2 step equations with 8 as solution

a) The equation be [tex]$$(3 x+y)^4$$[/tex] then the binomial expression be [tex]$$81 x^4+108 x^3 y+54 x^2 y^2+12 x y^3+y^4$$[/tex].

b) The equation be [tex]$$(x-2 y)^6$$[/tex] then the binomial expression be[tex]$$x^6-12 x^5 y+60 x^4 y^2-160 x^3 y^3+240 x^2 y^4-192 x y^5+64 y^6$$[/tex]

The algebraic terms of the form (x + y)n are expanded using the binomial theorem. [tex](x + y)^n = ^nC_0 x_ny_0 +^ nC_1 x_{n-1}y_1,... + ^nC_{n-1} x_1y_{n-1} + ^nC_n x_0y_n[/tex].

In this case, there are n + 1 terms in the binomial expansion with an exponent of n. In a progressive way, the second term's exponent is gradually rising while the first term's exponent in the expansion is steadily declining. The Pascals triangle or the combination formula

[tex]^nC_r[/tex] = n! / [r! (n - r)!]! can be used to determine the coefficients of the binomial expansion.

a) Let the given equation be [tex]$$(3 x+y)^4$$[/tex]

Apply binomial theorem, we get

[tex]$(a+b)^n=\sum_{i=0}^n\left(\begin{array}{l}n \\ i\end{array}\right) a^{(n-i)} b^i$[/tex].

[tex]$a=3 x, b=y$[/tex]

[tex]=\sum_{i=0}^4\left(\begin{array}{l}4 \\i\end{array}\right)(3 x)^{(4-i)} y^i[/tex]

simplifying the equation, we get

[tex]$\frac{4 !}{0 !(4-0) !}(3 x)^4 y^0+\frac{4 !}{1 !(4-1) !}(3 x)^3 y^1+\frac{4 !}{2 !(4-2) !}(3 x)^2 y^2+\frac{4 !}{3 !(4-3) !}(3 x)^1 y^3+\frac{4 !}{4 !(4-4) !}(3 x)^0 y^4$[/tex]

Simplifying the above equation, we get

[tex]$\frac{4 !}{0 !(4-0) !}(3 x)^4 y^0= 81 x^4$[/tex]

[tex]$\frac{4 !}{1 !(4-1) !}(3 x)^3 y^1= 108 x^3 y$[/tex]

[tex]$\frac{4 !}{2 !(4-2) !}(3 x)^2 y^2=54 x^2 y^2$[/tex]

[tex]$\frac{4 !}{3 !(4-3) !}(3 x)^1 y^3= 12 x y^3$[/tex]

[tex]$\frac{4 !}{4 !(4-4) !}(3 x)^0 y^4= y^4$[/tex]

[tex]$$=81 x^4+108 x^3 y+54 x^2 y^2+12 x y^3+y^4$$[/tex]

b) Let the given equation be [tex]$$(x-2 y)^6$$[/tex]

Apply binomial theorem: [tex]$(a+b)^n=\sum_{i=0}^n\left(\begin{array}{l}n \\ i\end{array}\right) a^{(n-i)} b^i$[/tex]

a = x, b = -2y

simplifying the equation, we get

[tex]$$=\sum_{i=0}^6\left(\begin{array}{l}6 \\i\end{array}\right) x^{(6-i)}(-2 y)^i$$[/tex]

[tex]$=\frac{6 !}{0 !(6-0) !} x^6(-2 y)^0+\frac{6 !}{1 !(6-1) !} x^5(-2 y)^1+\frac{6 !}{2 !(6-2) !} x^4(-2 y)^2+\frac{6 !}{3 !(6-3) !} x^3(-2 y)^3+[/tex][tex]$\frac{6 !}{4 !(6-4) !} x^2(-2 y)^4+\frac{6 !}{5 !(6-5) !} x^1(-2 y)^5+\frac{6 !}{6 !(6-6) !} x^0(-2 y)^6$[/tex]

simplifying the equation, we get

[tex]$\frac{6 !}{0 !(6-0) !} x^6(-2 y)^0= x^6$[/tex]

[tex]$\frac{6 !}{1 !(6-1) !} x^5(-2 y)^1=-12 x^5 y$[/tex]

[tex]$\frac{6 !}{2 !(6-2) !} x^4(-2 y)^2= 60 x^4 y^2$[/tex]

[tex]$\frac{6 !}{3 !(6-3) !} x^3(-2 y)^3=-160 x^3 y^3$[/tex]

[tex]$\frac{6 !}{4 !(6-4) !} x^2(-2 y)^4= 240 x^2 y^4$[/tex]

[tex]$\frac{6 !}{5 !(6-5) !} x^1(-2 y)^5 = -192 x y^5$[/tex]

[tex]$\frac{6 !}{6 !(6-6) !} x^0(-2 y)^6= 64 y^6$[/tex]

[tex]$$=x^6-12 x^5 y+60 x^4 y^2-160 x^3 y^3+240 x^2 y^4-192 x y^5+64 y^6$$[/tex]

To learn more about Binomial Theorem refer to:

https://brainly.com/question/13672615

#SPJ1

The number of books Eli reads each month is 1 / 5 books.

Eli read 1 book in 5 months.  He reads at a constant rate. Therefore, the number of books he read each month can be calculated as follows:

He reads 1 book in 5 months.

Recall, he reads at a constant rate.

Therefore, the number of book he reads each month is as follows:

5 months = 1 book

1 month  = ?

cross multiply

number of book read each month = 1 / 5

Therefore, he reads 1 / 5 books each month.

learn more on rate here: https://brainly.com/question/21895700

#SPJ1

The best route to take to Boston so that you can spend the least amount of time on the bus is D. Route 4.

To find the route that would involve spending the least amount of time on the bus, you need to find the difference between the time the bus leaves and the time it arrives.

The time for Route 1 is:

= 6 : 15 - 4 : 45

= 1 hour 30 minutes

Route 2:

= 7 : 15 - 5 : 30

= 1 hour 45 minutes

Route 3 :
= 6 : 50 - 5 : 15

= 1 hour 35 minutes

Route 4 :

= 7 : 00 - 5 : 45

= 1 hour 15 minutes

Route 4 is therefore the best route.

Find out more on routes at https://brainly.com/question/17429103

#SPJ1

Therefore , the solution of the given problem of triangle comes out to be KY = 16/3 inches , ZJ = 8 inches and  LY =2.66 inches.

The fact that a triangle contains four or segments qualifies it as a polygon. It is an elementary geometric form. Triangle ABC is the name given to a square with angles A, B, or C. Euclidean geometry creates one plane and square when side are not collinear. It is a polygonal if a triangle includes three sides + three corners. The intersection of a triangle's three sides is at its corners. Three triangle angles added together equal 180 degrees.

Here,

Given : A triangle XYZ

side length XY = 8 inches

and ZX = 12 inches

So,

Using centroid theorem:

We get

=> KY = 2/3 * 8

=> KY = 16/3 inches

and

=> ZJ = 2/3 * 12

=> ZJ = 8 inches

and For LY

=>  8 - 16/3

=> 2.66 inches

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

KY = 16/3 inches , ZJ = 8 inches and  LY =2.66 inches.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Using subtraction it is found that Elerie needs to pour 350 ml more milk in the jug and not 440 ml.

What is subtraction?

The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).

Eleri needs half a litre of milk, which is a = 500 ml

According to the diagram Eleri has already poured some amount of milk in the jug, which is b = 150 ml.

Let the remaining amount of milk that needs to be poured be x.

So, use the arithmetic operation of subtraction to solve the equation -

x = a - b

x = 500 - 150

x = 350

Eleri is not correct about pouring 440 ml more milk in the jug.

Therefore, Eleri needs 350 ml of more milk in the jug.

To learn more about subtraction from the given link

https://brainly.com/question/13378503

#SPJ1

The equation of line is y = 6x

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Let the point be represented as P ( -1 , -6 )

Now , the slope of the line is perpendicular to the line x + 6y = 6

Subtracting x on both sides of the equation , we get

6y = -x + 6

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

y = - ( 1/6 )x + 1

Now , the slopes of perpendicular lines = -1

m₁ x m₂ = -1

Substituting the values in the equation , we get

m₂ = 6

So , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -6 ) = 6 ( x - ( -1 ) )

y + 6 = 6 ( x + 1 )

y + 6 = 6x + 6

Subtracting 6 on both sides of the equation , we get

y = 6x

Hence , the equation of line is y = 6x

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ1

the equation of the line that passes through the point (−1, −6) and is perpendicular to the line x + 6y = 6 is y = 6x.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, There is an equation of the line that passes through the point (−1, −6) and is perpendicular to the line x + 6y =6

The general formula of the slope-intercept form of a line:

y = mx + b,

where m is the slope

b is the y-intercept

For the Given equation

In the form of slope intercept:

y = -1/6x+ 1

Thus,

Slope = -1/6

Since Another equation is Perpendicular to this given equation:

Thus, The Slope of the other line = -1/ slope of first line

The Slope of the other line = 6

Thus, the Equation of the line will be:

y = 6x + c

Since the line passes through the point (-1, -6)

-6 = -6 + c

c = 0

Therefore, the equation of the line that passes through the point (−1, −6) and is perpendicular to the line x + 6y = 6 is y = 6x.

Learn more about Linear equations here:

https://brainly.com/question/11897796

#SPJ1

There is a circular cross-section with a center at (1, 1) and radius of 1 is rotated about the line y = 1 so it should be a sphere.

If a cylinder is cut along to its circular base, its cross-sectional area is the same as the area of a circle. The area of a two-dimensional shape created when a three-dimensional object, like a cylinder, is cut perpendicular to a predetermined axis at a point is known as the cross-sectional area.

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the specified point represents its center.

Learn more about Sphere :

https://brainly.com/question/22121106

#SPJ4

Answer:

sphere

Step-by-step explanation:

i took the quiz

Answer: X = -7   because -6 times -7 equals 42 and 42 minus 9 equals 33

Answer:

Step-by-step explanation:

Step 1: Add 9 to both sides, 33+9=42, the 9s cancel out.

Step 2: divide -6x to both sides 42/-6x is -7x, the 6s cancel out.

You can check the answer by substituting x with 7, so it should look like this: -6(-7)-9=33 :)

Answer: 14

Step-by-step explanation:

7 * 2 = 14

Answer:

Sum = 14

Step-by-step explanation:

The sum refers to addition. Quotient refers to division.

The sum of 4 and 3 is written as 4+3. The quotient of 4 and 2 is written as 4/2.

4 + 3 = 7

4 / 2 = 2

Multiply 7 by 2

7 * 2 = 14

The sum of 4 and 3 multiplied by the quotient of 4 and 2 is 14.

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

n =4 for the length of chord.

Each spot that is a certain distance from that other point in the plane forms a circle (center). As a result, it is a curve composed of vertices that are isolated from one another in the plane by a specific distance. Furthermore, it is axis of rotation symmetric about the center at all angles. The circle's enclosed, two-dimensional plane has every pair of endpoints uniformly separated from the "center." Draw a line thru the circle to create a circular symmetry line. Additionally, at every angle, it rotates equally about the center.

Here,

Given :

2 cords AB & CD can intersect at point P,

according to the following theorem:

|AP| |PB| = |CP| |PD|

We obtain

=>(n-2) x 16 = 8x (n+8)

using the theory of intersection between two cords.

Use the following formula:

=>16n+32 = 8n +64

=>8n -32 = 0

=>8n=32.

8 divided by both sides.

n = 32/8

n = 4

Consequently, n has a value of 4.

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

n =4 for the length of chord.

To know more about circle visit:

https://brainly.com/question/29142813

#SPJ1

Each of the tire has traveled 10000km / 5 tires = 2000km.

To determine how many km each tire has traveled, you can use the following formula:

Total distance traveled / Number of tires = KM per tire

For example, if the car has traveled 10000 km and there are 5 tires, you would divide 10000 by 5 to get 2000 km per tire.

Another way is to use a tire tread depth gauge to measure the depth of the tread on each tire, when the tread wear reaches a certain point, it means the tire has traveled a certain distance.

Learn more about problem solving and division here: https://brainly.com/question/941863

#SPJ4

Answer:

2 + 2 equal 4.

Step-by-step explanation:

2 + 2 equals 4.

Answer: 2 + 2 = 4

Step-by-step explanation: you have two markers and then you have two more markers and you add them together you get four

The correct statement that describes the two functions A

Function is a type of relation, or rule, that maps one input to specific single output.

Given;

Ryan: 3 boxes per hour

Daniel: y=4h

Ryan's function;

In 1 hour, he can pack 3 boxes.

In hours, he can pack 3h boxes.

So, the equation will become;

y=3h

Now, we have;

y=3h Ryan

y=4h Daniel

Both functions represent direct proportional functions.

So, when h increases y also increases.

Therefore, Daniel's function has a greater rate of change because implies that he can pack 4 boxes per hour while Ryan can pack 3;

Learn more about function here;

https://brainly.com/question/2253924

#SPJ1

Answer:

Part A: You can use unitary method as the shadow is directly proportional to the height of the initial object.

Part B:

1.5 : 5 :: 4.5 :: Height of street sign

5 : 1.5 :: Height of street sign : 4.5

Part C

You can use the first proportion,

If 1.5 ft : 5 ft

4.5 : 4.5 x 5/1.5 = 15 ft.

You can use the second proportion.

5 : 1.5

x : 4.5

5/1.5 = x/4.5

x = 4.5 / 1.5 x 5 = 15 ft

There u go mate.

Cheers! Also, pls mark as brainliest if possible.

-1

9 - 9 -1

0-1

-1

Basically subtracting 9 then subtracting 1, leading to -1

Answer: A

Step-by-step explanation:

The domain and the range of y = 12x - 35 are the set of all real numbers

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

y = 12x - 25

There is no restriction on the input values, x

So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).

The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).

This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.

Read more about domain and range at

brainly.com/question/2264373

#SPJ1

Complete Question

Use the drop-down menus to identify the domain and range of each function below.

y = 12x - 25

Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph can be used to display a certain kind of data.

Using a bar graph, you may rapidly and visually communicate related information. The bars show the value for each type of data in question. The y-axis refers to the vertical axis on the left or right side of the bar graph.

Information and data are visualized using circle graphs or pie charts. To quickly and proportionally display the findings of an investigation, a circle graph is frequently employed.

A line graph, sometimes referred to as a line chart or a line plot, is frequently used to display data that varies over time. Several points connected by straight lines can be used to plot it. It includes of the "x-axis" and the "y-axis,".

To learn more about graph and its type link is here

brainly.com/question/16374169

#SPJ4

Answer:

A rhombus is not a trapezoid

Parallelograms have TWO pairs of parallel sides

a rectangle is only a rhombus if the rectangle has equal sides( making it be a square)

A rectangle is also a parallelogram

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So

1) No

2)No

3) i think that it could be both yes and no because of the answer up there  ^

4) Yes

A non-deterministic environment is one in which actions are characterized by their possible outcomes, but no probabilities are attached to them.

It is impossible to predict the outcome because it is likely to differ every time: We can take a non-deterministic stance and consider the social structure to be a complex, unstable, and dynamic system.

A non-deterministic environment is one where actions are characterized by their potential consequences but no probabilities are associated with them. The term "stochastic" normally indicates that uncertainty about outcomes is quantified in terms of probability.

Know more about non-deterministic

https://brainly.com/question/28104525

#SPJ4

When dividing the polynomial 3x^2 + 8x -3 by x + 3, we get the quotient as 3x - 1.

The given polynomial is 3x^2 + 8x -3.

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial:

(x)(3x) = 3x^2

Thus, we multiply the divisor (x+3) by 3x which gives 3x^2 + 9x.

Now we subtract this from the polynomial which gives -x -3.

In the same way we multiply the divisor by -1 which gives -x-3. Subtracting the same from the remaining polynomial -x -3 we get the remainder 0.

Thus, the quotient is 3x - 1.

The question is incomplete, the complete question is:

What is the quotient (3x^2 + 8x -3) ÷ (x + 3)?

To know more polynomial division:

https://brainly.com/question/27777983

#SPJ4

The location of the scuba diver is 34.25 feet relative to the surface after 7 1/2 seconds.

Speed refers to the rate at which a distance varies over time. The speed is equated to s = D/T if D is the object's distance in period T. The units are identical to those used for velocity.

Given, the speed of the scuba driver = 2.5 ft/s

The distance covered by her in 7.5 seconds is given by

= 2.5 × 7.5

= 18.75 ft

According to the question, when she started she is 15.5 ft below the surface  of the water

So, her total distance from the surface after 7.5 s is given by

= 15.5 + 18.75

= 34.25 ft

To know more about distance, visit:

https://brainly.com/question/26862717

#SPJ1

A pyramid has a volume of 173.88 ft3, is 10.5 feet tall, and has a rectangle-shaped base that is 7.2 feet by 6.9 feet in size.

A rectangular pyramid has five faces altogether. Its rectangular base serves as one face, and the remaining four faces are all triangular in shape. All of the triangles in this are congruent with the triangle to the opposite. The formula for a pyramid's total surface area is 12 pl + B, where p is the base's perimeter, l is the pyramid's slant height, and B is the base's area.

The volume of a rectangular pyramid is found using the formula Volume = 1/3 × base area × height.

height is 10.5 feet

dimensions of 7.2 feet by 6.9 feet.

volume = L× B × H /3

volume = 7.2·6.9·10.5 /3

volume = 173.88ft³.

To know more about pyramid visit:-

https://brainly.com/question/23857979

#SPJ1

Answer: 4

Step-by-step explanation:

The x intercept is where the line intersects with the x axis

Counting from the origin (0,0), you can see that the x intercept is 4

Answer:

Step-by-step explanation:

4x = -4

x = -1

-2 + y = 2

y = 4

(-1, 4)

Purple:  plot (-1, 4) and (0, -6)

Yellow: plot (-1, 4) and (0, 2)

The point of intersection between the two equations is (-1, 4). The graph is given below.

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

We have,

2x - y = -6

or, y = 2x + 6 ....... (i)

2x + y = 2

or, y = 2 - 2x ........... (ii)

Now,

The point of intersection:

2x + 6 =  2 - 2x

or, 4x = -4

or, x = -1

now, putting the value of x in equation (i), we get -

y = 2(-1) + 6

y = 4

(-1, 4) is the point of intersection.

Now, the graph of the equation is given below.

Learn more about equations here:

brainly.com/question/17194269

#SPJ1

Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."

A scalar quantity known as distance measures "how much ground an object has traversed" while moving.

The entire journey that an object takes can be used to define its distance. An illustration. An automobile must cover a total distance of 13 km if it drives for 5 km in the east before turning and driving for another 8 km in the north.

The meter is the metric unit of length.

The speed distance time formula is given as. d=xt.

Distance traveled d = x × t.

To know more about Distance visit :

https://brainly.com/question/26711747?referrer=searchResults

#SPJ4

Answer:

15/72

Step-by-step explanation:

15/36 ÷ 2. First Make 2 into a fraction, which is 2/1. Now we have 15/36 ÷ 2/1. Turn the division into multiplication. And switch 2/1 into 1/2. 15/36 x 1/2 is 15/72.

Answer:

the answer is in the picture

Answer:

21 - 20i

Step-by-step explanation:

Simplify the following:

(-2 i + 5)^2

(-2 i + 5)^2 = 25 - 10 i - 10 i - 4 = 21 - 20 i:

Answer: -20i +21 = 21 - 20i

The number of women working for the company is 161 if the ratio of men to women working for a company is 5:7.

The ratio of men to women working for a company is 5:7

Let 5x be the total men and 7x be the total women working for the company:

Total employees  = 276

5x + 7x = 276

12x = 276

x =276/12

x = 23

Total men = 5x = 5(23) = 115

Total women = 7x = 7(23) = 161

Thus, the number of women working for the company is 161 if the ratio of men to women working for a company is 5:7.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

Learn more about Ratios :

https://brainly.com/question/4239280

#SPJ4