Answer:
z in terms of x is ![\mathbf{z=16\left(\frac{x+5}{2}\right)^3}](https://tex.z-dn.net/?f=%5Cmathbf%7Bz%3D16%5Cleft%28%5Cfrac%7Bx%2B5%7D%7B2%7D%5Cright%29%5E3%7D)
Step-by-step explanation:
We are given:
![x=2y-5\: and\: z=16y^3](https://tex.z-dn.net/?f=x%3D2y-5%5C%3A%20and%5C%3A%20z%3D16y%5E3)
We need to find z in terms of x
First we can find value of y from x =2y-5
![x =2y-5\\x+5 = 2y\\y=\frac{x+5}{2}](https://tex.z-dn.net/?f=x%20%3D2y-5%5C%5Cx%2B5%20%3D%202y%5C%5Cy%3D%5Cfrac%7Bx%2B5%7D%7B2%7D)
Now, we can put value of y in
to find z in terms of x
![z=16y^3\\Put\:y=\frac{x+5}{2}\\z=16(\frac {x+5}{2})^3](https://tex.z-dn.net/?f=z%3D16y%5E3%5C%5CPut%5C%3Ay%3D%5Cfrac%7Bx%2B5%7D%7B2%7D%5C%5Cz%3D16%28%5Cfrac%20%7Bx%2B5%7D%7B2%7D%29%5E3)
So, z in terms of x is ![\mathbf{z=16\left(\frac{x+5}{2}\right)^3}](https://tex.z-dn.net/?f=%5Cmathbf%7Bz%3D16%5Cleft%28%5Cfrac%7Bx%2B5%7D%7B2%7D%5Cright%29%5E3%7D)
Answer:
10 pencils for $4.00 is better.
Step-by-step explanation:
If you divide 4.00 by 10 you'll find that each pencil is worth 40 cents. When you divide 2.70 by 6 then each pencil is worth 45 cents paying more for each pencil than the other deal.
Answer: ![r^\frac{1}{4}](https://tex.z-dn.net/?f=r%5E%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
![\sqrt[44]{\frac{r^5}{r^-^6} }](https://tex.z-dn.net/?f=%5Csqrt%5B44%5D%7B%5Cfrac%7Br%5E5%7D%7Br%5E-%5E6%7D%20%7D)
When dividing by the same base (r) subtract exponents.
![\sqrt[44]{r^5^-^(^-^6^)}](https://tex.z-dn.net/?f=%5Csqrt%5B44%5D%7Br%5E5%5E-%5E%28%5E-%5E6%5E%29%7D)
![\sqrt[44]{r^5^+^6}](https://tex.z-dn.net/?f=%5Csqrt%5B44%5D%7Br%5E5%5E%2B%5E6%7D)
![\sqrt[44]{r^1^1}](https://tex.z-dn.net/?f=%5Csqrt%5B44%5D%7Br%5E1%5E1%7D)
A property of the roots say:
![\sqrt[n]{x^m}=x^\frac{m}{n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5Em%7D%3Dx%5E%5Cfrac%7Bm%7D%7Bn%7D)
Therefore;
![\sqrt[44]{r^1^1}=r^\frac{11}{44}=r^\frac{1}{4}](https://tex.z-dn.net/?f=%5Csqrt%5B44%5D%7Br%5E1%5E1%7D%3Dr%5E%5Cfrac%7B11%7D%7B44%7D%3Dr%5E%5Cfrac%7B1%7D%7B4%7D)
The year, where the number of cars sold exceed 46,000 is 13496
<h3>How to determine the year?</h3>
The equation of the function is given as:
y = 4x + 2
When the sales exceed 46000;
It means that y > 46000
So, we have:
4x + 2 > 46000
Subtract 2 from both sides
4x > 45998
Divide both sides by 4
x > 11499.5
The year is then calculated as:
Year = 1996 + x
So, we have:
Year > 1996 + 11499.5
Evaluate
Year > 13495.5
Approximate
y > 13496
Hence; the year, where the number of cars sold exceed 46,000 is 13496
Read more about linear equations at:
brainly.com/question/14323743
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