1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alexeev081 [22]
2 years ago
11

Part A: The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the a

rea expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (25x2 − 16y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Mathematics
1 answer:
Sladkaya [172]2 years ago
3 0

Answer:

Part A: The length of each side is 3x-2 units long.

Part B: The dimensions are 5x-4 and 5x+4 units long.

Step-by-step explanation:

Part A:

--> 9x^2-12x+4

--> Multiply 9 times 4 to see the factors of that product

--> 9 times4 = 36

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

Use the factor 6 and make it negative so -6

add another -6

Keep in mind that it is -6x

--> 9x^2-6x-6x+4

Separate the four terms into two different binomials

--> 9x^2-6x  and -6x+4

Factor the binomials

With 9x^2-6x you can factor a 3x

So it will 3x(3x-2)

Do the same thing with -6x+4

You can factor out a -2

-2(3x-2)

The reason you factor out a -2 and not 2 is because it has to be same so in this case it is (3x-2)

Take the two numbers that you factored and put them to make an expression so (3x-2)

--> (3x-2)(3x-2) or (3x-2)^2

3x-2 is the length of each side so it is 3x-2 units long

Part B:

-->25x^2-16y^2

Use the difference of squares

take the square root of 25x^2

that is 5x

take the square root of 16y^2

that is 4y

write it in this way (5x+4y)(5x-4y)

These are the dimensions of the rectangle

You might be interested in
Mechanics paper/Math (please helpp!!!)
sp2606 [1]

Answer:

  (i) 15 m, 6 m/s

  (ii) 90 m

Step-by-step explanation:

(i) For some acceleration (a) from rest, the distance covered (d) in time t is ...

  d = (1/2)at^2

The distance covered by Ben in the 5 seconds he is accelerating is ...

  d = (1/2)(1.2 m/s²)(5 s)² = 15 m

Of course, Ben's speed at that point is ...

  s = (1.2 m/s²)(5 s) = 6 m/s

__

(ii) When Ben has been walking 5 s, Alan has been walking 10 s, so Alan has covered (10 s)(4 m/s) = 40 m. Their distance difference of 40 -15 = 25 m is being made up at the rate of their speed differences: (6 m/s) -(4 m/s) = 2 m/s.

It will take (25 m)/(2 m/s) = 12.5 s additional time for Ben to catch Alan. In the 22.5 s that Alan has been walking before they meet, he will have walked ...

  (22.5 s)(4 m/s) = 90 m . . . the distance OP

4 0
3 years ago
A sofa is on sale for $283.80, which is
ikadub [295]
283.80 + 67% = 473.94
I believe that is it
4 0
3 years ago
Read 2 more answers
What fraction is equal to 66?
marysya [2.9K]
The fraction equal to .66 is <span>33⁄50</span> 

 
5 0
3 years ago
Read 2 more answers
On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviatio
DENIUS [597]

Answer:

Step-by-step explanation:

N(106,14²)

(calculated using excel, let me know if you were supposed to use a normal table) = 0.4715

85.34

Q1:96.56

Q3:115.44

IQR (which is Q3-Q1)= 115.44-96.56= 18.88

5 0
2 years ago
Which expression is rational? 6.27316543222718… square root of 2 square root of 14. square root of 49
iogann1982 [59]
A rational number<span> is any </span>number that can be expressed as the quotient or fraction. It is also a number that does not repeat and/or go on forever (ex. pi or <span>3.1415926535</span><span>)

Soo, the rational number is 
the √49 

√49 = 7 7 is a rational number, also a whole number as well, how bout that.</span>
8 0
3 years ago
Read 2 more answers
Other questions:
  • Help me please if you can
    12·1 answer
  • Find the equation of the tangent plane to (a) z = 4x 2 − y 2 + 2y at (−1, 2, 4)
    10·1 answer
  • The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much
    10·1 answer
  • Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either i
    15·2 answers
  • An amusment park sells 9 tickets for $12 and 12 tickets for $15 . Is this fair explain
    5·1 answer
  • 10m3 of air weigh 13 kg. Chapter Reference c How much does the air weigh in a room 4.2m long, 3.5m wide, and 2.6m high?
    11·1 answer
  • Select one of the factors of 4x^2 + 5x − 6
    5·2 answers
  • What is the difference between -6 and -3 on a number line?
    5·2 answers
  • Find the value x and write the property used here.
    7·2 answers
  • PLZ HeLP
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!