side.

-8b+15b-21b=-14

-14b=-14

Divide both sides by -14

b=1

Hence, the value of expression is 1 of the equation -8b+15b+14=21b

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Answer:1/36

Step-by-step explanation:

you have a 1 in 6 chance to get one out of a 6 sided die. U double that to get 1/36.

There are two ways in which one can show percent of change in bar diagram: Input helper column using error bars, and arrows of error bar.

Diagrams known as bar diagrams are ones in which data is shown using bars and rectangles.

First, an input helper column as indicated in the data below in order to produce a column chart with percentage change using error bars, and then base the chart on the helper data.

Second, use some arrows in place of the error bars; if the data rises in the following year, an up arrow is shown; if it falls in the following year, a down arrow is shown. The arrows and data labels will both be dynamically altered when the data changes at the same time.

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This study examines the relationship between long-term exposure to violent video games and desensitization as measured by empathy and attitudes to violence in children aged 5 to 12 years.

They completed a questionnaire assessing their experience and preference for video games and their empathy and attitudes toward violence. Children then played violent or non-violent video games and responded to snippets of everyday events.

vignette reactions were coded for aggression and empathy. Results showed that pre-existing empathy and attitudes toward violence were positively associated with the corresponding vignette scores.

Prolonged exposure to violent video games has been found to reduce empathy vignette scores. However, the study found no significant difference in vignette responses depending on whether children played violent or non-violent games.

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The distance the ball drops in the next 8 seconds is 320 meters.

Direct proportion is when two variables move in the same direction. If one variable increases, the other variable increases.

The equation that is used to represent direct proportion is: D = kt²

Where: k is the constant of variation

80 = k4²

80 = 16k

k = 80 / 16

k = 5

Distance the ball drops in the next 8 seconds : 5 x 8²

= 64 x 5 = 320 meters

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The possible variable terms are a2b3, a5b3, ab8, a3b5, a7b, and a6b5. These terms all contain the same number of a's and b's as the original expression, (2a4b)8.

The expansion of (2a 4b)8 can be found by multiplying the a coefficients and b coefficients by 8. The a coefficients would increase by a factor of 8 and the b coefficients would increase by a factor of 8. This means that the possible variable terms for (2a 4b)8 are all those that have 8 a's and 8 b's. This includes a2b3, a5b3, ab8, a3b5, a7b, and a6b5. These terms all contain the same number of a's and b's as the original expression, (2a4b)8, but with the coefficients multiplied by 8. For example, the term a2b3 would be the result of multiplying 2a4b by 8, which results in 16a32b. This can be simplified to a2b3. Similarly, a5b3 would be the result of multiplying 2a4b by 8, which results in 16a32b. This can be simplified to a5b3.

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A line which joins the midpoints of two sides of a triangle is Midsegment

A triangle's midsegment is a line formed by joining any two of the triangle's sides at their midpoints. All three sides of a triangle can be divided (split in half) in any triangle, whether it be right, isosceles, or equilateral. The midpoint of each side is the point that is equally spaced from either vertex.

Triangles can have three midsegments because they have three sides. Any two sides can be joined at their midpoints. Half the length of the base is represented by one midsegment (the third side not involved in the creation of the midsegment). That is the only intriguing aspect. It also:

Is consistently parallel to the triangle's third side; the base

Creates a tiny triangle that resembles the primary triangle.

The area of the smaller, comparable triangle is one-fourth that of the larger triangle.

Half of the original triangle's circumference is contained within the smaller, comparable triangle.

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The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.

1. The equation |x - 3| = 1 can be rewritten as x - 3 = 1 or x - 3 = -1.

2. Solving for x, x = 4 or x = 2.

3. The equation |x - 3| = 4 can be rewritten as x - 3 = 4 or x - 3 = -4.

4. Solving for x, x = 7 or x = -1.

5. The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.

The graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7. To find the two endpoints of the line segment, we need to solve for x in the equations |x - 3| = 1 and |x - 3| = 4. The equation |x - 3| = 1 can be rewritten as x - 3 = 1 or x - 3 = -1, and solving for x gives us x = 4 or x = 2. The equation |x - 3| = 4 can be rewritten as x - 3 = 4 or x - 3 = -4 and solving for x gives us x = 7 or x = -1. Therefore, the graph of the region 1 <|x - 3| < 4 is a line segment from x = -1 to x = 7.

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the complete question is

Which of the following is the graph of the region 1 <|x - 3| < 4

This is absolutely correct as dividing the rate per month by the rate per night gives the number of nights per month needed for the revenues to match: [tex]$$month$\div $night=r/month \cdot \ $night/r$=# $nights/month$$[/tex]

A company's income is the cash that is generated by its operations. Depending on the accounting technique used, there are various methods for calculating revenue.

Sales made with credit will be counted as revenue when it comes to the delivery of goods or services to the customer in accrual accounting. Even if payment hasn't yet been received, revenue may still be recognised in accordance with certain rules.

To evaluate how successfully a business collects debt, it is important to review the cash flow statement. Contrarily, sales are only recorded as revenue in cash accounting after money has been exchanged. A "receipt" is the term for a sum of money given to a business. Receivables without income are possible.

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As a result, the bus accelerates at a rate of -4 m/s2, and it travels 50 m after applying the brakes.

Bus's initial speed was 72 km/h.

Bus's last speed is 0 km/h.

(Therefore, the bus driver stops)

Bus travel time, t=5 s

To Locate

Bus acceleration and the distance it travels before stopping once the brakes are applied

Solution:

Final velocity is v.

Initial velocity is u.

Acceleration is a.

It takes time.

displacement is s.

Considering that

u = 20m/s

v = 0 m/s

Bus acceleration should be "a"

When using the first law of motion on a bus, we obtain

Let d represent the bus's distance traveled after braking.

a = -4 m/s²

Thus, when we use the third equation of motion on a bus, we obtain

As a result, the bus accelerates at a rate of -4 m/s2, and it travels 50 m after applying the brakes.

d = 50 m

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Using the Pythagorean theorem, the ramp extends 9.68 feet past the back of the van.

What is the Pythagorean theorem?

Pythagoras Theorem (also called Pythagorean Theorem) is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples. Pythagoras theorem is basically used to find the length of an unknown side and the angle of a triangle. By this theorem, we can derive the base, perpendicular and hypotenuse formulas.

Pythagoras formula:-

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse

Now,

For given situation,

Hypotenuse=10feet, perpendicular=2.5feet and we have to find base

Therefore

10^2=b^2+2.5^2

b^2=100-6.25

b=√93.75

b=9.68 feet

Hence,

The ramp extends 9.68 feet past the back of the van.

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The two expressions being cubed are p and q. The expression (p^3 - q^3) is equivalent to cubing both p and q. This means that the expression can be written as (p * p * p - q * q * q). Rewriting it in the form (p^3 - q^3) shows that the two expressions being cubed are p and q.

The expression (p^3 - q^3) is equivalent to cubing both p and q. This means that the expression can be written as (p * p * p - q * q * q). Rewriting it in the form (p^3 - q^3) shows that the two expressions being cubed are p and q.

The expression (p^3 - q^3) is the result of cubing two different expressions, p and q. This is equivalent to multiplying each expression by itself three times. Rewriting the expression in the form (p^3 - q^3) indicates that the two expressions being cubed are p and q. In other words, the expression is the result of taking p and raising it to the third power and then taking q and raising it to the third power. The result is then subtracting q^3 from p^3. This is commonly referred to as cubing both p and q, and the two expressions being cubed are p and q.

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a. The two numbers whose product is 75 and whose sum is -28 are -25 and 3.

b. -28x = -25x + 3x

c. -5x² - 25x + 3x + 15

= -5x(x-5) + 3(x-5)

= (3x-15) + (-5x+25)

= (-5x+3x) + (25-15)

= -2x +10

The trinomial -5x² - 28x + 15 can be factored by grouping as (-2x+10)

Answer:

Provided an explanation below.

The examples are not asking you to solve, only to simplify the expression

For the examples you posted, not sure if you want the solutions are not; I have gone ahead and simplified

[tex]1.\; -8x^3y^5\\\\2\; \dfrac{2y^3}{3}\\\\3.\; They are both equal\\\\4.\; 3x^2\\\\[/tex]

Step-by-step explanation:

First let's understand what an exponent is.

When a number or a term or an expression is multiplied repeatedly by itself, an exponent can be used to represent this situation

for example,

5 x 5 x 5 x 5 x 5 x 5 = 5⁶ since 5 is multiplied by itself 6 times

Here the number being multiplied(5) is called the base and the number of times it is multiplied(6) is called the exponent.

There are some rules regarding exponentiation

1 Zero Exponent

Any number raised to the power zero is 1

[tex]4^0 = 1\\\\123.456^0 = 1\\\\x^0 = 1[/tex]

2. Negative Exponent
If the exponent if negative, the expression is equivalent to the reciprocal of the term raised to the positive exponent

In general

[tex]a^{-m} = \dfrac{1}{a^m}\\\\and\\\\\dfrac{1}{a^{-m}} = a^m\\\\[/tex]

Examples:

[tex]x^-1 = \dfrac{1}{x}\\\\\left({x + y}\right)^{-a} = \dfrac{1}{(x+y)^a}[/tex]  

[tex]\dfrac{1}{x^{-3}} = x^3[/tex]

3. Product Rule
When you multiply exponents with the same base the exponents get added

In general
[tex]\displaystyle {a^m a^n = a^{m + n}}[/tex]

Examples

[tex]x^3x^6 = x^{(3+6)} = x^9\\\\[/tex]

4. Quotient Rule

When you divide an exponentiated term by another exponentiated term with the same base the resulting exponent is the difference between the two exponents:

In general

[tex]\dfrac{a^m}{a^n} = a^{m-n[/tex]

Examples

[tex]\dfrac{y^3}{y^2} = y^{3-2} = y^1 = y[/tex]

5. Power Rule 1

An exponent term raised to another power will be the base raised to the product of the two exponents

In general

[tex](a^m)^n = a^{mn}[/tex]

[tex](x^3)^4 = x^{3 \cdot 4} = x^{12}[/tex]

6. Power Rule 2

If the base is the product of two or more terms and the whole expression is raised to a power then each individual term gets raised to that power.

[tex](ab)^m = a^mb^m\\\\(2x^3y^2z^4)^4 = 2^4x^{3.4}y^{2.4}z^{4.4} = 16x^{12}y^8z^{16}[/tex]

7. One exponent
Any term raised to the power 1 is itself
[tex]a^1 = a[/tex]

example: 5¹ = 5

x¹ = x

You may have to use some or all of the rules when confronted with a specific problem

There are plenty of excellent resources on the web which can explain far more lucidly than I can.

Here are a few. Just search for them and you will get the site links
LibreTexts, OpenStax, cK-12.org etc

As for the specific examples you posted:

[tex]1. (4xy^2)(-2x^2y3)\\[/tex]

 [tex]\textrm{2. }\dfrac{6y^2}{18x}\cdot 2xy[/tex]

3. Which expression has the greater value?
[tex]2^3.2^5 \; or\; \dfrac{4^7}{4^3}[/tex]

[tex]2^3\cdot2^5 = 2^8\\\\\dfrac{4^7}{4^3}= 4^{7-3}=4^4\\\\\mathrm{Since \;4 = 2^2, 4^4 = (2^2)^4=2^8}[/tex]

[tex]4. \dfrac{\left(3x^{\frac{1}{3}}\cdot 3x^{\frac{7}{3}}\right)}{3x^{\frac{2}{3}}}[/tex]

The correlation is that;  The warmer the air temperature, the more people there are in the pool. Option A

We know that the correlation would help us to obtain the relationship that we have between the two variables that have been shown in the scatter plot.

The correlation coefficient is the determinat of the relationship between the variables. As we look at the scatter plot that have been shown here, we would need to use it to know the way that the air temperature and the people in the pool are related.

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a) Over the intervals (−∞,−9),(-6,-2) and (3,7) the function is increasing.

b) At x-values x=-6 and x=3 the function have local minima.

c) The sign of the function's leading coefficient is negative.

d) The possibility for the degree of the function is 5 or 7.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

A function is said to increasing if the value of y increases as the value of x increases.

From the graph, the function is increasing on (−∞,−9),(-6,-2) and (3,7)

The local minima is a point where the function has minimum value in its local neighbour.

From the graph, the function has a local minima at x=-6 and at x=3.

In the end, the value of f(x) decreases as the value of x increases therefore the sign of the function's leading coefficient is negative.

The graph intersects the x-axis 2 times and also the function have 5 turning points both the these information indicates that the function is of 5 degrees or 7 degrees.

Therefore, interval, local minima, coefficient value and degree of function is obtained.

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Statistics describes the examination of events subject to probability. Choices are therefore 6 and 3.

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.

Statistics describes the examination of events subject to probability.

a) Six options

(b) 3 Options

Given:

(3) Colors

Red, Blue, and Green are the options.

(a) The choices that were considered in the following order:

There are three color options when choosing the first hue.

There are two options when choosing the second color, and so on.

As a result, there are a total of = 3*2 = 6 options.

(b) The order of the options not taken into account:

When selecting this option, we decide on 3*2 and then eliminate duplicates.

Choices are therefore 6/2=3 Choices.

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The least common denominator of 1/2x-6 and 2x/7x-21 is (2x -6)(7x - 21)

A fraction can be described as the part of a whole variable, element or number.

There are some number of fractions in mathematics which includes;

Examples of simple fractions 1/2, 1/3

Examples of proper fractions; 3/4, 5/6

Examples of improper fractions; 4/3, 6/3

Examples of mixed fractions; 1 2/3, 5 4/6

From the information given,

1/2x-6 and 2x/7x-21

The least common denominator is (2x -6)(7x - 21)

Hence, the value is (2x -6)(7x - 21)

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Answer:

[tex]2\sqrt{2}[/tex]

Step-by-step explanation:

Think of it in terms of a and b if its too difficult to understand what it is in its current state.

[tex]\sqrt{3} = a & \sqrt{2} = b\\(\sqrt{3} + \sqrt{2}) - (\sqrt{3} - \sqrt{2})\\(a + b) - (a - b)\\a + b - a + b\\2b \\2\sqrt{2}[/tex]

The value of g becomes 64% of its value on the surface of the earth when it is at a height of 3200km above the surface, with the radius of the earth being 6400km.

Radius of Earth = 6400 km

Height above the surface of Earth = 3200 km

Gravitational Acceleration on surface of Earth = 9.8 m/s2

Gravitational Acceleration at 3200 km above the surface of Earth = 9.8 x 0.64 = 6.272 m/s2

The gravitational acceleration (g) on the surface of the earth is 9.8 m/s2. This value is constant, regardless of the height of an object above the surface. However, as the height of an object increases, the gravitational force experienced by the object decreases. The radius of the earth is 6400 km, so at a height of 3200 km above the surface, the gravitational acceleration experienced by an object is 64% of its value on the surface of the earth, which is 6.272 m/s2. This is because the gravitational force decreases as the object moves further away from the surface, and at 3200 km the force is only 64% of the force at the surface.

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The correct statement regarding the slope and the intercept of the linear function are is given as follows:

The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour.

The two most important features of a linear function are the slope and the intercept, and their meaning is explained as follows:

The input and output variables for this problem are given as follows:

Two points of the function are:

(0, 8) and (3,6).

Given two points, the slope is calculated as the change in y divided by the change in x, hence:

m = (6 - 8)/(3 - 0)

m = -2/3.

Meaning that the candle's height decays at a rate of 2/3 of an inch an hour.

When x = 0, y = 8, hence the intercept of b = 8 represents the initial height of the candle.

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The two consecutive natural numbers that satisfy the given equation are 3 and 4.

Let the two numbers be x and x+1

x(x+1) = 1.5x^2

x^2 + x - 1.5x^2 = 0

x^2 - 0.5x = 0

(x-3)(x+0.5) = 0

x = 3, x+1 = 4

The given equation is the product of two consecutive natural numbers, which is equal to 1.5 times the square of the lesser number.

Therefore, we can set up an equation by substituting x for the lesser number and x+1 for the greater number.

x(x+1) = 1.5x^2

We can then simplify the equation by subtracting 1.5x^2 from both sides.

x^2 + x - 1.5x^2 = 0

We can then factor this equation to find the solution.

x^2 - 0.5x = 0

(x-3)(x+0.5) = 0

The solutions to this equation are x = 3 and x+1 = 4. Therefore, the two consecutive natural numbers are 3 and 4.

The two consecutive natural numbers that satisfy the given equation are 3 and 4.

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Answer:

2.64

Step-by-step explanation:

The evaluation of the expression using the order of operations, indicates the operations that come first as follows;

(5 + 5)² + 15 - 10 Parenthesis

40 ÷ 8 · 4  + 2; Division

4 - 2 + 3 · 5; Multiplication

(3² + 8) ÷ 7 - 5; Parenthesis

The order of operations is a rule that serves as a guide for the correct sequence of performing operations in an equation or expression.  

The evaluation expressions can be presented as follows;

First operation;

(5 + 5)² + 15 - 10

The order of operations, PEMDAS, indicates that we get;

1) Parenthesis first

2) Exponents

3) Multiplication and division

4) Addition and subtraction

Based on the above PEMDAS order of operation, the step that should be completed first is the operation within the parenthesis, which is the addition operation (5 + 5)

The correct option is; Parenthesis

Second expression;

40 ÷ 8 · 4 + 2

The operations in the expression are; division, multiplication, and addition

The order of operations indicates that division, which comes first, from the left, should be performed first. The correct option is therefore;

40 ÷ 8 · 4 + 2; division

Third expression;

4 - 2 + 3 · 5

The subtraction is the first operation from the left, but the order of operations, PEMDAS, indicates that the multiplication, 3 · 5 should be performed first, therefore;

Fourth expression;

(3³ + 8) ÷ 7 - 5

The parenthesis which comes first in the order of operations and first among the operations from left to right comes first

Therefore, the parenthesis comes first;

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