How is a "series" different than a "sequence"?

We must factor the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial.

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

We must factorize the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial. The zeros of the three-degree polynomial are then easily ascertainable.

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Both triangles ABC and DEF are similar to each other based on angle angle similarity

Two triangles are said to be similar if the ratio of the corresponding sides of both triangles are proportional to each other. Also, all the three angles of one triangle are equal to that of the other triangle.

The angle angle (AA) similarity theorem states that two triangles are similar if two angles of one triangle is equal to that of the other triangle.

Both triangles ABC and DEF are similar to each other

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The expressions that could represent the amount Bo would pay for the game: 0.82B and  B - 0.18B

The correct options are: option (a) and option (e)

Given that the board game costs B dollars.

And the price is reduced by 18%.  

So, the discount percentage is 18%

i.e., the price is reduced by 0.18

To find out discount amount on  the board game, we multiply cost of the board game by discount percentage.

So, we get an expression for the discount amount = 0.18B

Now we calculate total price of the board game.

Subtract the discount amount from original price B

So, we get an expression for the total price of the board game.

B - 0.18B

As the  discount percentage is 18%, then the original percentage of pay is about 100 - 18 = 82%

i.e., total price of the board game would be 0.82B

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The complete question is:

Bo is buying a board game that usually costs BBB dollars. The game is on sale, and the price has been reduced by 18\%18%18, percent.Which of the following expressions could represent how much Bo pays for the game?

a) 0.82B

b) 1.18 B

c) B - 0.18

d) B - 18

e)  B - 0.18B

The function which shows how much Jasmine earns (c) for working (h) hours is c-4.2h=0.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Given that, One day, Jasmine earned $25.20 for 6 hours of work. Another day, she earned $16.80 for 4 hours of work.

Here, the coordinate points are (6, 25.20) and (4, 16.80)

Now, slope m=(16.80-25.20)/(4-6)

m= -8.4/(-2)

= 4.2

Jasmine earns (c) for working (h) hours

Let c=y and x=h

Substitute (x₀, y₀)=(6, 25.20)

(y-y₀)=m(x-x₀)

c-25.20=4.2(h-6)

c-25.20=4.2h-25.2

c-4.2h=0

Therefore, the function which shows how much Jasmine earns (c) for working (h) hours is c-4.2h=0.

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Answer: 5x

Step-by-step explanation:

If -3x is a negative and 8x is a positive, its the same as subtracting 3x from 8x, which equals 5x.

Answer:

[tex]5x[/tex]

Step-by-step explanation:

Using the distributive property which states that [tex]A(B+C) = AB + AC[/tex], the equation [tex]-3x + 8x[/tex] can be rewritten as [tex]x(-3+8)[/tex]. From here, we can evaluate the expression inside of the parentheses: [tex]-3 + 8 = 5[/tex], and then we can plug the simplified value inside of the parentheses back into the original expression: [tex]x(5)[/tex]. This can be rewritten as [tex]5x[/tex].

This process is known as combining like terms.

Here are the above steps listed out rather than in paragraph form:

[tex]-3x + 8x[/tex]

↓ undistribute [tex]x[/tex]

[tex]x(-3 + 8)[/tex]

↓ evaluate the value inside the parentheses

[tex]-3 + 8 = 8 - 3 = 5[/tex]

↓ plug that value back into the expression

[tex]x(5)[/tex]

↓ rewrite with the constant before the variable

[tex]5x[/tex]

Answer:

Step-by-step explanation:

Find angle U

180 - 42 - 62 = 76°

Find interior angle s

62° because it's an opposite angle

Find angle R

180 - 78 - 76 = 40°

no, the triangles are not similar, angles are different, so answer n° 4

Answer:

8 in each bag 32 total hoped this helped :)

Step-by-step explanation:

Answer:

(6, 0)

Step-by-step explanation:

n to the power of 6, also written as n⁶, is a mathematical operation that raises the number n to the sixth power. This means that n is multiplied by itself six times.

For example, if n = 2, then n⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64.

Exponentiation is a mathematical operation that is used to represent repeated multiplication. The number that is being multiplied is called the base, and the number that represents how many times the base is being multiplied is called the exponent. In the case of n⁶, the base is n and the exponent is 6.

In general, when raising a number to a power, the result is the product of that number multiplied by itself the number of times represented by the exponent. For example, n³ = n × n × n and n⁴ = n × n × n × n.

In addition to being a mathematical operation, exponentiation also has practical applications in fields such as computer science, engineering, and physics.

For example, in computer science, exponentiation is used to perform fast computations, such as in the process of encryption and decryption. In engineering and physics, exponentiation is used to calculate rates of growth, such as in the case of compound interest and radioactive decay.

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The angle at the vertex of an isosceles triangle has a measure of 80 degrees.

According to the information provided:

A right triangle, also known as an isosceles triangle, is characterized by having two sides that are equal in length and an angle sum of 180 degrees.

8:5 is the ratio of the angle at the vertex to the angle at the base.

Let's say the angles come out to be 5x, 5x, and 8x.

To calculate the angle formed by the vertex, we can apply the formula as follows:

5x + 5x + 8x = 180°

18x = 180°

X = 10°

Thus, the vertex angle would be 8 x 10° = 80°

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The number line represents an inequality. The inequality is x  ≤ 1.

What is a number line?

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

If a number line contains a close circle, then the number includes in the inequality.

If a number line contains an open circle, then the number does not include in the inequality.

In the graph, there is a close circle on 1.

The line represents all real numbers less than 1.

Since there is a close circle on 1, thus 1 include in the inequality.

The given variable is x.

The graph represents all real numbers less than or equal to 1.

The inequality is x ≤ 1.

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Answer:

-6 7 2.62 20 54

Step-by-step explanation:

The rectangle's area is 54 square centimeters, and its diameter is 30 centimeters. The rectangle's length is 9 centimeters.

An example of a quadrilateral is a rectangle, which has four vertices that are all 90 degrees apart and parallel sides that are equal to one another. As a result, it is sometimes referred to as an equiangular quadrilateral. The rectangle is a 2D shape with 4 sides, 4 corners, and 4 right angles. The length of each pair of the diagonal sides of a rectangle is equal, with one pair being longer than the other. If all the sides of a rectangle were the same size, the shape would be referred to as a square.

given

Area of a rectangle is defined as length times width, 

When we now swap l=9 and A=54, 

P=2l+2b,

 P=2(9)+2(6)=18+12=30cm, is the formula for the rectangle's perimeter.

The rectangle's area is 54 square centimeters, and its diameter is 30 centimeters. The rectangle's length is 9 centimeters.

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Answer:

-3x^2 +3x +18

Step-by-step explanation:

Y= -3(x+2)(x-3)

= - 3 (x^2 - x - 16)

= - 3x^2 - 3(-x) - 3(-6)

= - 3x^2 +3x +18

It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are smaller than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 10.2 and 5.8

10.2 + 5.8 > 4.5

16 > 4.5

Now we add 10.2 and 4.5

10.2 + 4.5 > 5.8

14.7 > 5.8

Now we add 5.8 and 4.5

5.8 + 4.5 > 10.2

10.3 > 10.2

It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are smaller than third sides.

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The division of 16 - 8x - 7x² + 2x³ by x - 4 will have a quotient of 2x² + x - 4 and a remainder of 0 using synthetic division.

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall rearrange 16 - 8x - 7x² + 2x³ to become 2x³ - 7x² - 8x + 16 and then divide by x - 4 as follows;

2x³ divided by x equals 2x²

x - 4 multiplied by 2x² equals 2x³ - 8x²

subtract 2x³ - 8x² from 2x³ - 7x² - 8x + 16 will give x² - 8x

x² divided by x equals x

x - 4 multiplied by x equals x² - 4x

subtract x² - 4x from x² - 8x will give us -4x + 16

-4x divided by x equals -4

x - 4 multiplied by -4 equals -4x + 16

subtract -4x + 16 from -4x + 16 will result to a remainder of 0

Therefore by synthetic division, 16 - 8x - 7x² + 2x³ divided by x - 4 is equal to the quotient of 2x² + x - 4 with a remainder of 0.

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The statement that best compares the theoretical and experimental probability for a spin to land on blue is A. The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.

Theoretical probability is calculated by analyzing the total number of possible outcomes of an event and the number of favorable outcomes. Experimental probability, on the other hand, is calculated by conducting an experiment and observing the results.

This means that the theoretical probability of landing on blue is:

= Number of sections of blue / Number of total sections

= 1 / 4

The experimental probability of landing of blue is :

= Number of times blue is spun / Number of spins

= 7 / 20

= 35 %

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Answer: A 35%

Step-by-step explanation:

The classroom has 50 girls. The solution was achieved by adding the ratio values (3+5) to get the total parts, dividing the total students by this value to find the value of each part, and then multiplying this by the number of parts for girls.

The subject of this question is a problem in Mathematics that deals with ratios and proportions. Specifically, the ratio of boys to girls in a classroom of students. The ratio given is 3:5, which means for every 3 boys, there are 5 girls. In a classroom with 80 students, we first need to calculate the total parts of this ratio by adding 3 (boys) and 5 (girls), which gives us a total of 8 parts. Having done that, we can now determine the value of a single part by dividing the total number of students (80) by the total parts (8). This gives us 10 students per part. To find out the number of girls, we multiply the number of parts for girls (5) by the number of students per part we computed (10), which equals 50. Therefore, in this classroom, there are 50 girls.

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Any combination of rotations, reflections, and translations that maintain the size and shape of the original figure would be considered a series of transformations that would result in a congruent shape.

A congruent square would be produced, for instance, by rotating a square by 90 degrees and then reflecting it over a line of symmetry. A congruent triangle would also result from shifting a triangle to a different place on the plane while maintaining its orientation.

Transformation vital.

It is necessary to realign an institution's structures, cultures, and business models in order to establish a learning environment that significantly and fairly improves student results and educational value. This process can be described as transformation.

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Based on the information, it can be inferred that Gustave gives 2,100 steps for every mile he walks.

To calculate the number of steps Gustave takes in a mile, we must take into account the information available about the ratio of steps to the distance he covers. In this case, we know that for every 3 miles, Gustave takes 6,300 steps.

To find how many steps he takes in a mile we must divide the number of steps into the number of miles he walked as shown below:

According to the above, Gustave takes 2,100 steps for every mile he walks.

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Answer:

The break even point is 380.

Step-by-step explanation:

36x + 200 = 76x

200 = 76x - 36x

200 = 40x

200/40 = x

5 = x

C = 36(5) + 200            R = 76(5)

C = 180 + 200              R = 380

C = 380

Answer:

The breakeven point is 5 units

Step-by-step explanation:

C is the cost ($) and R is the revenue ($).

We are told that :

R=76x

C=36x+200

Profit would be the Revenue minus the Cost:

Profit = R - C

The "breakeven point" is the situation in which there is neither a profit nor a loss.  That means that the total profit equals the total cost for x units. We want to find the value of x that would result in no profit or loss: Profit = 0.

0 = R-C

====

Profit = 76x - (36x+200)

Profit = 40x - 200

0 = 40x - 200         [The Breakeven Point]

-40x = -200

x = 5 units

5 units results in 76*5 or $380 in revenue.

5 units results in a cost of 36*(5)+200 or $380 in costs.

The result is breakeven (Profit = $390 - $380) of $0.00

Answer:

Step-by-step explanation:

so basically Use the Triangle Sum Theorem to find the measure of each angle. Drag and drop the angle measures into the correct boxes to show the measure of each angle.

your welcome lol. -_-

The exponential equation that matches the number of bacteria after 3 hours is given as follows:

y = 50(4)^3.

An exponential function is used to model this situation as the output is multiplied for each unit of the input.

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

y = a(b)^x.

In which:

In a lab experiment, a population of 50 bacteria is able to quadruple every hour, hence the parameters a and b are given as follows:

a = 50, b = 4.

Thus the exponential function that gives the population after x hours is of:

y = 50(4)^x.

After three hours, we have that x = 3, hence the population is given as follows:

y = 50(4)^3.

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Therefore , the solution to the given problem of slope intercept comes out to be y = 3/4x + 2 * 1/5.

The place where the the line slope intersects the y-axis is known as the intersection point. where, on a line or a curve, the una crosses that location. This is demonstrated by using y = changes in different as the formula for the single direction, where m denotes the slope while c denotes the y-intercept. In the intercepting form of the equation, the line's slope (m) the y-intercept (b) are indicated. Slope and y-intercept are, respectively, m and b for equations with the intercept form (y=mx+b). Additionally, certain equations might be modified to look like slope intercepts. When y=x is written as y=1x+0, for example, the slope and una become 1 and 0, respectively.

Here,

In this case, you must first set up your equation in the "Slope intercept" form.

6x=8y+10

Because your y should be alone, add 8y to each of your sides.

8y + 6x = 10

Since subtraction is the exact reverse of addition, multiply 6 times on both sides.

8y = 6x + 10

You will now divide both sides by 8. You will be alone yourself while completing this.

y= 6/8x + 10/8

Though you might leave it as is, you should probably simplify.

either y = 3/4x + 2 1/5 or y = 3/4x + 5/2

Therefore , the solution to the given problem of slope comes out to be

y = 3/4x + 2 * 1/5.

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Answer:

9 hours.

Step-by-step explanation:

Ella earned $54 in total.

We know she makes $6 an hour, so we just divide 54/6 to find the amount of hours she babysat last week.

54/6 = 9 hours

Side note: You are obviously competent enough to make this question, so I am sure you can do the basic math too.

Answer: 9 hours.

Step-by-step explanation:

Divide 54 by 6. 54/6 = 9.

(A) The optimal solution to this problem = 2.125

(B) If a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution is, = 10.625

(C) Instead of an increase in the profit coefficient X to $ 8, suppose that profit was overestimated and should only have been $ 3 is, = 10.625

Given that,

The following LP problem:

Maximize profit = 5X + 6Y

Subject to 2X+Y= 120

2X+ 3Y = 240

X,Y= 0

Maximize C = 5X + 6Y

2X+Y= 120

2X+ 3Y = 240

and x = 0, y = 0

Plot the lines on graph,

2X+Y= 120

2X+ 3Y = 240

x = 0, y = 0

So, boundary points of feasible region are (0,1.7) , (2.125,0) and (0,0)

Substitute the points in  Maximize C

At  (0,1.7)

Maximize C = 5X + 6Y

C = 5(0) + 6(1.7)

C = 0 + 10.2

Maximize C = 10.2

At  (2.125,0)

Maximize C = 5(2.125) + 6(0)

Maximize C = 10.625

At   (0,0)

Maximize C = 5(0) + 6(0)

Maximize C = 0

So, Maximum value is attained at   (2.125,0)

So, the optimal value of x is 2.125

The optimal value of y is 0

The maximum value of the objective function is 10.625

There are several ways to calculate optimal solution; one of them, is by using graphs.

The optimal value of x is 2.125

The optimal value of y is: 0

The maximum value of the objective function is: 10.625

Therefore,

(A) The optimal solution to this problem = 2.125

(B) If a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution is, = 10.625

(C) Instead of an increase in the profit coefficient X to $ 8, suppose that profit was overestimated and should only have been $ 3 is, = 10.625

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Answer:

I think its 5.6  

Step-by-step explanation:

Well I divided 28 by 5 and got 5.6.

Answer:

Step-by-step explanation:it is 38

Answer:

No solution.

Step-by-step explanation:

2y-8=6x

y=3x+2

-----------

2(3x+2)-8=6x

6x+4-8=6x

6x-4=6x

6x-6x=4

0=4