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anonymous
 one year ago
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)
anonymous
 one year ago
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)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have the answer just not the steps! Part A:(2x 3)^2 Part B:(4x+3y)(4x−3y)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Do you know these? \[a^2b^2=(ab)(a+b) \\ (a+b)^2=a^2+2ab+b^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Because 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 \(4x^212x+9\)Start by taking the square roots of the first and last coefficients. Can you do that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you help me work it ut step by step plz

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the square root of the first term, \(4x^2\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not 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
 one year ago
Best ResponseYou've already chosen the best response.0Do you understand that\[x \times x = x^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. So the square root of \(x^2\) is \(x\). OK with that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0All right. So the square root of \(4x^2\) is \(2x\). In other words\[2x \times 2x = 4x^2\]Make sense now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. So now you need the square root of the last term, +9. What is it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great. With these two square roots, you have determined that the two factors must be\[4x^212x+9 = \left( 2x \text{ ? }3 \right)\left( 2x \text{ ? }3 \right)\]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
 one year ago
Best ResponseYou've already chosen the best response.0Perfect. Then that is the sign you use in the factors. Therefore,\[4x^212x+9 = \left( 2x3 \right)\left( 2x3 \right)\]and you have your answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Keep in mind that this technique only works for factoring a perfect square trinomial.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are 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)(2x3) length of each side is 2x3 Part B) 16x^2 − 9y^2 (4x)^2  (3y)^2 (4x  3y) (4x+3y) dimensions are 4x3y, 4x+3y.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, you are correct. Very well done!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ospreytriple can you help with 1 more?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0An expression is shown below: f(x) = –16x2 + 60x + 16 Part A: What are the xintercepts 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
 one year ago
Best ResponseYou've already chosen the best response.0Part A: To find the xintercepts, 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
 one year ago
Best ResponseYou've already chosen the best response.0OK. Go ahead. What do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you refresh me on the formula.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For the general quadratic, \(ax^2 + bx + c=0\), the xintercepts are found using\[x=\frac{ b \pm \sqrt{b^24ac} }{ 2a }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you help me through this one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am really confused.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Have you used the quadratic formula before?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. I'll help you set it up.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay 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
 one year ago
Best ResponseYou've already chosen the best response.0This 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\[x=\frac{ b \pm \sqrt{b^24ac} }{2a } = \frac{ 60 \pm \sqrt{60^24\left( 16 \right)\left( 16 \right)} }{ 2\left( 16 \right) }\]Can you complete these calculations?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0One second. I'm working it out...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait is it... x = 4 and x = 1/4.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yayyyy! You got it. Those are the xintercepts, \(x=4\) and \(x=\frac{1}{4}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yay :V. can you help with part B and C too?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Part 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
 one year ago
Best ResponseYou've already chosen the best response.0These are my answers so far are they correct? Part A.) f(x) = –16x^2 + 60x + 16 4(x4)(x+1/4) x4=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
 one year ago
Best ResponseYou've already chosen the best response.0OK. 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
 one year ago
Best ResponseYou've already chosen the best response.0Oh. I wrote that down for notes rofl
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