anonymous
  • anonymous
Part A:The area of a square is (4x2 − 12x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (16x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@Mackenzie_Willa
anonymous
  • anonymous
@welshfella
anonymous
  • anonymous
I have the answer just not the steps! Part A:(2x -3)^2 Part B:(4x+3y)(4x−3y)

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anonymous
  • anonymous
@Nnesha
amilapsn
  • amilapsn
Do you know these? \[a^2-b^2=(a-b)(a+b) \\ (a+b)^2=a^2+2ab+b^2\]
anonymous
  • anonymous
Because the first shape is a square, the length and the width must be the same. So the area must be a perfect square. We need to find an expression that , when multiplied by itself, will give \(4x^2-12x+9\)Start by taking the square roots of the first and last coefficients. Can you do that?
anonymous
  • anonymous
Can you help me work it ut step by step plz
anonymous
  • anonymous
*out
anonymous
  • anonymous
What is the square root of the first term, \(4x^2\)?
anonymous
  • anonymous
2x^2?
anonymous
  • anonymous
Not quite. The square of 4 is 2, so you got that part right, but what is the square root of x^2? What can you multiply by itself to give x^2?
anonymous
  • anonymous
*square root of 4
anonymous
  • anonymous
I am confused
anonymous
  • anonymous
Do you understand that\[x \times x = x^2\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
OK. So the square root of \(x^2\) is \(x\). OK with that?
anonymous
  • anonymous
oh okay.
anonymous
  • anonymous
All right. So the square root of \(4x^2\) is \(2x\). In other words\[2x \times 2x = 4x^2\]Make sense now?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
OK. So now you need the square root of the last term, +9. What is it?
anonymous
  • anonymous
3
anonymous
  • anonymous
Great. With these two square roots, you have determined that the two factors must be\[4x^2-12x+9 = \left( 2x \text{ ? }3 \right)\left( 2x \text{ ? }3 \right)\]All that is left is to choose the correct sign, plus or minus. For that, look at the second term in the given trinomial. What sign does it have?
anonymous
  • anonymous
Minus.
anonymous
  • anonymous
Perfect. Then that is the sign you use in the factors. Therefore,\[4x^2-12x+9 = \left( 2x-3 \right)\left( 2x-3 \right)\]and you have your answer.
anonymous
  • anonymous
Keep in mind that this technique only works for factoring a perfect square trinomial.
anonymous
  • anonymous
Are these the answers. I have been working them out too: Part A) 4x2 − 12x + 9 4x^2 -6x -6x + 9 2x( 2x - 3) -3(2x - 3) (2x - 3)(2x-3) length of each side is 2x-3 Part B) 16x^2 − 9y^2 (4x)^2 - (3y)^2 (4x - 3y) (4x+3y) dimensions are 4x-3y, 4x+3y.
anonymous
  • anonymous
Yes, you are correct. Very well done!
anonymous
  • anonymous
Thank you!
anonymous
  • anonymous
You're welcome.
anonymous
  • anonymous
@ospreytriple can you help with 1 more?
anonymous
  • anonymous
An expression is shown below: f(x) = –16x2 + 60x + 16 Part A: What are the x-intercepts of the graph of the f(x)? Show your work. (2 points) Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points) Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
anonymous
  • anonymous
Part A: To find the x-intercepts, you must solve the equation \(-16x^2+60x+16=0\). Which method would you use; factoring by completing the square, or the quadratic formula?
anonymous
  • anonymous
quadratic formula?
anonymous
  • anonymous
OK. Go ahead. What do you get?
anonymous
  • anonymous
Can you refresh me on the formula.
anonymous
  • anonymous
For the general quadratic, \(ax^2 + bx + c=0\), the x-intercepts are found using\[x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]
anonymous
  • anonymous
can you help me through this one
anonymous
  • anonymous
I am really confused.
anonymous
  • anonymous
Have you used the quadratic formula before?
anonymous
  • anonymous
Just learning it.
anonymous
  • anonymous
OK. I'll help you set it up.
anonymous
  • anonymous
Okay thank you! I do have 1 request can you say like part a and like part b and part c because i will get confused and don't know what to say.
anonymous
  • anonymous
This is for Part A. If you look at the given trinomial and compare it with the general quadratic, you'll see that \(a=-16\), \(b=60\) and \(c=16\). Putting these values into the quadratic formula, you have\[x=\frac{ -b \pm \sqrt{b^2-4ac} }{2a } = \frac{ -60 \pm \sqrt{60^2-4\left( -16 \right)\left( 16 \right)} }{ 2\left( -16 \right) }\]Can you complete these calculations?
anonymous
  • anonymous
is it -5?
anonymous
  • anonymous
One second. I'm working it out...
anonymous
  • anonymous
okay ;]
anonymous
  • anonymous
Wait is it... x = 4 and x = -1/4.
anonymous
  • anonymous
Yayyyy! You got it. Those are the x-intercepts, \(x=4\) and \(x=-\frac{1}{4}\)
anonymous
  • anonymous
Yay :V. can you help with part B and C too?
anonymous
  • anonymous
Part B: Vertex a maximum or minimum? What it means is, is the parabola opening upward or downward? If the parabola opens upward, then the vertex is a minimum. If the parabola opens downward, then the vertex is a maximum.|dw:1440091745676:dw| Do you know how to tell which direction the parabola opens?
anonymous
  • anonymous
These are my answers so far are they correct? Part A.) f(x) = –16x^2 + 60x + 16 -4(x-4)(x+1/4) x-4=0 x+1/4=0 x=4 and x=-1/4 Part B.) vertex (15/8, 289/4) it is a maximum because the coeffficient of x^2 is -16 which is negative Part C.) You can graph the x intercepts and the vertex. That will give you the overall shape of the function.
anonymous
  • anonymous
OK. That saves me a lot of work. Hope I'm not wasting your time. I see in Part A you factored instead of using the quadratic formula. Parts B & C are correct. Good job>
anonymous
  • anonymous
Part c is correct?
anonymous
  • anonymous
Yes.
anonymous
  • anonymous
Oh. I wrote that down for notes rofl
anonymous
  • anonymous
Thank you!
anonymous
  • anonymous
You're welcome

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