Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?
a-3) a² + ab +3²
a + b) a ² - ab +6²
o a+ba? +la+b+Dab? - 53
a-ba? +da+b+Dab? - b​

Answers

Answer 1

The long division problem can be used to prove the formula for factoring the difference of two perfect cubes (a-b)(a²+ab+b²).

The difference of two perfect cubes: a³-b³  = (a-b)(a²+ab+b²)

let the two perfect cubes be a³ and b³. Factoring the  difference between these two perfect cubes we have: a³ - b³

First, we need to factorize (a-b)³:

(a-b)³ = (a-b) (a-b)²

(a-b)³ = (a-b)(a²-2ab+b²)

(a-b)³ = a³-2a²b+ab²-a²b+2ab²-b³

(a-b)³ = a³-b³-2a²b-a²b+ab²+2ab²

(a-b)³ = a³-b³ - 3a²b+3ab²

(a-b)³  = (a³-b³) -3ab(a-b)

Then we will make a³-b³ the subject of the formula from the result equation;

a³-b³ =  (a-b)³+ 3ab(a-b)

a³-b³  = a-b{(a-b)²+3ab}

a³-b³  = a-b{a²+b²-2ab+3ab}

a³-b³  = (a-b)(a²+b²+ab)

a³-b³  = (a-b)(a²+ab+b²)

The long division problem that can be used is (a-b)(a²+ab+b²).

To know more about Perfect cubes:

https://brainly.com/question/16982622

#SPJ4


Related Questions

Consider this series.
16+32/3 +64/9 +128/27 +...
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
The series Choose... You know this because the series is
Choose....

Answers

The series converges to 16 * 3 = 48

What is a series?

A number series is a continues chain of number identical of non-identical depending on the logic behind the series. It can contain letters, number, variable, fraction, and numbers with power or exponents.

How to find the series coverage?

The series converges.

This series is in the form of 16 * (1 + 1/3 + 1/9 + 1/27 + ...)

The series 1 + 1/3 + 1/9 + 1/27 + ... is a geometric series with a common ratio of 1/3.

A geometric series converges if |r| < 1, where r is the common ratio. In this case, |1/3| < 1, so the series converges to lim (1/(1-1/3)) = 3.

So the series converges to 16 * 3 = 48

To know more about number series visit:

https://brainly.com/question/12474324

#SPJ1

Help pls I really need help

Answers

Answer:

b

Step-by-step explanation:

Select all the true statements about the table.


x y
2 7
6 21
8 28
14 49


The slope is 3.5.


There is a proportional relationship between the variables x and y.


The slope is 7.


There is a linear relationship between the variables x and y, but not a proportional relationship.


The graph does not pass through the point (0, 0).

Answers

Answer:

Slope is 3.5

There is a proportional relationship between the variables x and y

The other statements are false.

The slope is 3.5, not 7

A linear relationship is the same a proportional relationship so statement 4 is always false

The graph does pass through (0, 0)

Step-by-step explanation:

Consider the first 2 pairs of coordinates, (2, 7) and (6, 21);

The increase in x is from 2 to 6, i.e. an addition of 4, the increase in y is from 7 to 21, i.e. an addition of 14;

Now consider the the 2nd and 3rd pairs of coordinates, (6, 21) and (8, 28);

The increase in x is from 6 to 8, i.e. an addition of 2, the increase in y is from 21 to 28, i.e. an addition of 7;

So, with the first 2 pairs of coordinates, an increase of 4 in x resulted in an increase of 14 in y and with the second 2 pairs of coordinates, an increase of 2 in x resulted in an increase of 7 in y, i.e. (+4, +14) and (+2, + 7);

2 × (+2, +7) = (+4, 14)

Or:

(+4, +14) ÷ 2 = (+2, +7)

This means a line from the 1st point to the 2nd point and a line from the 2nd point to the 3rd point will have the same gradient:

To find the slope simple, find the increase in y resulting from an increase of 1 in x, so:

(+2, +7) ÷ 2 = (+1, +3.5)

The gradient (or slope) is 3.5;

If there is a line with a fixed gradient that passes through all the points, then the relationship is proportional, also linear;

This is the case for this question;

If we follow the pattern backwards as well, so the point:

(2, 7) - (+2, +7) = (0,0)

This means (0,0) lies on the line.

(0,0), (2, 7), (4, 14), (6, 21), (8, 28), (10, 35), (12, 42), (14, 49), etc.

All these points would lie on the line, just add 2 to x, add 7 to y;

You would find the same points plus others by the rule, add 1 to x, add 3.5 to y.

2. Amy has a room that is 6 feet by 10 feet. She bought tiles
that are 8 inches by 6 inches. How many tiles will she
need to cover the floor?

Answers

What are units?

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Because we are dealing with different units here, we first would need to know how many inches are in one foot.

1 foot = 12 inches

Now that we know how many inches are in a foot, we can convert the length and width of the room from feet to inches.

6 feet = 72 inches

10 feet = 120 inches

Taking these numbers, we now need to figure out the area of the floor.

72 × 120 = 8640

Now, find the area of each tile.

6 × 8 = 48

Taking 8640, we can now divide that by 48 to get the number of tiles needed.

8640 ÷ 48 = 180

Therefore, 180 tiles are needed to cover the floor.

Write a real-world problem that you could represent with the equation 20 2n5 4. Solve the equation to find the answer to your problem

Answers

The solution of the given equation is 1.6. It has been represented and solved as a real-world problem below.

The given equation is = - 20 + 2x5 = 4

We can rewrite this equation as = - 4 + 2x5 = 20

Let us suppose that person A has x number of bananas that they have taken out from a stock full of bananas. They continue taking x number of bananas two more times. They then stop and see that person B has already taken 4 bananas from the stock. We can write this equation as -

= 4 + 2x

Person A saw knew that there were 20 bananas in total. So, we can write it as -

= 4 + 2x = 20

Person A then resumed and took x number of bananas again 5 more times. We can rewrite this as -

= 4 + 2x5 = 20

Solving this equation, we get -

= 4 + 10x = 20

= 10x = 20-4 = 16

= x = 16/10

= x = 1.6

Learn more about real-world problems on

https://brainly.com/question/2776063?referrer=searchResults

#SPJ4

how do i find the missing angles?! please help this is due today! please and thxx!

Answers

The measure of each angle are

<1 =46<2=164<3= 46<5= 46<6= 164<7= 46<8= 134What are Parallel lines?

The fundamental characteristics listed below make it simple to recognise parallel lines.

Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.

Given:

<4 = 134

So, <4 = <2 = 134 (Vertical opposite angle)

<4= <8= 134 (Corresponding Angle)

<1 + <4 = 180 (Linear Pair)

<1 = 180-134

<1 = 46

<1 = <3= 46 (Vertical opposite angle)

<2= <6= 164 (Corresponding Angle)

<3= <7 (Corresponding Angle)

<1= <5 (Corresponding Angle)

Learn more about Parallel line here:

https://brainly.com/question/16701300

#SPJ1

For events A, B, and C we have that
P(A)=0.24,
P(B)=0.26,
P(A n B)=0.05,
P(A n C)=0.05,
P(B n C)=0.05,
P(A n B n C)=0.02 and P((A u B uC)^/)=0.33,
find P(C)

How should i go about this

Answers

Answer:

give me brainlist please

Step-by-step explanation:

We can use the formula for conditional probability and the formula for the probability of the union of events to find P(C).

Using the formula for conditional probability, we can find P(A|B) = P(A n B) / P(B) = 0.05 / 0.26 = 0.192

Using the formula for conditional probability again, we can find P(A|C) = P(A n C) / P(C) = 0.05 / P(C)

Since A and C are independent events, we know that P(A|C) = P(A), so we can write:

0.05 / P(C) = 0.24

Solving for P(C) we get P(C) = 0.05/0.24 = 0.208

Alternatively, we can use the formula for the probability of the union of events:

P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C)

We know that P(A u B u C) = 1 - P((A u B u C)^/) = 1 - 0.33 = 0.67

and we know the values of P(A), P(B), P(A n B), P(A n C), P(B n C), P(A n B n C)

We can substitute these values into the above equation to find P(C)

P(C) = 0.67 - 0.24 - 0.26 + 0.05 + 0.05 + 0.05 - 0.02 = 0.208

So P(C) = 0.208

Need answer of number 3,4,5

Answers

A linear equation - y = 5x -7 is a slant line with intercepts for linear equations. A vertical line is x = 2. A line that runs through the origin is y = 3/4x.

A slant line with intercepts is y = 1/2x + 3. A horizontal line is y = 9. The line x = -1 runs vertically.

A linear equation is what?

A direct condition is one that has a level of 1 as its most extreme worth. As a result, there is no variable in a linear equation with an exponent greater than 1. The graph of a linear equation will always be straight.

                  y = 5x -7 is the first line equation.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line does not traverse the origin. As a result, this equation has intercepts and slant lines.

                         x = 2 is the second line equation.

Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.

Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.

                       y = 3/4x is the third equation for the line.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line actually traverses the origin. As a result, the origin of this equation is traversed by slant lines.

                             y = 1/2x + 3 is the fourth equation for a line.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line does not traverse the origin. This equation is therefore a slant line with intercepts.

                                   y = 9 is the fifth line equation.

Since there is no x-intercept in this equation, it will be a horizontal line that runs parallel to the x-axis.

Additionally, this line does not traverse the origin. As a result, there is a horizontal line in this equation.

                     x = -1 is the sixth line equation.

Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.

Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.

Learn more about Linear equation :

brainly.com/question/12788590

#SPJ1

Select the procedures that cannot be used to show the converse of the Pythagorean theorem using side lengths chosen from 3 cm, 4 cm, 5 cm, and 6 cm.
A.
Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.
B.
Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.
C.
Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.
D.
Knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

Answers

The procedure that cannot be used are:

A. Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.

B.

Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

C.

Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.

What is the Pythagorean theorem?

The Pythagorean theorem states that the result obtained by squaring the value of the hypotenuse of a right angled triangle is equal to the sum of the squares of the values other two sides of the triangle.

The hypotenuse of a a given triangle is usually longer that the other two sides.

Therefore, the correct procedure when lengths such as 3 cm, 4 cm, 5 cm, and 6 cm should be knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

Learn more about triangle here:

https://brainly.com/question/28470545

#SPJ1

HELP ASAP !! :80 POINTS
How long is the shortest route from Ellport to Union Falls using the roads shown?

If necessary, round your answer to the nearest tenth.

Answers

The shortest route from Ellport to Union Falls using road is 18 miles

What is an equation?

An equation is an expression that shows the relationship between numbers and variables.

Pythagoras theorem is used to determine the measure of the sides of a right angled triangle. It is given by:

(hypotenuse side)² = (adjacent side)² + (opposite side)²

The distance from Larksville to Smithfield = 9 + 9 + 6 = 24 miles

The distance from Larksville to Union Falls = 19.5 + 6.5 = 26 miles

Let x represent the distance from Smithfield to Union falls, using Pythaoras:

26² = 24² + x²

x² = 100

x =  10 miles

the distance from Smithfield to Union falls is 10 miles.

Let y be the shortest route from Ellport to Union Falls, using Pythagoras:

y² = 10² + (9 + 6)²

y² = 10² + 15²

y² = 325

y = 18 miles

The distance from Ellport to Union Falls is 18 miles

Find out more on equations at: https://brainly.com/question/2972832

#SPJ1

Mock June 22 1F Overview Question Progress Exam Paper Progress 42/80 Marks 10 Eric throws a biased coin 10 times. He gets 3 Tails. Sue throws the same coin 50 times. She gets 20 Tails. 10 Grade For This Paper U 3 Aadi is going to throw the coin once. (i) Which one of the following statements is correct about the probability of Aadi getting Tails? 2/5 (ii) Use Eric's and Sue's results to work out an estimate for the probability that Aadi will get Tails. Write your fraction in the form a/b 13 A Sue's estimate is best because she throws it 50 times. B Sue's estimate is best because she gets more Tails. C Sue's estimate is best because she throws it more times than Eric (1) (1) 15 Total marks: 2 16 17​

Answers

The best estimate for the probability of getting tails is given as follows:

C Sue's estimate is best because she throws it more times than Eric.

How to obtain the probabilities?

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

For this problem we calculate an experimental probability, as the outcomes are obtained from the previous trials of Eric and Sue.

The higher the number of trials, the closer the experimental probability is to the theoretical probability, meaning that the correct option is given by option C.

More can be learned about probabilities at https://brainly.com/question/27899440

#SPJ1

A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. What is the surface area in square centimeters if the height is 2 centimeters?
60
120
180
240
*answer is 180. How?

Answers

The surface area of the triangular prism is 120[tex]cm^2[/tex]

Now, According to the question:

A triangular prism is a polyhedron with a triangle for a base, thus it is a three-sided prism. Given that the triangle has three sides and a height of h, the surface area would be A = Ph + ab where P is the perimeter of the triangle.

We have :

A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters.

Now,

Hypotenuse  = 13

a = 5 cm

b = 12 cm

h = 2 cm

The perimeter of the triangle is the sum of all the sides or:

P = 13 + 5 + 12

P = 30 cm

To get the surface area, substitute the values in the formula below:

A = Ph + ab

A = (30)(2) + (5)(12)

A = 60 + 60

A = 120

Hence, The surface area of the triangular prism is 120[tex]cm^2[/tex]

Learn more about Surface area of triangular at:

https://brainly.com/question/9764079

#SPJ4

The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class, in which there are 20 girls. How many boys are there in Mandy’s science class? Show your work

Answers

Number of boys in Mandy’s science class is 5.

Now, According to the question:

The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.

This ratio is the same in Mandy’s science class,

There are 20 girls.

To find the how many boys are there in Mandy’s science class?

Based on the given condition:

Let the ratio be 3x and 12x

Now, According to the statement:

12x = 20

x = 20/12

x = 5/3

So, Number of boys = 3 × 5/3 = 5

Learn more about Ratio at:

https://brainly.com/question/13419413

#SPJ4

3. Two apples and 3 pears cost $2.40. Five times the cost of an apple less three times the
cost of a pear is 65 ¢. What is the unit cost of an apple and a pear?

Answers

The unit cost of an apple and a pear are $1.27 and $1. 98 respectively.

What are algebraic expressions?

Algebraic expressions are defined as expressions that comprises of variables, factors, constants, terms and coefficients.

They are also made up of arithmetic operations like;

Floor divisionMultiplicationAdditionSubtractionBracketParenthesesDivision

From the information given, we have that;

Let the apples be x

Let the pears by y

2x + 3y = 2.40

5x - 3y = 6.5

Let's solve the simultaneous equation

-1(2x + 3y = 2.40)

-2x - 3y = -2. 40

5x - 3y = 6.5

-2x - 5x = -2. 40 - 6.5

-7x = -8.9

x = $1.27

substitute the value for y

-2y -5(1.27) = -2.40

y = $1. 98

Hence, the values are $1.27 and $1. 98

Learn about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28 degrees
. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.

Answers

Step-by-step explanation:

this creates a right-angled triangle 2.5 ft above the ground.

the string is the Hypotenuse (the side opposite to the 90° angle). the air distance to the height of the kite is one leg, and the height of the kite minus the 2.5 ft is leg 2.

in the trigonometric triangle the up/down side is sine (multiplied by the Hypotenuse or radius of the circle) of the angle at the center of the circle. and the left/right side is cosine (again multiplied by the Hypotenuse or radius) of the angle.

so, the height of the kite above ground is

105×sin(28°) + 2.5 = 51.79451409... ≈ 51.79 ft.

To be a member at Sal's gym, there is a one-time sign-up fee plus a monthly fee for each month of membership. The table shows the total cost to be a member of the gym for different numbers of months.


Number of Months Total Cost

3 $53. 97

6 $77. 94

12 $125. 88



Create a function that gives the total cost,

C

C

, in dollars, to be a member of the gym given the number of months,

m

m

, of membership.


Enter your function in the space provided

Answers

A function that gives the total cost, C in dollars, to be a member of the gym given the number of months, m is C = 7.99m + 30

The table that shows the total cost to be a member of the gym for different numbers of months is:

Number of Months     Total Cost

           3                        $53. 97

          6                         $77. 94

          12                        $125. 88

The rate of change of total cost per month would be,

m = [tex]\frac{77. 94-53. 97}{6-3}\\\\[/tex]

m = 7.99

so, the function for the total cost would be,

C = 7.99m + d          .......(1)

where d is the fixed cost of the gym

For m = 3, C = 53.97

53. 97 = 7.99m + d

53. 97 = 7.99(3) + d

d = 30

So, function (1) would be,

C = 7.99m + 30

Learn more about the function here:

https://brainly.com/question/28193994

#SPJ4

Answer 8 and 9.
Find the measure of an arc from the central angle.

Answers

8) The Length of major arc MQN is; ⁵/₄πr

Length of minor arc MPN is; ³/₄πr

9) Length of major arc HJK is; ¹³/₁₅πr

Length of minor arc MPN is; ⁴/₁₅πr

How to find the length of an arc?

The formula that is used to find the length of an arc is;

L = (θ/360) * 2πr

where;

L is length of arc

θ is central angle

r is radius

8) We are not given the radius and as such;

Length of major arc MQN = (225/360) * 2πr

= ⁵/₄πr

Length of minor arc MPN = ((360 - 225)/360) * 2πr

= ³/₄πr

9) Length of major arc HJK = (312/360) * 2πr

= ¹³/₁₅πr

Length of minor arc MPN = ((360 - 312)/360) * 2πr

= ⁴/₁₅πr

Read more about length of arc at; https://brainly.com/question/2005046

#SPJ1

Some animal become endangered and a trict law ha to be
implemented to protect them. What will you do to protect and help
them?

Answers

One of the most important things to do to protect endangered animals is to reduce the amount of habitat destruction caused by human activities.

This can be done by creating protected areas and limiting or banning activities like logging, mining, or development in sensitive areas. Additionally, it is important to reduce over-hunting and poaching of these animals. This can be accomplished by establishing quotas and strict regulations on allowable hunting and fishing, as well as increasing enforcement efforts to catch violators. It is also important to understand the life cycles and behaviors of the threatened species so that we can better protect them. This can be done through field research, monitoring, and analyzing population trends. Finally, it is important to develop conservation plans and strategies to protect the species. These could include habitat restoration, reintroduction programs, captive breeding, and other measures to ensure their survival.

Learn more about measures here:

https://brainly.com/question/18827844

#SPJ4

Identify the number of terms and then the resend themselves for each algebraic expression

Answers

The number of terms in the algebraic expressions are:

6y + 14 ⇒ 2 terms3x³ + 7x² + x - 5 ⇒ 4 terms

How to determine the number of terms in the algebraic expressions

From the question, we have the following parameters that can be used in our computation:

6y + 14 and 3x³ + 7x² + x - 5

Consider an expression given as

ax + b

The number of terms in the expression is 2 and the terms are ax and b

Using the above as a guide, we have the following:

6y + 14 ⇒ 2 terms3x³ + 7x² + x - 5 ⇒ 4 terms

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

Complete question

Identify the number of terms and then the resend themselves for each algebraic expression

6y + 14 and 3x³ + 7x² + x - 5

A student went on a two-day hike. • On day one, the student hiked 11 kilometers. On day two, the student hiked at a rate of 2 kilometers per hour for x hours. Which of the following graphs represents y, the total distance, in kilometers, the student hiked over both days after hiking for x hours on day two?​

Answers

The slope is 2, which equals the distance travelled each hour. The total distance hiked at the start of the second day is represented by the y-intercept, which is 4, which is also the y-value. intercept's

Explain about the Slope?

We locate the rise/run before calculating the slope. Since the line increases by 2 between each point, the rise is 2. It travels over 1 between the points, hence the run is 1. The slope is now 2/1, or 2.

Given that it is rise/run, this gives us miles/hours, which indicates the number of miles she treks per hour.

The line's crossing of the y-axis is known as the y-intercept. At four, this is.

The fact that the y-value at this time is 4 and the x-value at this point is 0 tells us that she has trekked 4 miles in the 0 hours since the start of the second day, which is the distance she has covered so far.

To learn more about  Slope refer to:

https://brainly.com/question/3493733

#SPJ1

Let f(x) = 3x2 – 2x + 6 and g(x) = 7x – 4. Identify the rule for f + g.

Answers

The sum between the functions:

f(x) = 3x² - 2x + 6

g(x) = 7x - 4

is (f + g)(x) = 3x² + 5x + 2

How to add the two functions?

Here we have two functions which are:

f(x) = 3x² - 2x + 6

g(x) = 7x - 4

And we want to add these to get f + g,  so we only need to add the two functions, we will get:

f(x) + g(x) = (3x² - 2x + 6) + (7x - 4)

Grouping like terms we will get:

(3x² - 2x + 6) + (7x - 4) = (3x²) + (-2x + 7x) + (6 - 4)

And now we can simplify that to get:

(3x²) + (-2x + 7x) + (6 - 4) = 3x² + 5x + 2

The sum is:

(f + g)(x) = 3x² + 5x + 2

Learn more about adding functions at:

https://brainly.com/question/2328150

#SPJ1

which inequality represents the graph??

Answers

Answer:

C

Step-by-step explanation:

the meaure of the exterior angel of a hexagon are x,3x,,4x,5x,8x, and 9x find the meaure of the larget exterior angel

Answers

The largest exterior angle of hexagone is 108°.

Given that exterior angle of a hexagon are x, 3x, 4x, 5x, 8x and 9x.

Exterior angles are those that run parallel to a polygon’s inner angles but are located outside of polygon.

We know that sum of exterior angle of any polygon is 360°.

So, sum of exterior angle of hexagon will be 360°.

x + 3x + 4x + 5x + 8x + 9x = 360°

30x = 360°

x = 360° / 30

x = 12°

Now the largest angle = 9 * 12 = 108°

Therefore, the largest angle of hexagon is 108°.

To learn more about polygon visit: https://brainly.com/question/10441863

#SPJ4

Does the point (0, 0) satisfy the equation y = x?

Answers

Answer:

yes

Step-by-step explanation:

when y equals 0, x equals 0 also

y = x will produce a straight line passing through the point of origin (0,0)

(x,y) => (0,0)

Plug in the point into the equation, y=x.

We get,

0=0, which is true.

Thus, the point, (0,0), satisfies the equation, y=x.

What is the product of the polynomials?

Answers

Answer:

Multiply all of the terms of each polynomial and then combine like terms. Example: Multiply: ( 2 x 2 + x − 3 ) ( x 2 − 2 x + 5 ) . Solution: Multiply each term of the first trinomial by each term of the second trinomial and then combine like terms.

An experimental plant has an unusual growth pattern. On each day. The plant doubles its height of the previous day. On the first day of the experiment, the plant grows to twice, or 2 times, its original height. On the second day, the plant grows to 4 times its original height. On the third day, the plant grows to 8 times its original height.


A. How many times its original height does the plant reach on the sixth day? On the nth day?

Answers

A. On the sixth day, the plant grows to 64 times its original height.

B. On the nth day, the plant would  [tex]2^n[/tex] time its original height.

A. From the given condition we can that the growth of the plant shows a geometric progression with a first term of 2 and a common ratio of 2.

On the first day, the plant grows to [tex]2^1[/tex] = 2 times its original height.

On the second day, the plant grows to [tex]2^2[/tex] = 4 times its original height.

Similarly, on the sixth day, the plant grows to [tex]2^6[/tex] = 64 times its original height.

B. The nth term of the progression can be calculated by multiplying the first term by the common ratio raised to the power of n-1.

In this case, the first term is 2 and the common ratio is 2. So the nth term is [tex]2 * 2^{n-1} = 2^n[/tex]

Hence, on the nth day, the plant grows to [tex]2^n[/tex] times its original height.

Read about geometric progression:

brainly.com/question/15978376

#SPJ4

Find the inverse of this function question (i) only please

Answers

The inverse of the function will be x=(4y-2)/(y+2) where x is the inverse of the function given in i.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x.

Now,

As given

f(x)=2(x+1)/4-x

from here x will be inverse of the function

Therefore

y(4-x)=2x+2

4y-yx=2x+2

4y-2=x(y+2)

x=(4y-2)/(y+2)

To know more about functions visit the link

https://brainly.com/question/12431044?referrer=searchResults

#SPJ1

in a randomly selected 100 students in a large college, 20 of them had at least one sibling. does this provide strong evidence that more than 15% of college students in america have at least one sibling? test using

Answers

Answer:

No

Step-by-step explanation:

It could only represent large colleges, not all colleges.  Sampling requires similar characteristics to represent the entire population of testing.

the sum of the cube of a number and the product of the number and twelve is equal to seven times the square of the number. find the number.

Answers

Answer:

4 or 3

Step-by-step explanation:

X³+12X=7X²

X³-7X²+12X=0

X(X²-7X+12)=0

SOLVING THE QUADRATIC EQUATION

you have X=3 or X=4

Express tan Y as a fraction in simplest terms.

Answers

Tan θ = Opposite side/Adjacent side
Other Questions
according to the monitoring the future study conducted annually by the university of michigan on marijuana use among 12th-graders, which of the following statements is true of changes over time in the rates of drug use?multiple choice question.while marijuana use increased steadily from 1975 to 1992, its availability declined after 1992, affecting its use.while marijuana use has decreased gradually from 1975 to 1978, the perception of associated risk has remained unchanged.there has been no decline in the rates of marijuana use since 1978.changes in the rates of marijuana use since 1997 have been small. although cellulose and starch are identical in terms of stored chemical energy, our ability to harvest the energy from these two polysaccharides differs considerably. what is responsible for this difference? i need help me alot plss How many days has Roman Reigns been Universal Champion 2022? HISTORY PLEASE HELP1. What is Howe suggesting in this excerpt? Human cells divide every day for normal growth, replacement of cells, and tissue repair. The dividing cells proceed through the three phases of the cell cycle as shown in the figure. When a person experiences a cut, damaged skin cells secrete a protein called epidermal growth factor (EGF). Epidermal (skin) cells in the vicinity of the injury possess proteins in their cell membranes called epidermal growth factor receptors (EGFR)(a) Identify the THREE major stages of interphase, and describe the sequence in which they occur.(b) Describe the most likely role of EGF and the role of EGFR in a cell signaling pathway. Describe how the cellular response to EGF results in tissue repair.(c) Cancer can result from disruptions in cell cycle control. Mutations that increase the production of EGFR have been associated with skin cancer of the head and neck. Describe how a mutation outside of the coding region of a gene that encodes EGFR could lead to the overproduction of EGFR protein in a skin cell. which action would the nurse take when a parent expresses concern that their preschooler isn't eating enough? Dostoevsky, Notes from UndergroundWho is the main character of the novel?A) AlyoshaB) IvanC) DmitriD) None of the above if you perform a binary search on an array of one million integers, which of the following is closest to the number of elements that the search algorithm will need to examine? group of answer choices all 1,000,000 of the integers roughly half (500,000) of the integers less than 1% (10,000 or fewer) roughly 3/4 (750,000) of the integers roughly 1/10 (100,000) jersey medical earns $12.00 a share, sells for $90, and pays a $3 per share dividend. the stock is split three for one and a $1 per share cash dividend is declared. what will be the new price of the stock? round your answer to the nearest dollar. $ if the firm's total earnings do not change, what is the payout ratio before and after the stock split? round your answers to one decimal place. payout ratio before the split: % payout ratio after the split: % Directions: Choose the role of each character and use the RAFT strategy to write about Chielos abduction of Ezinma in Chapter 11. While in the role, write what your character is thinking, using the pronoun I, from the time Chielo, as Priestess of Agbala, comes for Ezinma until the end of the chapter. Highlight your RAFT elements below (Sentence Count: 8-10 per role):Role: Okonkwo, Ekwefi, Ezinma, and ChieloAudience: Who are you writing to? (Another character, self, a god)Format: What format are you writing in? (Letter, monologue, diary entry, song, prayer) Topic: Characters reaction to the events of Chapter 11---------------------------------------------------------------------------------------------------------------------I am stunned and shocked to see that Chielo has come for Enzinma. Ezinma has done nothing to warrant this and she has been through enough, especially with her sickness. Is this a sign of the gods work? reynolds corp. has 100,000 shares of $1 par value common stock issued and outstanding. reynolds declares a 20% stock dividend when the fair value of the stock is $8 per share. the debit to retained earnings is a client with early-stage cancer of the esophagus is treated with laser therapy. when oral intake is permitted, which type of dietary selection should the nurse recommend to the client? Three gang members, Joe, Larry, and Bob, are all convicted felons. The three were speeding in excess of the posted speed limit in a stolen car together when they noticed a group of rival gang members two blocks away. Joe, the front seat passenger, told the others he was going to shoot at the group with a gun he concealed in his waistband; Larry the driver, drove the car closer to their rivals. When the car came to a stop sign, Bob, who was a back seat passenger, exited the car after he told his friends he could not go to jail as he was on parole. Larry then drove past their rivals as Joe fired several shots; one person was killed and one other was shot in the leg Mia estimated 5/8 + 1/9 by replacing 5/8 with 1 and 1/9 with 0. Her estimated sum was 1 + 0 = 1. Explain why Mia's estimate is Not accurate? NOT accurate. T/F the progress bar indicates how many concepts you have completed, how many are in progress, and how many are still left in the assignment. Black Friday and Cyber Monday shopping would both be examples of what factor that influences supply? a. Number of sellers b. Input Prices c. Taxes d. Productivity 20) What could be said to be this story's theme? A) Sometimes fishermen have luck, other times they do not. B) Sometimes fishermen lose their way, and forget where they are. C) Sometimes mysterious forces in the universe treat us with inexplicable favor. D) Sometimes mysterious forces in the universe treat us with unaccountable contempt. You expect to have 49.2 g of KCl but only make 37.5 g of KCl. What is the actual yield? fill in the blank. the___was established by the wagner act to oversee labor-management relations. group of answer choices commission on labor relations federal trade commission national labor relations board equal employment opportunity commission