I need help with this question

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).

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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.

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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

[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]

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 value -2 is the rate of change of the linear equation.

A general linear equation is:

y = a*x + b

Where a is the rate of change and b is the y-intercept.

The rate of change tells us how the variable y changes when the variable x changes.

In this case we have:

y=-2x+10

So the "-2" is the rate of change, it tells us that each time that x increases 1 unit, the value of y decreases by 2 units.

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Answer:

Expression for number of girls:

2b + 15

Equation for number of boys and girls:

b + (2b + 15) = 84

Number of boys

23

Number of girls

61

Step-by-step explanation:

b = number of boys

g = number of girls

b + g = 84

g = 2b+15

b + (2b + 15) = 84

3b + 15 = 84

3b = 69

b = 23

b + g = 84

23 + g = 84

g = 61

Answer: 3/5

The total number of slices is 10, and the number of yellow or red slices is 2 yellow slices + 4 red slices = 6 slices.

So, the probability of the dial stopping on a yellow or red slice is 6 slices / 10 total slices = 3/5.

This is the final answer, and it is already in its simplest form.

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

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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.

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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.

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Answer: x = 14; y = 74; Isosceles and Acute

Step-by-step explanation: 3(x+7) = 3x + 21

Isosceles triangles have congruent base angles making 63 = 3x +21

Solve for x.

All angles of a triangle add up to 180 making y = 180 - 63 - 63.

Isosceles because two sides are congruent. And acute because all angles are under 90.

Step-by-step explanation:

well, you have it further up :

P(A) = 17x = 17 × 1/32 = 17/32 = 0.53125

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).

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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).

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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

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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.

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The error in River's analysis is that it is known if LM and MJ are perpendicular to KL and KJ.

What is error analysis?

Error analysis is a technique used to track out errors in learner language, ascertain whether they are systematic, and (if possible) provide an explanation for why they occurred.

It is given that -

Line segment KM is the bisector of ∠LKJ.

Also, line segment LM = MJ.

According to the angle bisector theorem if a line is a bisector of an angle then the corresponding sides of the angle should be perpendicular to the third side which is getting bisected.

Although it is given that  LM = MJ, but it is not known that if LM and MJ are   perpendicular to the sides of ∠LKJ.

Therefore, River cannot conclude that KM is the bisector of ∠LKJ.

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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  

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Answer:

E

Step-by-step explanation:

just looking for the ration if scale factor is 2

multiply it and fimd the ans

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 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

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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.

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.

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)

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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.

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The statement that A triangular prism contains two parallel hexagonal faces is False

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

A triangular prism contains two parallel hexagonal faces.

As a general rule, the parallel faces in a triangular prism are triangles

This is so because a triangular prism is a 3-dimensional object with a triangular base and three rectangular sides.

The two parallel faces of a triangular prism are congruent triangles, not hexagons.

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