5,000. Four in under five therefore, it would be 5,000.
Answer:
D. There is no mistake.
Step-by-step explanation:
The following lines show the process of factorization by using common factor.
<u>Line 1:</u>
In line 1, the equation is given and is completely fine.
![y^{2}+8xy+2y+16x=0](https://tex.z-dn.net/?f=y%5E%7B2%7D%2B8xy%2B2y%2B16x%3D0)
The only thing missing was equate to zero, but the options below talk about correct factors only, therefore this can't be considered as a mistake and can be ignored completely.
<u>Line 2:</u>
In line 2, the terms are grouped, from which we can factor out common terms.
![(y^{2}+8xy)+(2y+16x)=0](https://tex.z-dn.net/?f=%28y%5E%7B2%7D%2B8xy%29%2B%282y%2B16x%29%3D0)
This is also fine.
<u>Line 3:</u>
In line 3, the common term y is taken out from group 1 and 2 from other group.
![y(y+8x)+2(y+8x)=0](https://tex.z-dn.net/?f=y%28y%2B8x%29%2B2%28y%2B8x%29%3D0)
which is exactly what is given in line 3.
<u>Line 4:</u>
In line 4 the common factors can be seen and easily split into 2 factors.
![(y+2)(y+8x)=0](https://tex.z-dn.net/?f=%28y%2B2%29%28y%2B8x%29%3D0)
which is exactly what is given in line 4.
Options:
A. The grouping is correct in line 2. So this option is does not hold.
B. Common factor was factored correctly from group 1. So this option does not hold.
C. Common factor was factored correctly from group 2. So this option does not hold.
D. There is no mistake. This is correct. Thus we choose this option as correct answer.
The right answer is: <em>The binomial expression 2w + 6 represents the length of the fish tank.</em>
Dylan has a fish tank, so we assume that this tank is a cube. In this way, the volume of the tank is given by this expression:
![V = w.h.l](https://tex.z-dn.net/?f=V%20%3D%20w.h.l)
Where:
h: height
w: width
l: length
We know the following things:
FIRST.<em> He knows its height, h, is one inch less than twice the width, w.</em>
This can be expressed as the following equation:
![h=2w-1](https://tex.z-dn.net/?f=h%3D2w-1)
SECOND. <em>The length, l, of the fish tank is seven inches longer than the height.</em>
We can express this statement as follows:
![l=h+7 \\ \\ \therefore l=2w-1+7 \\ \\ \therefore l=2w+6](https://tex.z-dn.net/?f=l%3Dh%2B7%20%5C%5C%20%5C%5C%20%5Ctherefore%20l%3D2w-1%2B7%20%5C%5C%20%5C%5C%20%5Ctherefore%20l%3D2w%2B6)
By substituting
in
:
![V=w.h.l \\ \\ \therefore V=w(2w-1)(2w+6) \\ \\ \therefore V=w(4w^2-12w-2w-6) \\ \\ \therefore \boxed{V=4w^3-14w^2-6w}](https://tex.z-dn.net/?f=V%3Dw.h.l%20%5C%5C%20%5C%5C%20%5Ctherefore%20V%3Dw%282w-1%29%282w%2B6%29%20%5C%5C%20%5C%5C%20%5Ctherefore%20V%3Dw%284w%5E2-12w-2w-6%29%20%5C%5C%20%5C%5C%20%5Ctherefore%20%5Cboxed%7BV%3D4w%5E3-14w%5E2-6w%7D)
3
7/2 or 3 1/2
9
12
You multiply the number on the top with whatever you are multiplying it with then divide by the number on the bottom
No it is not an acute angle triangle because it matters on the construction of the triangle