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)
Y = number of songs she can still download
y + 8 ≤ 11
- 8 -8
------------
y ≤ 3
She can only download 3 more songs
Answer:
4 * f + g = 6g
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
Answer:
![\displaystyle x = \frac{216}{7}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B216%7D%7B7%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define</u>
<u />
<u />
<u />
<u>Step 2: Solve for </u><em><u>x</u></em>
- Cross-multiply:
![\displaystyle 6(2x - 2) = 19(x - 12)](https://tex.z-dn.net/?f=%5Cdisplaystyle%206%282x%20-%202%29%20%3D%2019%28x%20-%2012%29)
- Distribute:
![\displaystyle 12x - 12 = 19x - 228](https://tex.z-dn.net/?f=%5Cdisplaystyle%2012x%20-%2012%20%3D%2019x%20-%20228)
- Isolate <em>x</em> terms:
![\displaystyle -12 = 7x - 228](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-12%20%3D%207x%20-%20228)
- Isolate <em>x</em> term:
![\displaystyle 216 = 7x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20216%20%3D%207x)
- Isolate <em>x</em>:
![\displaystyle \frac{216}{7} = x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B216%7D%7B7%7D%20%3D%20x)
- Rewrite:
![\displaystyle x = \frac{216}{7}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%20%5Cfrac%7B216%7D%7B7%7D)
Y = 3/5 x - 5
slope = 3/5
y-intercept = -5