What are the zeros of (x-2)(x^2-9)

Answers

Answer 1

Answer: So because the factors of the equation are (x-2), (x+3) and (x-3), you set them equal to zero and you get x=2, -3, and 3

Answer 2

Answer:    (x - 2)(x² - 9) = 0
      (x - 2)(x² + 3x - 3x - 9) = 0
(x - 2)(x(x) + x(3) - 3(x) - 3(3)) = 0
   (x - 2)(x - 3)(x + 3) = 0
x - 2 = 0 or x - 3 = 0 or x + 3 = 0
+ 2 + 2    + 3 + 3 - 3 - 3
   x = 2    x = 3    x = -3

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Cory’s average score after 8 tests is 91%. If he gets a 78% on his 9th test what will his new average be?

Answers

The new average will be 89.55%.

What is an average?

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

It is given that,

Average score after 8 tests = 91%.

Therefore, Total score of 8 tests = Average score*Number of tests

Total score of 8 tests = 91*8

Total score of 8 tests = 728

Now, Cory scored 78% in 9th test,

So, Total score of 9 tests = Total score of 8 tests + 78

Total score of 9 tests = 728 + 78

Total score of 9 tests = 806

Hence, Average score of 9 test = Total score of 9 tests/9

Average score of 9 test = 806/9

⇒ Average score of 9 test = 89.55%

Hence, the new average will be 89.55%.

More about average :

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add all the scores together and the divided by the number of scores there are

8 tests will be 8x91 = 728

Then add on his latest test result 728+78 = 806

Now divide by the number of tests (9) 806/9 = 89.55555555
89.555%

Prove-: sin5A = 5cos^4 A sinA - 10cos^2 A sin^3 A + sin^5 A

Answers

$A=x\n\nsin5x=5cos^4xsinx-10cos^2xsin^3x+sin^5x\n\nL=sin(3x+2x)=sin3xcos2x+sin2xcos3x=(*)\n-------------------------------\nsin3x=sin(2x+x)=sin2xcosx+sinxcos2x\n=2sinxcosxcosx+sinx(cos^2x-sin^2x)\n=2sinxcos^2x+sinxcos^2x-sin^3x=3sinxcos^2x-sin^3x\n-------------------------------$

$sin3xcos2x=(3sinxcos^2x-sin^3x)(cos^2x-sin^2x)\n=3sinxcos^4x-3sin^3xcos^2x-sin^3xcos^2x+sin^5x\n=3sinxcos^4x-4sin^3xcos^2x+sin^5x\n-------------------------------$

$cos3x=cos(2x+x)=cos2xcosx-sin2xsinx\n=cosx(cos^2x-sin^2x)-2sinxcosxsinx\n=cos^3x-sin^2xcosx-2sin^2xcosx=cos^3x-3sin^2xcosx\n-------------------------------$

$sin2xcos3x=2sinxcosx(cos^3x-3sin^2xcosx)\n=2sinxcos^4x-6sin^3xcos^2x\n-------------------------------$

$(*)=3sinxcos^4x-4sin^3xcos^2x+sin^5x+2sinxcos^4x-6sin^3xcos^2x\n\n=5sinxcos^4x-10sin^3xcos^2x+sin^5x=R$

$=======================================\n\nsin(\alpha+\beta)=sin\alpha cos\beta+sin\beta cos\alpha\n\ncos(\alpha+\beta)=cos\alpha cos\beta-sin\alpha sin\beta\n\nsin2\alpha=2sin\alpha cos\alpha\n\ncos\alpha=cos^2\alpha-sin^2\alpha$

According to the Tristate Transportation Authority, making certain improvements to the main commuter rail line would increase ridership dramatically. The authority plans to finance these improvements over the course of five years by raising automobile tolls on the two high-way bridges along the route the rail line serves. Although the proposed improvements are indeed needed, the authority’s plan for securing the necessary funds should be rejected because it would unfairly force drivers to absorb the entire cost of something from which they receive no benefit.Which of the following, if true, would cast the most doubt on the effectiveness of the authority’s plan to finance the proposed improvements by increasing bridge tolls?

(A) Before the authority increases tolls on any of the area bridges, it is required by law to hold public hearings at which objections to the proposed increase can be raised.

(B) Whenever bridge tolls are increased, the authority must pay a private contractor to adjust the automated toll-collecting machines.

(C) Between the time a proposed toll increase is announced and the time the increase is actually put into effect, many commuters buy more tokens than usual to postpone the effects of the increase.

(D) When tolls were last increased on the two bridges in question, almost 20 percent of the regular commuter traffic switched to a slightly longer alternative route that has since been improved.

(E) The chairman of the authority is a member of the Tristate Automobile Club that has registered strong opposition to the proposed toll increase.

Answers

Answer:

Options A and B are true

(A) Before the authority increases tolls on any of the area bridges, it is required by law to hold public hearings at which objections to the proposed increase can be raised.

B. (B) Whenever bridge tolls are increased, the authority must pay a private contractor to adjust the automated toll-collecting machines.

Step-by-step explanation:

A. In a developed society, it's imperative for the authority to hold public hearings with stake holders to air their views before the tolls are increased, this would enable the authority to carry out proper assessment to know both the positive and negative impact of increasing the toll.

B. Increasing the tolls implies that there must be adjustment in the automated tolling machines and this would incur cost on the authority, this contract would be executed by private contractors.

Please helpThese are Honors Geometry problems that I don't understand. Please explain how you got your answers and show you work so I can understand what to do

Please don't erase any answers. I really need help

Answers

First we know that a circle is 360 degrees. From the center of the pentagon if you draw a segment to each point M N P Q R, you create 5 triangles from the center. So 360/5 = 72 degrees. Each 'turn' from letter to letter is a 72degree rotation about the center O.
Moving N 72 degrees maps it onto M. Moving N 144 degrees maps it onto P. Mapping P to Q would be a 72 degree rotation since they are one rotation away from each other. I hope you understand.

Find the surface area and volume of a cube with sides of 5.5 cm each.

Answers

Answer:

$V= 166.375cm^3$ and $As = 181.5cm^2.$

Step-by-step explanation:

First, let's calculate the volume. The volume of a cube is $V= s^3$ where s is the side. Then,

$V = (5.5cm)^3 = 166.375cm^3$

Now, the surface area will be the sum of the areas of each face. Each face of the cube is a square and the area of a square is $A=s^2$ , also we know that the cube has 6 faces, then the surface area of the cube will be

$As = 6*s^2$ , so

$As = 6*(5.5cm)^2$

$As = 6*30.25cm^2$

$As = 181.5cm^2.$

The equation to find the surface area of a cube is: 2*base+lateral area. The base of a cube is just the area of the square. So you would multiply 5.5*5.5. That would equal 30.25
The equation to find the lateral area is: perimeter*height. So you would add 5.5 four times since its a square. It would equal 22. Then you would multiply it by the height of which is also 5.5. 5.5*22=121.

Now that you have all the information just plug it back in the equation.(side note, because cubes are prisms you have two bases which is why you multiply them by two.) 2*30.25+121=181.5

your awnser is 185.5cm squared

HELP ME ASP I NEED A GOOD GRADE ON THIS.

Answers

Answer: Just follow the chart

Step-by-step explanation:

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