Answer:
<h2>-5</h2>
Step-by-step explanation:
![A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] \\\\\det A=\left|\begin{array}{ccc}a&b\\c&d\end{array}\right|=ad-bc](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5Cdet%20A%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%7C%3Dad-bc)
![\left\{\begin{array}{ccc}x+2y=5\\x-3y=7\end{array}\right\\\\A=\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] \\\\\det A=A=\left|\begin{array}{ccc}1&2\\1&-3\end{array}\right|=(1)(-3)-(1)(2)=-3-2=-5](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B2y%3D5%5C%5Cx-3y%3D7%5Cend%7Barray%7D%5Cright%5C%5C%5C%5CA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%5C%5C1%26-3%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5Cdet%20A%3DA%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D1%262%5C%5C1%26-3%5Cend%7Barray%7D%5Cright%7C%3D%281%29%28-3%29-%281%29%282%29%3D-3-2%3D-5)
Answer:
m = 17.5
Step-by-step explanation:
Given 0.2m=3.5, we want to solve for m. This involves isolating m on the left side. To accomplish this, divide both sides by 0.2, obtaining:
m = 3.5/0.2, or m = 17.5
Constant rates are used to illustrate linear functions.
- The average rate of change is $9.0 per hour
- The function that models the table is:
![\mathbf{f(x) = 9x }](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%209x%20%7D)
- The amount earned in 7.5 hours is $67.5
<u>(a) The average rate of change</u>
This is calculated using:
![\mathbf{Rate = \frac{y_2 -y_1}{x_2 -x_1}}](https://tex.z-dn.net/?f=%5Cmathbf%7BRate%20%3D%20%5Cfrac%7By_2%20-y_1%7D%7Bx_2%20-x_1%7D%7D)
So, we have:
![\mathbf{Rate = \frac{31.5-22.50}{3.5 - 2.5}}](https://tex.z-dn.net/?f=%5Cmathbf%7BRate%20%3D%20%5Cfrac%7B31.5-22.50%7D%7B3.5%20-%202.5%7D%7D)
![\mathbf{Rate = \frac{9}{1.0}}](https://tex.z-dn.net/?f=%5Cmathbf%7BRate%20%3D%20%5Cfrac%7B9%7D%7B1.0%7D%7D)
![\mathbf{Rate = 9.0}](https://tex.z-dn.net/?f=%5Cmathbf%7BRate%20%3D%209.0%7D)
Hence, the average rate of change is $9.0 per hour
<u>(b) A function that models the table of values</u>
Let x represent hours, and y represent the earnings.
So, we have:
![\mathbf{y =m (x - x_1) + y_1}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3Dm%20%28x%20-%20x_1%29%20%2B%20y_1%7D)
Where:
m =Rate = 9.0
So, we have:
![\mathbf{y = 9(x - 2.5) + 22.5}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%209%28x%20-%202.5%29%20%2B%2022.5%7D)
Expand
![\mathbf{y = 9x - 22.5 + 22.5}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%209x%20-%2022.5%20%2B%2022.5%7D)
![\mathbf{y = 9x }](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%209x%20%7D)
Represent as a function
![\mathbf{f(x) = 9x }](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%209x%20%7D)
Hence, the function that models the table is: ![\mathbf{f(x) = 9x }](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%209x%20%7D)
<u>(c) Amount earned for 7.5 hours</u>
This means that x = 7.5
So, we have:
![\mathbf{f(7.5) = 9 \times 7.5 }](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%287.5%29%20%3D%209%20%5Ctimes%207.5%20%7D)
![\mathbf{f(7.5) = 67.5}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%287.5%29%20%3D%2067.5%7D)
Hence, the amount earned in 7.5 hours is $67.5
Read more about constant rates at:
brainly.com/question/23184115
Answer: ![x=-2.8](https://tex.z-dn.net/?f=x%3D-2.8)
Step-by-step explanation:
Given the following equation:
![0.7x+6=0.3(4x+6)-2x](https://tex.z-dn.net/?f=0.7x%2B6%3D0.3%284x%2B6%29-2x)
You can follow these steps in order to solve for "x" and find its value:
1. Apply Distributive property on the right side of the equation:
![0.7x+6=0.3(4x+6)-2x\\\\0.7x+6=1.2x+1.8-2x](https://tex.z-dn.net/?f=0.7x%2B6%3D0.3%284x%2B6%29-2x%5C%5C%5C%5C0.7x%2B6%3D1.2x%2B1.8-2x)
2. Subract
from both sides and add the like terms:
![0.7x+6-(0.7x)=1.2x+1.8-2x-(0.7x)\\\\6=-1.5x+1.8](https://tex.z-dn.net/?f=0.7x%2B6-%280.7x%29%3D1.2x%2B1.8-2x-%280.7x%29%5C%5C%5C%5C6%3D-1.5x%2B1.8)
3. Subtract 1.8 from both sides:
![6-(1.8)=-1.5x+1.8-(1.8)\\\\4.2=-1.5x](https://tex.z-dn.net/?f=6-%281.8%29%3D-1.5x%2B1.8-%281.8%29%5C%5C%5C%5C4.2%3D-1.5x)
4. Finally, divide both side of the equation by -1.5:
![\frac{4.2}{-1.5}=\frac{-1.5x}{-1.5}\\\\x=-2.8](https://tex.z-dn.net/?f=%5Cfrac%7B4.2%7D%7B-1.5%7D%3D%5Cfrac%7B-1.5x%7D%7B-1.5%7D%5C%5C%5C%5Cx%3D-2.8)
If you are saying the washer is 1/8" thick, then its volume is (1/8)(π/4 - π/16) = 3π/128 in^3
<span>Numerically, the volume is 0.07363 cubic inches
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!</span>