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sergey [27]
3 years ago
8

The area of a square can be represented by the trinomial 9x^2 - 54x + 81. Which of the following is the length of one side of th

e square?
*free response question
Mathematics
1 answer:
Mnenie [13.5K]3 years ago
3 0

Use\ (a-b)^2=a^2-2ab+b^2\\\\9x^2-54x+81=\underbrace{(3x)^2-2(3x)(9)+9^2}_{(*)}=(3x+9)^2\\\\\text{The formula of an area of a square with a side x:}\ A=x^2.\\\\\text{Therefore we have answer:}\ The\ length\ of\ side\ of\ the\ square\ is\ 3x+9.

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Which equation represents this situation?
Tatiana [17]
The answer would be h+(h+2.5)=22
The h represents Williams hours and the h+22 represents jose's hours. Together, they add to 22 hours :)
Hope this helps!
8 0
3 years ago
Read 2 more answers
The junior and senior students at Mathville High School are going to present an exciting musical entitled, "Math, What is it Goo
xeze [42]

Some parts are missing in the queston. Find attached the picture with the complete question

Answer:

                   \large\boxed{\large\boxed{161}}

Explanation:

Let's put the information in a table step-by step.

                                                (number of remaining students)

                                                        Juniors          Seniors

Condition

  • Initially                                           J                     S
  • 15 seniors left                                                   S - 15
  • Twice juniors as seniors         2(S - 15)
  • 3/4 of the juniors left              1/4×2(S - 15)
  • 1/3 of seniors left                                             2/3×(S - 15)

At the end, there were 8 more seniors than juniors:

  • 2/3×(S - 15) -  1/4×2(S - 15) = 8

Now you have obtained one equation, which you can solve to find S, the number of senior students, and then the number of junior students.

Solve the equation:

2/3\times (S - 15) -  1/4\times 2(S - 15) = 8

  • Mutilply all by 12:

8(S - 15)-6(S - 15)=96

  • Distribution property:

8S-120-6S-90=96

  • Addtion property of equalities:

8S-6S=96+120+90

  • Add like terms:

2S=306

  • Division property of equalities:

S=306/2=153

That is the number of senior students that came out to the information meeting, but the number of students remaining to perform in the school musical is (from the table above):

2/3\times (S-15)+1/4\times 2(S-15)

Just substitute S with 153 fo find the number of students that remained to perfom in the musical:

          2/3\times (153-15)+1/4\times 2(153-15)\\ \\ 2/3(138)+1/2(138)

          161

5 0
3 years ago
Suppose the circumference of a circle is 2pi what is its area?
soldi70 [24.7K]
Circumference=2πr
2π=2πr
r=1

area=πr^2
area=π(1)^2
area=π
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3 years ago
CAN SOMEONE PLEASE HELP ME PLEASE PLEASE!!!
Galina-37 [17]

Step-by-step explanation:

this is really simple : we only need to put the given x and y coordinate values into both equations and see, if both equations remain true.

(-2, -1) means x = -2, y = -1

first equation :

-1 = 3×-2 + 5 = -6 + 5 = -1

so, -1 = -1

true.

second equation :

-2 + -1 = -3

-3 = -3

true.

therefore, (-2, -1) is a solution to the linear system.

the point is the crossing point of both lines.

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2 years ago
Provide a possible situation that the graph shown could represent
ANTONII [103]
It depends on what the graph shows. I need to see the graph to help you. sorry
6 0
3 years ago
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