Mathematics : asked on xojade
 26.01.2023

What is the degree here?
2x2 + 4x - 1
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09.07.2023, solved by verified expert
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Always start with multiplication.

What is the degree here? 2x2 + 4x - 1 - Help, №18010678, 26.01.2023 06:44

Your answer should be 19.

The answer will always vary if you assign a different value to x, so please be careful with this in the future.

Hope this helps! Have a great day. ♣

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Mathematics
Step-by-step answer
P Answered by Master

Always start with multiplication.

2*2 + (4x) - 1\\4 * number\\number = 4\\4 * 4 = 16\\\\2 * 2 = 4\\\\4 + 16 = 20\\20 - 1 = 19

Your answer should be 19.

The answer will always vary if you assign a different value to x, so please be careful with this in the future.

Hope this helps! Have a great day. ♣

Mathematics
Step-by-step answer
P Answered by PhD

QUESTION 16



If the demand and supply are equal, then we equate the two functions in p and solve for p.



That is



S(p)=D(p)


400 - 4p + + 0.00002 {p}^{4} = 2800 - 0.0012 {p}^{3}



We can rearrange to obtain,



0.00002 {x}^{4} + 0.0012 {x}^{3} - 4x - 2400 = 0



2 {p}^{2} + 1200 {p}^{3} - 400000p - 240000000 = 0



The real roots of this polynomial equation are:



p = - 118.26 \: p = 96.24



Since price can not be negative, we discard the negative value ,


p = 96.24


The correct answer for question 16 is C.



QUESTION 17



We were given the solution to this polynomial as



x=2,x=-4, x=1+3i



We need to recognize the presence of the complex root and treat it nicely.



There is one property about complex roots of polynomial equations called the complex conjugate property. According to this property, if


a + bi



is a solution to


p(x)


then the complex conjugate


a - bi


is also a root.



Since


x = 1 + 3i



is a solution then,



x = 1 - 3i


is also a solution.



Therefore we have



f(x) = (x - 2)(x + 4)(x - (1+3i))(x - (1 - 3i)



f(x) = ( {x}^{2} + 4x - 2x - 8)( {x}^{2} - (1 - 3i)x - (1 + 3i)x + (1 + 3i)(1 - 3i))



We expand to obtain,



( {x}^{2} + 4x - 2x - 8)( {x}^{2} - x + 3xi - x - 3xi + 1 + 9)


Note that:



{i}^{2} = - 1



f(x) = ( {x}^{2} + 2x - 8)( {x}^{2} - 2x + 10)



We now expand to obtain,



f(x) = {x}^{4} - 2 {x}^{3} + 10 {x}^{2} + 2 {x}^{3} - 4 {x }^{2} + 20x - 8 {x}^{2} + 16x - 80



We simplify further to obtain,



f(x) = {x}^{4} + 2 {x}^{2} + 36x - 80



The correct answer for question 17 is A.



QUESTION 18



If



-2i


is a zero of the polynomial,



f(x)=x^4-45x^2-196



then the complex conjugate



2i



is also a zero,



This means that ,


(x+2i), (x-2i)



are factors of the polynomial.



The product of these two factors,



(x+2i), (x-2i) =x^2-(2i)^2=x^2+4



is also a factor , so we use it to divide and get the remaining factors.



see diagram for long division.



The above polynomial can therefore factored completely as,



f(x)=(x^2+4)(x^2-49)



Applying our knowledge from difference of two squares, we obtain,



f(x)=(x+2i)(x-2i))(x-7)(x+7)



Hence all the zeroes of these polynomial can be found by setting



(x+2i)(x-2i))(x-7)(x+7)=0


This implies,



x=-2i,x=2i,x=7,x=-7



The correct answer for question 18 is B



QUESTION 19



We were asked to find the horizontal and vertical asymptote of



f(x)=\frac{2x^2+1}{x^2-1}



To find the horizontal asymptote, divide the term with the highest degree in the numerator by the term with the highest degree in the denominators. That is the horizontal asymptote is given by,



y=\frac{2x^2}{x^2}=2



For vertical asymptote, equate the denominator to zero and solve for x.



x^2-1=



\Rightarrow x=-1, x=1



None of the options is correct, so the correct answer for question 19 is A.



QUESTION 20



We are converting,



\frac{5\pi}{6}



to degrees .



To convert from radians to degrees, multiply by,



\frac{180\degree}{\pi}



That is,



\frac{5\pi}{6}=\frac{5\pi}{6} \times \frac{180\degree}{\pi}



We simplify to obtain,



\frac{5\pi}{6}=\frac{5}{1} \times \frac{180\degree}{1}=5\times30\degree =150\degree



The correct answer is B.



QUESTION 21



Recall the mnemonics, SOH CAH TOA



The sine ratio is given by,



\sin(B)=\frac{21}{75}=\frac{7}{25}



From the diagram,



\tan(B)=\frac{21}{72}=\frac{7}{24}



The correct answer is C.



QUESTION 22



From the above diagram, We can determine the value of x using the sine or cosine ratio, depending on where the 17 is placed.



Using the cosine ratio, we obtain,



\cos(58\degree)=\frac{17}{x}



We can simply switch positions to make x the subject.



x=\frac{17}{\cos(58\degree)}



x=\frac{17}{0.5299}



x=32.08



Hence the correct answer is A.



QUESTION 23



Coterminal angles have the same terminal sides.



To find coterminal angles, we keep adding or subtracting 360 degrees.



See diagram.



x=202\degree



is coterminal with



202\degree +360\degree =562\degree



or



202\degree -360\degree =-158\degree



The correct answer is D.



See the attached file for continuation.


16. photon lighting company determines that the supply and demand functions for its most popular lam
16. photon lighting company determines that the supply and demand functions for its most popular lam
16. photon lighting company determines that the supply and demand functions for its most popular lam
16. photon lighting company determines that the supply and demand functions for its most popular lam
16. photon lighting company determines that the supply and demand functions for its most popular lam
Mathematics
Step-by-step answer
P Answered by PhD

QUESTION 16



If the demand and supply are equal, then we equate the two functions in p and solve for p.



That is



S(p)=D(p)


400 - 4p + + 0.00002 {p}^{4} = 2800 - 0.0012 {p}^{3}



We can rearrange to obtain,



0.00002 {x}^{4} + 0.0012 {x}^{3} - 4x - 2400 = 0



2 {p}^{2} + 1200 {p}^{3} - 400000p - 240000000 = 0



The real roots of this polynomial equation are:



p = - 118.26 \: p = 96.24



Since price can not be negative, we discard the negative value ,


p = 96.24


The correct answer for question 16 is C.



QUESTION 17



We were given the solution to this polynomial as



x=2,x=-4, x=1+3i



We need to recognize the presence of the complex root and treat it nicely.



There is one property about complex roots of polynomial equations called the complex conjugate property. According to this property, if


a + bi



is a solution to


p(x)


then the complex conjugate


a - bi


is also a root.



Since


x = 1 + 3i



is a solution then,



x = 1 - 3i


is also a solution.



Therefore we have



f(x) = (x - 2)(x + 4)(x - (1+3i))(x - (1 - 3i)



f(x) = ( {x}^{2} + 4x - 2x - 8)( {x}^{2} - (1 - 3i)x - (1 + 3i)x + (1 + 3i)(1 - 3i))



We expand to obtain,



( {x}^{2} + 4x - 2x - 8)( {x}^{2} - x + 3xi - x - 3xi + 1 + 9)


Note that:



{i}^{2} = - 1



f(x) = ( {x}^{2} + 2x - 8)( {x}^{2} - 2x + 10)



We now expand to obtain,



f(x) = {x}^{4} - 2 {x}^{3} + 10 {x}^{2} + 2 {x}^{3} - 4 {x }^{2} + 20x - 8 {x}^{2} + 16x - 80



We simplify further to obtain,



f(x) = {x}^{4} + 2 {x}^{2} + 36x - 80



The correct answer for question 17 is A.



QUESTION 18



If



-2i


is a zero of the polynomial,



f(x)=x^4-45x^2-196



then the complex conjugate



2i



is also a zero,



This means that ,


(x+2i), (x-2i)



are factors of the polynomial.



The product of these two factors,



(x+2i), (x-2i) =x^2-(2i)^2=x^2+4



is also a factor , so we use it to divide and get the remaining factors.



see diagram for long division.



The above polynomial can therefore factored completely as,



f(x)=(x^2+4)(x^2-49)



Applying our knowledge from difference of two squares, we obtain,



f(x)=(x+2i)(x-2i))(x-7)(x+7)



Hence all the zeroes of these polynomial can be found by setting



(x+2i)(x-2i))(x-7)(x+7)=0


This implies,



x=-2i,x=2i,x=7,x=-7



The correct answer for question 18 is B



QUESTION 19



We were asked to find the horizontal and vertical asymptote of



f(x)=\frac{2x^2+1}{x^2-1}



To find the horizontal asymptote, divide the term with the highest degree in the numerator by the term with the highest degree in the denominators. That is the horizontal asymptote is given by,



y=\frac{2x^2}{x^2}=2



For vertical asymptote, equate the denominator to zero and solve for x.



x^2-1=



\Rightarrow x=-1, x=1



None of the options is correct, so the correct answer for question 19 is A.



QUESTION 20



We are converting,



\frac{5\pi}{6}



to degrees .



To convert from radians to degrees, multiply by,



\frac{180\degree}{\pi}



That is,



\frac{5\pi}{6}=\frac{5\pi}{6} \times \frac{180\degree}{\pi}



We simplify to obtain,



\frac{5\pi}{6}=\frac{5}{1} \times \frac{180\degree}{1}=5\times30\degree =150\degree



The correct answer is B.



QUESTION 21



Recall the mnemonics, SOH CAH TOA



The sine ratio is given by,



\sin(B)=\frac{21}{75}=\frac{7}{25}



From the diagram,



\tan(B)=\frac{21}{72}=\frac{7}{24}



The correct answer is C.



QUESTION 22



From the above diagram, We can determine the value of x using the sine or cosine ratio, depending on where the 17 is placed.



Using the cosine ratio, we obtain,



\cos(58\degree)=\frac{17}{x}



We can simply switch positions to make x the subject.



x=\frac{17}{\cos(58\degree)}



x=\frac{17}{0.5299}



x=32.08



Hence the correct answer is A.



QUESTION 23



Coterminal angles have the same terminal sides.



To find coterminal angles, we keep adding or subtracting 360 degrees.



See diagram.



x=202\degree



is coterminal with



202\degree +360\degree =562\degree



or



202\degree -360\degree =-158\degree



The correct answer is D.



See the attached file for continuation.


16. photon lighting company determines that the supply and demand functions for its most popular lam
16. photon lighting company determines that the supply and demand functions for its most popular lam
16. photon lighting company determines that the supply and demand functions for its most popular lam
16. photon lighting company determines that the supply and demand functions for its most popular lam
16. photon lighting company determines that the supply and demand functions for its most popular lam
Mathematics
Step-by-step answer
P Answered by Specialist

Step-by-step explanation:

Part A

A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.

Graph the function g(x) = x3 − x2 − 4x + 4. See attached picture.

It has x-intercepts at (-2,0), (1,0) and (2,0). The y-intercept is (0,4). As x-> -∞ then y -> -∞. As x->∞, y->∞.

Part B

Use the quadratic function f(x) = -x^2 - 6x. The parabola faces downward with y -intercept (-3,9) and zeros (-6,0) and (0,0). See the attached graph.

The axis of symmetry will serve as a ladder through the coaster at x = -3.

Part C and D will use the math above to create the coaster and ad campaign.

Mathematics
Step-by-step answer
P Answered by Master

Step-by-step explanation:

Part A

A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.

Graph the function g(x) = x3 − x2 − 4x + 4. See attached picture.

It has x-intercepts at (-2,0), (1,0) and (2,0). The y-intercept is (0,4). As x-> -∞ then y -> -∞. As x->∞, y->∞.

Part B

Use the quadratic function f(x) = -x^2 - 6x. The parabola faces downward with y -intercept (-3,9) and zeros (-6,0) and (0,0). See the attached graph.

The axis of symmetry will serve as a ladder through the coaster at x = -3.

Part C and D will use the math above to create the coaster and ad campaign.

Mathematics
Step-by-step answer
P Answered by Master

See below.

Step-by-step explanation:

Part A

A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.

Graph the function g(x) = x3 − x2 − 4x + 4. See attached picture.

It has x-intercepts at (-2,0), (1,0) and (2,0). The y-intercept is (0,4). As x-> -∞ then y -> -∞. As x->∞, y->∞.

Part B

Use the quadratic function f(x) = -x^2 - 6x. The parabola faces downward with y -intercept (-3,9) and zeros (-6,0) and (0,0). See the attached graph.

The axis of symmetry will serve as a ladder through the coaster at x = -3.

Part C and D will need to be using the math above to create the coaster and ad campaign.


Roller coaster crewray and kelsey have summer internships at an engineering firm. as part of their i
Roller coaster crewray and kelsey have summer internships at an engineering firm. as part of their i
Mathematics
Step-by-step answer
P Answered by Specialist

See below.

Step-by-step explanation:

Part A

A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.

Graph the function g(x) = x3 − x2 − 4x + 4. See attached picture.

It has x-intercepts at (-2,0), (1,0) and (2,0). The y-intercept is (0,4). As x-> -∞ then y -> -∞. As x->∞, y->∞.

Part B

Use the quadratic function f(x) = -x^2 - 6x. The parabola faces downward with y -intercept (-3,9) and zeros (-6,0) and (0,0). See the attached graph.

The axis of symmetry will serve as a ladder through the coaster at x = -3.

Part C and D will need to be using the math above to create the coaster and ad campaign.


Roller coaster crew ray and kelsey have summer internships at an engineering firm. as part of their
Roller coaster crew ray and kelsey have summer internships at an engineering firm. as part of their
Mathematics
Step-by-step answer
P Answered by Master

Part A) Kesley is correct

Part B) g'(x)=3x2-2x-4

Part C) Graph attached

Part D) Explained

Step-by-step explanation:

Part A)

Kelsey is correct because no. of 0s in a 3rd degree polynomial be 3. which means the no. of intercepts will be 3. Thus Ray is incorrect as no. of 0s and x-intercept are similar thing.

Further a graph is attached of g(x) = x3 − x2 − 4x + 4 to describe the key features of g(x), including the end behavior. We can see that there are 3 x-intercepts at (2,0), (1,0) and (-2,0) which validates the point of Kelsey that the function can have as many as 3 zeros only because it is 3rd degree polynomial.

Part B)

As the second part of the new coaster is a parabola. To create a unique parabola in the pattern f(x) = ax2 + bx + c

finding derivative of g(x) picked in Part A) i.e.

g(x) = x3 − x2 − 4x + 4

g'(x)=3x2-2x-4

Graph of above is also attache.

From the graph we can see that its downwards directed parabola having vertex at (0.33, -4.33)

x-intercept at -0.87 and 1.53

y-intercept at (0,-4)

The axis of symmetry equation is a vertical line around which the parabola is symmetric is  given by equation of a vertical line that passes through the vertex i.e. x=0.33

Part C)

Graph 3 is also attached.

Part D)

For a 15 seconds ad campaign, following features can be included:

Roller coaster that have a three rise

two sharp dips

the 2nd dip goes more deeper than the first one!


90 points i need  asap on everything but part a (will give brainliest) roller coaster crew ray and k
Mathematics
Step-by-step answer
P Answered by Master

The process of obtaining the equation is similar, but it is more algebraically intensive. Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)^2 / (m^2 +1) = (x - h)^2 + (y - k)^2.

1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.

2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.

3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.

These three main forms that we graph parabolas from are called standard form, intercept form and vertex form. Each form will give you slightly different information and have its own unique advantages and disadvantages.

Mathematics
Step-by-step answer
P Answered by PhD
Both of them can be correct because a third degree polynomial can have upto three x-intercepts and a y-intercept.

For g(x) = x^3 - x^2 - 4x + 4
the zeros are 2, -2 and 1

The vertex of a parabola is the point at which the parabola turns. A parabola is maximum when the coeficient of the leading term is negative and is manimum when it is positive.

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