Which expression is equivalent to (-3) × (-3)²?

The general rule is power of power. It can be represented by (x^m)^n = x^mn.

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Now complete the given table:

Problem to           First repeated        second repeated               Power of

simplify                 multiplication         multiplication              the form of a^n

(2²)³                         2²×2²×2²               2×2×2×2×2×2                           2⁶

(5³)⁴                     5³ × 5³ × 5³ × 5³      5×5×5×5×5×5×5×5×5×5×5×5    5¹²

(7³)⁴                     7³ × 7³ × 7³ × 7³      7×7×7×7×7×7×7×7×7×7×7×7        7¹²

((3x)²)³                   (3x)²×(3x)²×(3x)²    3x×3x×3x×3x×3x×3x                    (3x)⁶

(4y²)³                   (2y)²×(2y)²×(2y)²    2y×2y×2y×2y×2y×2y                    (2y)⁶

The general rule is  (x^m)^n = x^mn. The name of the rule is power of power.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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In one min Charlie can read is [tex]2\frac{1}{7}[/tex] pages at a constant rate.

A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilize this technique for math computations.

In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or less quantities are subsequently determined. This approach is known as the unitary method for this reason. Due to the fact that they generate two distinct sorts of variations, there are two different types of unitary approaches.

In [tex]\frac{2}{3}[/tex] min Charlie can read [tex]1\frac{3}{7} = \frac{10}{7}[/tex] pages

In one min Charlie can read is: [tex]\frac{10}{7}*\frac{3}{2} = \frac{30}{14} = 2\frac{2}{14} =2\frac{1}{7}[/tex]

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Answer:

For this example they are all the same thing.  

530:1 or 530 mph

Step-by-step explanation:

A unit rate is when the denominator is 1.  In this case, the denominator is already 1 hour.

The expression for area of the rectangles are obtained as x² + 10x + 21 and  x² - 9x + 8 respectively. The correct options for both parts are (C) and (B) respectively.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The dimension of both the rectangles are given as,

First rectangle : (x + 3) and (x + 7)

Second rectangle : (x - 1) and (x - 8)

Since, the area of a rectangle is product of its dimensions.

It can be obtained as,

Area of first rectangle is given as,

⇒ (x + 3) × (x + 7)

⇒ x² + 10x + 21

Area of second rectangle is given as,

⇒ (x - 1) × (x - 8)

⇒ x² - 9x + 8

Hence, the area of both the rectangles are obtained as  x² + 10x + 21 and  x² - 9x + 8 respectively.

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The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.

What is the equation of the parabola?

The equation can be written as

f(x) = 1/(4p)(x -h)^2 +(k-p)

where (h, k) is the focus, and p is half the distance between focus and directrix.

Here, We have the upward parabola;

Focus at (9,27)

P/2 = 27-19 = 8        Nature of focus

P = 16

so (x-9)^2 = 2py = 32y

y = 1/32(x-9)^2 + 19

The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.

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To prove that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x, we can start by expanding the expression:

(4x - 5)^2 - 5x(3x - 8) = 16x^2 - 40x + 25 - 15x^2 + 40x = -14x^2 + 80x - 25

Now, we can complete the square to find that this expression is always positive:

-14x^2 + 80x - 25 = (-14x^2 + 80x) - 25

= (-14x^2 + 80x + (80/2)^2 - (80/2)^2) - 25

= (-14x + 40)^2 - 25 - 40^2 + 40^2

= 15^2 - 25

= (15 - 5)(15 + 5)

= 10(20)

= 200

Since this expression is equal to 200, which is a positive number, we can conclude that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x.

The degree of the polynomial 2x² 5x³ 7 is 5.

The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the highest exponent of the variable is 5, which appears in the term 5x³. The degree of a polynomial is a whole number that tells us how many times the variable is multiplied by itself. The degree of the polynomial is 5.

It's worth noting that polynomials can be constant or non-constant, meaning they don't have to have a variable in them, in that case the degree is 0. And also a polynomial with only one term, the degree of that polynomial is the exponent of that term.

In this case, we only have one term with variable x in it, 5x³, and the degree is the exponent of that term which is 5.

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$164.86 more is needed to reach the goal of $1,200.00.

First, we need to find out how much money Mrs LeBlanc's class has raised since they have raised 50% of the total needed. We can do this by multiplying the total needed by 50%:

$1,200.00 * 50% = $600.00

Next, we need to find out how much money Ms Warner's class has raised since they have raised one-third as much as Mrs LeBlanc's class. We can do this by multiplying the amount raised by Mrs LeBlanc's class by one-third:

$600.00 * 1/3 = $200.00

Now we can add up the amount raised by all three classes to see how much has been raised in total:

$600.00 (Mrs. LeBlanc's class) + $235.14 (Mr. Patel's class) + $200.00 (Ms. Warner's class) = $1035.14

Finally, we can subtract the total amount raised from the goal amount to find out how much more is needed:

$1,200.00 - $1,035.14 = $164.86

So $164.86 more is needed to reach the goal of $1,200.00.

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Answer:

c) 16 cm²

Step-by-step explanation:

Given information,

→ Base = 4 cm

→ Height = 8 cm

Area of triangle formula,

→ Area = ½ × b × h

Now the area of triangle is,

→ ½ × b × h

→ ½ × 4 × 8

→ 2 × 8

→ 16 cm²

Hence, the area is 16 cm².

The three types of solutions for systems are:

A consistent system is one where the number of equations is equal to the number of unknowns, and a unique solution can be found. An inconsistent system is one where the number of equations is greater than the number of unknowns and there is no solution.

A dependent system is one where the number of equations is less than the number of unknowns and an infinite number of solutions exist. In a consistent and dependent system, the solution can be found by using methods such as elimination or substitution.

In an inconsistent system, the system has no solution. In dependent system, the solution can be found by using methods such as elimination or substitution, but the solution is not unique it has infinite solutions.

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The probability that you correctly guess the letter section and then guess the correct number section where your car is located is 0.01.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Total possible outcomes.

= 8 x 22

= 176

Now,

Probability of guessing the correct letter.

= [tex]^8C_1[/tex] / 176

Probability of guessing the correct section.

= [tex]^{22}C_1[/tex] / 176

The probability that you correctly guess the letter section and then guess the correct number section.

= [tex]^8C_1 \times ^{22}C_1[/tex] / 176 x 176

= 8 x 22 / 176 x 176

=  1 / 176

= 0 .005

= 0.01

Thus,

The probability that you correctly guess where your car is located is 0.01.

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Answer:

42000

Step-by-step explanation:

Original price (before VAT) is 100% of price.

VAT is 13%, of the original price so final price is 113% of original price.

113% = 1.13

original price = 47460/1.13 = 42000

Business-to-Business (B2B): This segment involves transactions between two businesses, Business-to-Consumer (B2C): This segment involves transactions between a business and a consumer and Consumer-to-Consumer (C2C): This segment involves transactions between two consumers.

1. Business-to-Business (B2B): This segment involves transactions between two businesses. Examples of B2B include sales of raw materials by a manufacturer to a wholesaler or the sale of supplies by an office supply company to a retailer.

2. Business-to-Consumer (B2C): This segment involves transactions between a business and a consumer. Examples of B2C include online retailers selling products directly to consumers, subscription services, and digital content providers.

3. Consumer-to-Consumer (C2C): This segment involves transactions between two consumers. Examples of C2C include online marketplaces, auctions, and classifieds where individuals can buy and sell items to other individuals.

the complete question is : What are the 3 segments of  e-commerce ?

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Step-by-step explanation:

the given ratio is

8 / 20/10 = 8 / 2 = 4

for x mathletes we need to keep the same ratio :

x / 30/5 = 4

x / 6 = 4

x = 4×6 = 24

24 mathletes.

Answer:

y = [tex]\frac{1}{3}[/tex] x - 6

Step-by-step explanation:

9y - 3x = -54

We want in the form

y = mx + b

9y - 3x = -54  Add 3x to both sides

9y - 3x + 3x =  3x - 54

9y = 3x - 54   Divide all the way through by 9

[tex]\frac{9y}{9}[/tex] = [tex]\frac{3x}{9}[/tex] - [tex]\frac{54}{9}[/tex]

y = [tex]\frac{3}{9}[/tex] x - 6

We can simplify [tex]\frac{3}{9}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{1}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x - 6

The graph of the inequality 2x+3y>6 is a half-plane the neither contains origin nor the points of the the line 2x+3y=6.

A linear inequality is a mathematical statement involving a linear function and one of the symbols <, >, ≤, or ≥. It represents a range of values for the variables that satisfy the inequality. The solution to a linear inequality is the set of all points that make the inequality true. These points form a region in the coordinate plane, which is known as the solution set. The solution set can be represented graphically as a half-plane, a line, or a combination of lines and half-planes, depending on the inequality.

The graph of the inequality 2x+3y>6 is the set of all points (x,y) that satisfies the inequality 2x+3y>6. It can be represented by a line 2x+3y=6 and all the points on one side of the line. This side is determined by the inequality sign ( > in this case).The side is away from the origin and the line 2x+3y=6 is the boundary line, and all the points on one side of the line satisfy the inequality while all the points on the other side do not.

The line 2x+3y=6's origin and its points are not present on the half-plane that represents the inequality 2x+3y>6.

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answer: 47.5 cups

Step-by-step explanation:

2.50 x 19 = answer

We can express √832 as 4(2√13).

A definite integral of a function can be represented as the signed area of the region bounded by its graph.

Given is the root of 832 or √832.

Assume that {4n} is equal to {y}. So, we can write -

y = 4n

Squaring both sides, we get -

y² = (4n)² = (√832)²

y² = 16n² = 832

16n² = 832

n² = (832/16)

n² = 52

n = √52

n = 2√13

So, we can write (√832) as 4(2√13).

Therefore, we can express √832 as 4(2√13).

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Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.

The slope of the line passing through the points (-8, 5) and (7,0) can be found by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we can use the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, using the coordinates (-8, 5) and (7,0), we have:

m = (0 - 5) / (7 - (-8)) = -5 / 15 = -1/3

Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.

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The area of a right-angled triangle is represented by the expression

x(x + 2) = 24 having area 24 square feet.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the area of a right-angled triangle is (1/2)×base×height.

Given, The area of a triangle is 24 square feet whose height is 2 more than it's base.

Let, The base of the triangle be 'x', Therefore the measure of the height is (x + 2).

Therefore, The area of the triangle is,

(1/2)×x(x + 2) = 24.

x(x + 2) = 24.

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Answer:

1/100, or 0.01, or 10^-2

Step-by-step explanation:

Simplify to get 1/10^2

and evaluate to get 1/100 or some the alternative forms (see above)

When two lines intersect the vertically opposite angles so formed are equal in measure.

When two lines intersect each other, then the opposite angles, created due to the intersection are called vertical angles or vertically opposite angles.

We can see in the figure two lines intersect each other at a point. Therefore the two pairs of vertically opposite angles are ∠1 and ∠3, ∠2 and ∠4.

From the figure, ∠1 + ∠2 = 180°  [Linear pair]     eqn(1)

∠2 + ∠3 = 180°  [Linear pair]   eqn(2)

From eqn(1) and eqn(2), we get

∠1 + ∠2 = ∠2 + ∠3

∴ ∠1 = ∠3

Similarly, we can prove ∠2 = ∠4 also.

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So, the bird visits 40 flowers per hour and approximately 347,750 flowers per year.

A. On average, a bird visits 950 flowers per day. To find the number of flowers visited per hour, we divide 950 by 24 (the number of hours in a day). This gives us approximately 39.58 flowers per hour. Rounded to the nearest whole flower, the bird visits 40 flowers per hour.

B. To find the number of flowers visited in a year, we multiply the number of flowers visited per day (950) by the number of days in a year (365). This gives us approximately 347,750 flowers visited per year.

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The exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12 is defined as follows:

f(x) = 5^x.

The general format of an exponential function is given as follows:

y = ab^x.

In which:

The slope of a line, given two points, is given by the division of the change in the output by the change in the input of these two points.

Considering that the slope of points (0, f(0)) and (2, f(2)) is equals to 12, we have that:

[f(2) - f(0)]/(2 - 0) = 12

f(2) - f(0) = 24.

One case that satisfies this involves these two following points.

Hence the parameter a is given as follows:

a = 1.

When x = 2, y = 25, meaning that the parameter b is calculated as follows:

b² = 25

b = 5.

Hence the exponential function is:

f(x) = 5^x.

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Solving for x in the angle bisector which resulted to the proportion  x over 18 = 45 over 20 results to x = 40.5

In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector.

By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.

The division from angle bisectors gave rise to the proportion which is given by

x / 18 = 45 / 20

cross multiplying

x = 18 * 45 / 20

x = 40.5

hence x is solved to get 40.5

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Answer: I can't answer that because it's not a question

Step-by-step explanation:

The equation of the parabola after the translation is:

g(x) = (x - 7)^2

We know that we start with a parabola of the form:

y = x^2

Now we know that the parabola has been translated 7 units to the left.

Remember tht for a general function y = f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

So a translation of 7 units to the left is written as:

g(x) =f(x - 7)

g(x) = (x - 7)^2

That is the equation of the parabola after the translation.

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Onr of the main differences between a 401(k) and a Roth 401(k): Contributions are taxed differently.

The correct answer is an option (C)

The difference between a 401(k) and a Roth 401(k) is that 401(k) is the income taxes on distribution whereas the Roth 401(k) is the income taxes on contribution.

Roth 401(k) is funded with after-tax money.

You can withdraw after-tax money once you reach retirement age.

A traditional 401(k) allows you to make contributions before taxes.

But in traditional 401(k) you have to pay income tax on the distributions in retirement.

Therefore, the main difference is:  the income taxes on your contributions.

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