Respuesta :
Answer A is correct for both questions.
Step-by-step explanation:
The area of the rectangle is lengthxwidth. To find the length, we can divide the area by the width.
[tex]\frac{(4x^2-43x+63)}{(4x-7)}[/tex] is the equation.
We need to simplify it (or just divide). Since the coefficient of the area (on the x^2) is the same as that on the width, we know that that same coefficient on the length is 1.
This gets us to the basic frame (1x+/-y).
To find the value of y, we need to pay attention to the "-43x+63" and "-7" aspects of the area and width, respectively. To get "63," the "-7" was multiplied by the y — by dividing 63 by -7, we know that the value of y is -9 (the numbers both have to be negative to multiply to a positive number).
We are left with the length (x-9). Put together, this means (x-9)(4x-7) is the area. Multiplying, that makes (4x^2-7x-36x+63), or (4x^2-43x+63). Since this is the area given to us, we know our answer is correct. For this question, the answer is A.
*****
Divide [tex]9x^4-2-6x-x^2[/tex] by [tex]3x-1[/tex]. First, put the first equation in order by exponents. We get [tex]\frac{9x^4-x^2-6x-2}{3x-1}[/tex]. Since the exponent on the upper equation goes up to x^4, and we are dividing by a simple x, we know that the first exponent in our answer will be x^3. Since our coefficient needs to have a product of 9 when multiplied by 3, it is 3. The first part of our answer is [tex](3x^3)[/tex]. Since there is no exponent of 3 for x in the upper equation, and since the "x^2" that has to be the next term in the equation due to it being present in each answer choice, we know that it as to be a "+x^2" — the "3x^3 that result from the "-1" (in the lower equation) being multiplied by 3x^3 have to be cancelled out by a "-3x^3", and if the sign for the term "x^2" is negative, we end up with tw0 "3x^3" that add up to "6x^3" instead of cancelling each other out.
Now, we have [tex](3x^3-x^2)[/tex]. We can immediately rule out C. Moving on.
We now have [tex](3x-1)(3x^3+x^2)=9x^4-x^2[/tex]. We can rule out answer choice B because it is incomplete - we are missing the second part of the upper equation, "-6x-2." Both of the remaining answers include "-2" as the next term, whether with an x or without.
Honestly, I haven't done algebra in a few years — while I know there's a way to deduce the rest of the equation, let's solve the equation using the two remaining answer choices and see which one is correct.
A: [tex](3x-1)(3x^3+x^2-2-\frac{4}{3x-1} )[/tex]
[tex]=9x^4+3x^3-6x -3x^3-x^2+2-4[/tex] (FOIL) (3x-1 times [tex]-\frac{4}{3x-1}[/tex] = -4)
[tex]=9x^4+3x^3-3x^3-x^2-6x+2-4[/tex] (in order of exponents)
[tex]=9x^4-x^2-6x+2-4[/tex] (simplify)
[tex]=9x^4-x^2-6x-2[/tex] (simplify)
D: [tex](3x-1)(3x^3+x^2-2x-\frac{4}{3x-1} )[/tex]
[tex]=9x^4+3x^3-6x^2-\frac{4}{1} -3x^3-x^2+3x+\frac{4}{1}[/tex](FOIL)
[tex]=9x^4+3x^3-3x^3-7x^2-4+4[/tex] (in order of exponents)
[tex]=9x^4-7x^2[/tex] (simplify)
A is exactly the long fraction we started with ([tex]9x^4-2-6x-x^2[/tex]), just in a different order! This means that answer A, when multiplied by (3x-1), equals the same thing which, if divided by (3x-1), yields answer A. Because of the rules of multiplication/division (xy=z, z/x=y, z/y=z), this means that we have the proper set of numbers. Answer A is correct.
I hope this helps!!!!! Let me know if there's anything else I can help with :)
(a)The length of the rectangle will be (x-9).
(b) The answer obtained is [tex]B= 3x^3-x^2+2x-4[/tex].
What is the area?
The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
The length of the rectangle is found as;
[tex]\rm A = L \times B \\\\\ (4x^2 -43x+63)=(4x-7)(B) \\\\\ (4x-7)(x-9)=(4x-7)(B) \\\\ B=(x-9)[/tex]
Hence the length of the rectangle will be (x-9).
(b) The answer obtained is [tex]B= 3x^3-x^2+2x-4[/tex].
The given equation is to be divided by (3x-1)
[tex]\rm B= \frac{4x^2-43 x + 63 }{(3x-1)} \\\\ B=\frac{(3x+1)(x-1)(3x^2+2x+2)}{(3x-1)} \\\\ B= 3x^3-x^2+2x-4[/tex]
Hence the answer obtained is [tex]B= 3x^3-x^2+2x-4[/tex].
To learn more about the area refer to the link;
https://brainly.com/question/11952845
