Please help me I’m struggling

The complete factorization of the polynomial  x³ + 2x² + 4x + 8 is  

(x² + 4)(x + 2).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A cubic polynomial x³ + 2x² + 4x + 8.

Now, Factoring this polynomial,

= x³ + 4x + 2x² + 8.

= x(x² + 4) + 2(x² + 4).

= (x² + 4)(x + 2).

Now, (x² + 4) can not be factored anymore.

So, The factor of  x³ + 2x² + 4x + 8 is  (x² + 4)(x + 2).

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The fundamental counting principal there will be 2*2*2*4*2 = 64 possible lunches.

What is fundamental counting principal ?

According to this concept, the sum of the outcomes of two or more independent events is equal to the product of the outcomes of each individual event. For instance, a youngster picking from a menu of six ice cream flavors and three types of cones will have a total of 6 x 3 = 18 options.

Here size has two types  say  2

Here cheese has two types say 2

Here type of bun has two types say 2

Here side order has four types say 4

Here fruit drink has two types say 2

So, according to the fundamental counting principal there will be 2*2*2*4*2 = 64 possible lunches.

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The equation of the line is y = 13/6x - 5

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

Points: (0, -5) and (6, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

c = -5

So, we have

y = mx - 5

Also, we have

(x, y) = (6, 8)

This means that

8 = m x 6 - 5

So, we have

6m = 13

This gives

m = 13/6

So, we have

y = 13/6x - 5

Hence, the equation is y = 13/6x - 5

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Answer:

d is the correct answer to your question

Answer:

9.2 units

Step-by-step explanation:

cause the last guy is right...

The best way to analyze their data for significance is to Conduct a two-way variable analysis.

As we can see, there is a 2x3 factorial design. Thus, we know that there will be a two level or two way analysis of variables, which is referred to as two way variables analysis. Factorial design is a research method that allows for the inquiry of a main and interaction effects of two or more independent variables on one or more outcome variables (s).

It has been argued that factorial designs represent the true beginning of modern behavioral research and have resulted in a significant paradigm shift in how social scientists conceptualize their research questions and produce objective results (Kerlinger & Lee, 2000).

Factorial design is an experimental methodology that goes beyond standard single-variable experimentation. Previously, social scientists were fixated on single independent variable experiments, foreshadowing the significance of extraneous variables that can attenuate or diminish research findings.

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Answer:

Square, rhombus, parralelogram

Step-by-step explanation:

Bro too much to type trust

Answer:

I'm not sure sorry sorry

The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder [tex]\frac{x^2}{25} +\frac{y^2}{9}[/tex] is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

[tex]\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)[/tex]

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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When a spring of stiffness K = 120N/m supporting a smooth cylinder of mass 6kg is subjected to a force of 60N, the velocity it moves downward when compressed a distance of 0.2m is 1.79m/s.

Therefore, the answer is 1.79m/s.

The compression of spring, say x₀ at equilibrium position can be determined by

F = Kx₀

mg = Kx₀

6 × 9.81 = 120 × x₀

Therefore x₀ = 0.4905m

When force F = 60N is applied the spring is compressed more and let new compression of spring be x₁. Then when string compresses additional s distance

x₁ = x₀ + s

Then spring force, F₁ = Kx₁

F₁ = 120 × (0.4905 + s)

F₁ = 58.86 + 120s

Let the cylinder accelerates downward at a m/s², then

60N + mg = ma + F₁

60 + 6×9.81 = 6a + 58.86 + 120s

a = (10 - 20s) m/s²

dv/dt = 10 - 20s

We know that ds/dt = v, that is 1/dt = v/ds

Therefore, vdv/ds = 10 - 20s

vdv = (10 - 20s)ds

Integrating both sides

v²/2 = 10s - 10s²

v = √(20s - 20s²)

At s = 0.2m,

v = √(20×0.2 - 20×0.2²)

v = 1.79m/s

--The question is incomplete, answering to the question below--

"The 6kg smooth cylinder is supported by the spring having a stiffness of kAB = 120 N/m. Determine the velocity of the cylinder when it moves downward s = .2m from its equilibrium position, which is caused by the application of the force F = 60 N. (The 60 N force is not present in the equilibrium position.)"

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i didn't learn it.. so im not sure.. but i thimk 3

In a dice, there is a six side

Probability of occurring a score = 1/18

                                           = 1*2/18*2

                                               = 2/36

                                        =   preferred outcome/ Total outcome

Only 5 is a number that has occurred twice

The score that has a probability of occurring of 1/18 is 5.

The two dice having different values 30/36 = 5/6 (because the probability of the two dice having equal values is 6/36 = 1/6.)

The probability of the second dice being less than the first dice is the same as the probability of the first dice is less than the second dice: (5/6) / 2 = 5/12.

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Answer:

18

Step-by-step explanation:

this seems to be an equilateral triangle so all sides are equal

5r+8=9r

-5r.   -5r

8=4r

/4 /4

2=r

now fill it in

5(2)+8

10+8

18

hopes this helps

Although part of your question is missing, you might be referring to this full question: What are the vertex and range of y = |2x + 6| + 2?

(0, 2); 2 < y < ∞

(0, 2); −∞ ≤ y < ∞

(−3, 2); 2 < y < ∞

(−3, 2); −∞ ≤ y < ∞

The vertex of the function is (–3, 2) and the range of the function is 2 < y < ∞.

The given modulus function:

y = |2x + 6| + 2

Now, we get two equations out of the absolute value function:

y = 2x + 6 + 2

y = 2x + 8

and

y = –2x – 6 + 2

y = –2x – 4

The vertex of the function will be at a point where these two equations are equal. So, we can calculate the vertex as follows:

2x + 8 = –2x – 4

2x + 2x = –4 – 8

4x = –12

x = –3

If x = –3, then y = 2(–3) + 8 = –6 + 8 = 2

Thus, the vertex of the function is (–3, 2).

Now, the values that y can take will range from 2 to infinity as y cannot take values below the vertex.

Thus, the range of the function is 2 < y < ∞.

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The number of years that the deposit was held for is 3 years.

From the information, Mr. Johnson deposited $2000 in an account that earns simple interest at an annual interest rate of 6%. and he received $360 as interest at the end of the tenure.

It should be noted that simple interest is Illustrated as:

I = PRT

Therefore, T = Interest / Principal × Rate

Time = 360 / (2000 × 6%)

Time = 360 / 120

Time = 3 years

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The number of students who like dressmaking and catering only is 7.

The number of students who did not choose any of the 3 vocations is 12.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

Total students = 40

The Venn diagram is given below.

The number of students who like dressmaking and catering only.

= 7

Total number of students who like at least one vocation.

= 28

The number of students who did not choose any vocation.

= 40 - 28

= 12

Thus,

7 students like dressmaking and catering only.

12 students did not choose any vocation.

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π/16 is the area enclosed by the curve r= sin(4θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = [tex]\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta[/tex]

where a and b is the boundary at which r=0

so after equation r=0

sin(4θ) =0

=> sin(4θ) =0

=> 4θ = 0,π

=> θ = 0, π/4

so a=0 , b= π/4

now  

  A =  [tex]\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta[/tex]   ------(i)

so   [tex]r^2[/tex] = (sin(4θ))^2

=>   [tex]sin^2[/tex]( 4θ )

ans we know that

cos(2α) = 1 -  [tex]2sin^2[/tex]2 α

so     [tex]sin^2[/tex]= (1- cos(8θ) )/2

putting the value of r in the equation (i) we get :-

A = [tex]\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta[/tex]

=> 1/4*  [tex]\int\limits^b_a {(1-cos8\theta) } \, d\theta[/tex]

here a=0 and b=π/4

after putting the value and solving the integral

A = π/16

so A is the area enclosed by r=sin(4θ) is π/16

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Answer:

C) cos A = 15/17

cos A = adjacent/hypotenuse = 15/17

What is trigonometric ratio for right angle triangle?

The trigonometric ratios for a right angle triangle are sine, cosine, and tangent. The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

The following are the trigonometric ratios of a right angle triangle:

Sine (sin): Opposite Side/Hypotenuse

Cosine (cos): Adjacent Side/Hypotenuse

Tangent (tan): Opposite Side/Adjacent Side

Cosecant (csc): Hypotenuse/Opposite Side

Secant (sec): Hypotenuse/Adjacent Side

Cotangent (cot): Adjacent Side/Opposite Side

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Graph 3 - linear

Graph 4 - linear

The line does not touch the same x more than once.

Answer:

putting more than question is against app rules but alr

Part A: The value of each of the houses after a fixed number of years can be described by a linear function. This is because the value of each house increases at a constant rate, with the same amount added each year.

Part B: The function for House 1 could be written as f(x) = 294,580 + 8,937.6x, and the function for House 2 could be written as f(x) = 295,000 + 9,000x.

Part C: After 25 years, the value of House 1 will be approximately $750,834.40, and the value of House 2 will be approximately $753,000. The difference in value between the two houses after 25 years will be approximately $2,165.60, which is not a significant difference in the overall value of the houses. Therefore, either house would be a good choice for Belinda to purchase.

Linearly because the table shows a constant percentage increase in temperature each month.

A graph is a diagram that depicts the relationship or connection between two or more quantities. Linear implies straight. The x and y coordinates of two points are connected by a straight line, or straight graph, to form a linear graph. Everyday life involves the utilization of linear relations, which can be graphed in a plane to produce a straight line.

In the first month it is 5

In the second month it is 7.2 so the increment in temperature is 7.2 - 5 = 2.2

In the third month it is 9.4 and the increment in temperature is 9.4 - 7.2 = 2.2

In the fourth month it is 11.6 and the increment in temperatue is 11.6 - 9.4 = 2.2

In the fifth month it is 13.8 and the increment in temperature is 13.8 - 11.6 = 2.2

So the increment is happening linearly

The equation which depicts this is y = (2.2)x+5 where x is the no.of month.

Linearly because the table shows a constant percentage increase in temperature each month.

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in a regression with 7 predictors and 62 observations,The degrees of freedom for a t-test for each coefficient would use 55 degrees of freedom (df = 62 - 7 = 55).

The degrees of freedom for a t-test for each coefficient is calculated by subtracting the number of predictors (7) from the number of observations (62) in a regression with 7 predictors and 62 observations,. This leaves us with 55 degrees of freedom (df = 62 - 7 = 55). Degrees of freedom measure the number of observations that are free to vary in estimating a parameter. In other words, they are the number of observations that are used to generate the estimate. In this case, there are 55 observations that can be used to estimate each coefficient.

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Answer: 50%

Step-by-step explanation:

Take 2.62 divided by 5.24, then times 100 = 50%

Then take 100% - 50% = 50%

The percentage discount is 50%

Answer:

0.4 x 10^-1

Step-by-step explanation:

4 x 10^0

=> 4

=> 0.4 x 10^-1

It is about 24% of the students could be expected to score between 70 and 90 on the exam.

To find the percentage of students who score between 70 and 90 on the exam, we need to determine what proportion of the exam scores falls within that range. We can do this by converting the scores to standard units and using a table of the standard normal distribution.

First, we need to convert the scores to standard units. We do this by subtracting the mean of 100 from each score and then dividing by the standard deviation of 60. For a score of 70, the standard units would be (70 - 100)/60 = -1.67. For a score of 90, the standard units would be (90 - 100)/60 = -0.67.

Next, we can use a table of the standard normal distribution to find the proportion of scores that fall within that range. For example, a table of the standard normal distribution might tell us that the proportion of scores between -1.67 and -0.67 standard units is about 0.24

Percentage of scores within range = 8.64/36 * 100% = 24%

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Answer:-2,0

Step-by-step explanation:

you have to ether multiply or divide by an easy number

Answer:

3.11(0) = 0

Step-by-step explanation:

D. 3.11(0) = 0 is an example of the identity property of 1. The identity property of 1 states that any number multiplied by 1 is equal to itself. In this case, 3.11 is multiplied by 0, which is equal to 0.

The equation of the Parabola is (y - 6 )² = 28 (x + 1)  of the given focus and directrix.

Given directrix x = -8

we know that    x = h - a = -8

              h -a =  -8  ...(i)

Given Focus  = ( 6,2)

we know that the Focus of the Parabola

        ( h + a , k ) = (6,2)

  comparing  h + a = 6 ...(ii)

                 k = 2

solving (i) and (ii) and adding

  h - a + h+ a = -8 +6

          2 h = -2

             h = -1

  Put h = 6 in equation (i)

 ⇒     h - a = -8

 ⇒   -1 + 8 = a

 ⇒      a = 7

The equation of the Parabola ( h,k) = (-1 , 7)

( y - k )² = 4 a ( x - h )

(y - 7 )² = 4 (7) (x -(-1))

(y - 6 )² = 28 (x + 1)

Hence, the equation of the Parabola is (y - 6 )² = 28 (x + 1)  of the given focus and directrix.

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lateral area of the cylinder = 2πrh

What is lateral area of the cylinder ?

The lateral area of a cylinder is the area on the outside, meaning if you would cut open a cylinder longitudinally, and folded it open, the rectangle that remains is the lateral area of the cylinder.

Area of rectangle = Lateral area

length is the circumference of the circle = 2πr

and length can be consider as h.

Hence, lateral area of the cylinder = 2πrh.

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The first three taylor polynomials of the function f(x) = e⁻ˣ at x = 0 is 1, 1 - x and 1 - x + x²/ 2.

Taylor polynomial of degree n for a function f(x) which is infinitely differentiable at a is

f(a) + f'(a)×(x - a)/ 1! + f''(a)×(x - a)²/ 2! + ... + (f⁽ⁿ⁾(a)×(x - a)ⁿ/ n! = ∑(i = 1 to n)(f⁽i⁾(a)×(x - a)^{i}/ i!)

where f⁽i⁾(a) denotes the ith derivative of f(x) at a

The first, second and nth derivative of the function f(x) = e⁻ˣ is

f'(x) = -e⁻ˣ

f''(x) = e⁻ˣ

f⁽ⁿ⁾x = (-1)ⁿe⁻ˣ

First Taylor polynomial, n = 1, here f(x) = e⁻ˣ and a = 0.

P₁(x) = f(0) = e⁻⁰ = 1

Similarly

P₂(x) = f(0) + f'(0)(x - 0)/ 1!

P₂(x) = 1 + -1×e⁻⁰×(x - 0)

P₂(x) = 1 - x

P₃(x) = f(0) + f'(0)(x - 0)/ 1! + f''(0)(x - 0)²/ 2!

P₃(x) = 1 - x + e⁻⁰×(x - 0)²/ 2

P₃(x) = 1 - x + x²/ 2

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