the square of the difference of 10 and j less than the product of ten cubed

[tex]\cfrac{x^2 - 49}{x+2}\div \cfrac{x^2-14x+49}{3x+6}\implies \cfrac{x^2 - 49}{x+2}\cdot \cfrac{3x+6}{x^2-14x+49}[/tex]

[tex]\cfrac{\stackrel{\textit{difference of squares}}{x^2 - 7^2}}{x+2}\cdot \cfrac{3(x+2)}{(x-7)(x-7)}\implies \cfrac{~~\begin{matrix} (x-7) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+7)}{~~\begin{matrix} x+2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{3~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{(x-7)~~\begin{matrix} (x-7) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \\\\\\ \cfrac{x+7}{1}\cdot \cfrac{3}{x-7}\implies \cfrac{3(x+7)}{x-7}[/tex]

The solution for the system of linear equations is given by ( 2,3) with cost of one ice cream cone as $2 and cost of one ice cream sandwich as $3.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: The system of linear equations are 2x+y=8

and x+y=5

Solving the system of linear equations by the method of elimination we get

2x+y=8

2x+2y=10

__________

  -y=-2

Thus y=2 and x=8-2 / 2

                         =3

Hence, The solution for the system of linear equations is given by ( 2,3)

Learn more about linear equations here:

https://brainly.com/question/29739212

#SPJ1

A baker had 24 cupcakes and wanted to divide them equally among 8 friends. How many cupcakes would each friend receive?

The problem can be represented by 8/3 ÷ 4, where 8 represents the number of friends, 3 represents the number of cupcakes each friend should receive, and 4 represents the number of groups the cupcakes should be divided into.

The division makes sense because first, we need to find out how many cupcakes each friend should receive, which is 24 ÷ 8 = 3. Then, we divide the number of cupcakes each friend should receive by the number of groups to find out how many cupcakes each group should receive, which is 3 ÷ 4 = 0.75 cupcakes per group.

The amount that will be in the account in 25 years is $16,282.298.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Given that,

Principal amount, P = $3000

Rate of interest, r = 7% = 0.07

Number of years, n = 25

The final amount in a compound interest where the interest is compounded annually is,

A = P (1 + r)ⁿ

Substituting the given values,

A = 3000 (1 + 0.07)²⁵

   = 3000 (1.07)²⁵

   = 16,282.298

Hence the final amount after 25 years is $16,282.298.

Learn more about Compound Interest here :

https://brainly.com/question/29335425

#SPJ1

The ordered pair of solutions is (11/5, 2).

What is the linear equations?

A linear equation is a mathematical equation that represents a straight line when graphed on a coordinate plane. It has the form of ax + b = y, where a and b are constants and x and y are variables. The coefficient "a" determines the slope of the line, and the constant "b" determines the y-intercept.

The elimination method is a method of solving a system of linear equations by adding or subtracting the equations to eliminate one of the variables.

Here is the solution for the system of equations 2x - 2y = 2 and 5x + 2y = 12 using the elimination method:

Multiply the first equation by 5: 10x - 10y = 10

Add the two equations: 15x - 8y = 22

Solve for x by dividing both sides of the equation by 15: x = 22/15 = 11/5

Substitute the value of x back into one of the original equations to solve for y:

2x - 2y = 2

2(11/5) - 2y = 2

22/5 - 2y = 2

22/5 - 2y = 2

22/5 = 2 + 2y

22/5 - 2 = 2y

20/5 = 2y

10/5 = y

The solution to the system of equations is (x, y) = (11/5, 10/5) = (11/5, 2).

So, the ordered pair of solutions is (11/5, 2).

To learn more about linear equations, Visit

https://brainly.com/question/2030026

#SPJ1

The ordered pair of solutions is written in the format (x, y) is (11/5, 2) .

When plotted on a coordinate plane, a linear equation is a mathematical equation that resembles a straight line. It takes the form axe + b = y, with a and b acting as constants and x and y as variables. The line's slope is determined by the coefficient "a," whereas the y-intercept is determined by the constant "b."

A system of linear equations can be solved using the elimination approach by adding or removing equations to get rid of one of the variables.

Here is the elimination technique solution for the system of equations 2x - 2y = 2 and 5x + 2y = 12:

The first equation is multiplied by 5: 10x - 10y = 10.

Equational sum: 15x - 8y = 22

Divide both sides of the equation by 15 to find the value of x: x = 22/15 = 11/5

To find the value of y, add the value of x back into one of the initial equations:

2x - 2y = 2

2(11/5) - 2y = 2

22/5 - 2y = 2

22/5 - 2y = 2

22/5 = 2 + 2y

Simplify the equation

22/5 - 2 = 2y

20/5 = 2y

10/5 = y

The system of equations has a solution of (x, y) = (11/5, 10/5) = (11/5, 2).

The pair of answers that are in order is (11/5, 2).

To learn more about system of equations refer to:

https://brainly.com/question/13729904

#SPJ1

Answer:

8

Step-by-step explanation:

f(4) = 3(4) - 4

f(4) = 12 - 4

f(4) = 8

Answer: 11

Step-by-step explanation:

3x2=6

6+5=11

Answer:

Then the two numbers are -11 and -6.

Step-by-step explanation:

-11+-6= -17

They are -11 and -6.

-11 + -6 = -17  

-11 x -6 = 66.

Mark me Brainliest. :D

Answer:

0.2

Step-by-step explanation:

as 0.2 is greater than 1

Answer:

0.2

Step-by-step explanation:

The diagram = 0.1

0.1 < 0.2

The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12%  and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)

Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)

Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470

Now

y = 1470 + 350
y = $1820

Learn more about models here:
https://brainly.com/question/22591166
#SPJ1

The area for each part of the figure is given as follows:

The area of a right triangle is given by half the multiplication of it's sides.

Triangle A has the side lengths given as follows:

Hence the area is given as follows:

A = 0.5 x 4 x 10 = 20 units squared.

Triangle D is has the side lengths given as follows:

Hence the area is given as follows:

D = 0.5 x 2 x 6 = 6 units squared.

The total area is given by the sum of the areas of each part of the figure, hence:

20 + 2 + 4 + 6 = 32 units squared.

More can be learned about areas at https://brainly.com/question/21735282

#SPJ1

The slope-intercept form of the function described by this table is y = x + 1

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

x   y

0   1

From the above table of values, we can see that

The difference between the x and the y value is 1

Mathematicallly, this can be represeted as

y - x = 1

Add x to both sides

y = x + 1

The above equation is in the slope intercept form, y = mx + c

Hence, the equation is y = x + 1

Read more about linear equation at

https://brainly.com/question/2030026

#SPJ1

The probability that a student studied for exactly 4 hours rounded to the nearest hundredth is C. 0.26.

The concept that will be used here is probability. From the question the first column of a table serves as the amount of hours a student spent studying math,  while the  second column can be seen as the total number of pupils.

We can see from the second column's total  which is  35. We can see that just only 9 of them spent 5 hours  in the process of going over their arithmetic.

Then the likelihood that a student studied for four hours  can be known which can be calculated as :

= [9/35]

= 0.257 or 26%.

Therefore, option C is correct.

Learn more about probability at:

#SPJ1

The number of sophomores in the class is 35.

The number of Juniors in the class is 19.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of sophomores = x + 16

Number of Juniors = x

Now,

Number of students in the class = 54

This means,

x + x + 16 = 54

2x + 16 = 54

2x = 54 - 16

2x = 38

x = 19

Thus,

Number of sophomores = 19 + 16 = 35

Number of Juniors = 19

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Therefore , the solution of the given problem of trigonometry comes out to be the five functions value are written above Cosθ = 3/5.

Relationships between cubic splines and trigonometry When the professions of mathematicians were united, it is thought that the field was founded during the third millennium BC. Precise mathematical methods can be used to solve a wide range of geometric issues or to determine the outcomes of calculations that use them. The study of the six fundamental trigonometric operations is known as trigonometry.

Here,

Given :

There are in 3 quadrant :

=> Sinθ = -4/5

=> Cosθ = √1 - Sin²θ

=>  Cosθ  = √1 - 16/25

=> Cosθ = 3/5

=>Tan θ = -4/5 / 3/5

=> Tan θ  = -4/3

=>Cot θ = -3/4

and

Cosec θ = -5/4

Sec  θ = 5/3

Therefore , the solution of the given problem of trigonometry comes out to be the five functions value are written above Cosθ = 3/5.

To know more about trigonometry visit:

https://brainly.com/question/29002217

#SPJ1

The explicit rule for the nth term of the geometric sequence: 3, 18, 108, 648, 3,888, … is aₙ = 3( 6ⁿ⁻¹ )

The geometric sequence is expressed as aₙ = a₁ × rⁿ⁻¹

Given the set of numbers in the question;

3, 18, 108, 648, 3,888, …

The first term a₁ = 3

Next, we determine the common ratio r.

Divide a term by the previous term gives the common ratio.

Common ratio r = 18/3

Common ratio r = 6

Now, plug in the values of first and common ratio into the above formula to determine the nth term.

aₙ = a₁ × rⁿ⁻¹

aₙ = 3 × 6ⁿ⁻¹

aₙ = 3( 6ⁿ⁻¹ )

Therefore, the nth term of the sequence is aₙ = 3( 6ⁿ⁻¹ ).

Option D) aₙ = 3( 6ⁿ⁻¹ ) is the correct answer.

Learn more about geometric series here: brainly.com/question/19458543

#SPJ1

A scale factor consists of two or more shapes who look the same but have different scales or measures. A scale factor of 2 means that the new triangle is two times the size of the original.

If we look at shape x, we can see it has a base of 4, and a height of 3. If we also know that a scale factor of two means that the new shape will be twice as large, we can use an equation that looks like this:

(Base/height × scale factor = new base length)

Now that we have these numbers, we can take them and see which shape matches the new length.

Shape D has a base of 8 and a height of 6, meaning that it has a scale factor 2 compared to shape x.

Therefore Shape D is the answer.

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

The ratio of the sides = 7: 3

The ratio of perimeter = 7: 3

The ratio of the areas = 49: 9

Area of green polygon = 23

The polygons which are in the same shape but different in size are known as similar polygons. For similar polygons, the ratio of sides is known as the scale factor which is equal to the ratio of perimeters. Here the ratio of the areas is the squares of the scale factor.

Note:

Here we have two polygons

Side of the yellow polygon = 7 units

By the given formulas,

Perimeter of polygon = 6(7) = 42 units

Area of the polygon = 127 units²

Side of the green polygon = 3 units

Perimeter of polygon = 6(3) = 18 units

Area of Polygon = (3√3)/2 × (3)² = 23.383 ≅ 23

The ratio of the sides of polygons yellow to green = 7: 3

The ratio of perimeter = 42: 18 = 7: 3

The ratio of the areas = (7/3)² = 49/9

=> 49: 9

Therefore,

The ratio of the sides = 7: 3

The ratio of perimeter = 7: 3

The ratio of the areas = 49: 9

Area of green polygon = 23  

Learn more about Polygons at

https://brainly.com/question/24464711  

#SPJ1

Factored form of -3n⁶ +12n⁴ - 6n² would be, (n² + 1)(-3n² + 6).

What is factorization?

The process of writing a number or any mathematical object as a product of several factors, usually smaller or simpler objects of the same kind, is known as factorization or factoring.

In mathematics, factorization is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number.

The factored form of -3n^6 +12n^4 - 6n² is:

-3n² (n⁴ - 2) + 6n² (1 - n²)

= -3n² (n⁴ - 2) + 6n² - 6n⁴

= -3n² (n⁴ - 2 + 2n²) + 6n²

= -3n² (n² + 1)² + 6n²

= (n² + 1)(-3n² + 6).

So, Factored form of -3n⁶ +12n⁴ - 6n² would be, (n² + 1)(-3n² + 6).

To know more about factorization visit,

https://brainly.com/question/25829061

#SPJ1

Answer:

$2970.42

Step-by-step explanation:

Take $71,290 and divide it by 12 then you get $5,940.83 then divide that by 2 and your answer is $2,970.42

The surface area of the sphere is 1519.8 yd².

Three-dimensional shapes or solids are the names given to 3D shapes in geometry. Three separate dimensions, such as length, width, and height, are used to describe 3D shapes. The lack of thickness or depth in 2D shapes is the only distinction between them and 3D ones.

Given a sphere

diameter = 22 yards

radius = d/2 = 22/2

radius = 11 yards

the surface area of the sphere = 4πr²

S = 4πr²

S = 4(3.14)11²

S = 1519.76 yd²

S = 1519.8 yd²

Hence option A is correct

Learn more about 3D shapes;

https://brainly.com/question/29287790

#SPJ1

The function that is represented by the graph is y = ∛(x + 3) + 3.

What is a function?

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

The general form of a cube root function is -

y = a∛(x - h) + k and the parent graph is y = ∛x.

So the parent function is found.

The coordinate point for the parent function is -

(-1,-1) , (0,0) and (1,1).

In the graph it can be seen that the coordinate points are -

(-4,2), (-3,3) and (-2,4)

So the graph is first moved 3 units up and then moved three units left.

So, the coordinated become - (x + (-3) , y + 3)

So, the function that represents the graph is -

y = ∛(x + 3) + 3

Therefore, the function is y = ∛(x + 3) + 3.

To learn more about function from the given link

https://brainly.com/question/2284360

#SPJ1

Answer:

[tex]\text{Choice C: }\boxed{b\le 1 \dfrac{7}{10}\\\\}[/tex]

Step-by-step explanation:

We are given inequality:

[tex]\dfrac{7}{2}\ge \:b\:+\:\dfrac{9}{5}[/tex]

The original amount of water is 15 cups.

The change in David's water intake is 3 cups.

And, The percent change is 20%. This is a percent decrease.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

David is tracking the amount of water he drinks each day.

Here, On Thursday, he drinks 15 cups of water.

And, On Friday, he drinks 12 cups of water.

Hence, We get;

The original amount of water = 15 cups.

And, The change in David's water intake = 15 - 12

                                                               = 3 cups

And, The percent change in his water intake is,

⇒ Percent = 3 / 15 × 100

⇒ Percent = 20%

Thus, The original amount of water is 15 cups.

The change in David's water intake is 3 cups.

And, The percent change is 20%. This is a percent decrease.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

Answer:

The number with the highest sum of prime factors is 27, as it has only two prime factors: 3 and 3. The sum of its prime factors is 6, so if you choose 27, you can move 6 spaces. The number 25 has two prime factors as well, but only 5 + 5 = 10. 26 is not a prime number, so it wouldn't be the best choice. So, if you want to move as many spaces as possible, you should choose 27.