Answer: x = (sqrt(7) + 2)/3 and
x = ( – sqrt(7) + 2)/3
Explanation:
3x^2 - 4x - 1 = 0
Divide both sides by 3:
3x^2/3 - 4/3x - 1/3 = 0/3
x^2 - 4/3x - 1/3 = 0
x^2 - 4/3x = 1/3
x^2 - 4/3x + (2/3)^2 = 1/3 + (2/3)^2
(x - 2/3)^2 = 1/3 + 4/9
(x - 2/3)^2 = 7/9
Sqrt both sides:
x - 2/3 = sqrt (7/9)
x - 2/3 = |sqrt(7)/3|
Set x -2/3 = sqrt(7)/3
=> x = (sqrt(7) + 2)/3
Set x - 2/3 = - sqrt(7)/3
=> x = ( - sqrt(7) + 2)/3
Answer:
Price of each phone: 
Price of each accessory: 
Step-by-step explanation:
Let be "p" the price in dollars of each phone and "a" the price in dollars of each accessory.
Set up a system of equations:

You can use the Elimination Method to solve the system.
Multiply the second equation by -2 and add both equations:

Substitute the value of "a" into the first equation and solve for "p":

![\left[ \begin{matrix} 2 & a \\ -1 & -2 \end{matrix} \right] + \left[ \begin{matrix} b & 4 \\ -2 & 1 \end{matrix} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%202%20%26%20a%20%5C%5C%20-1%20%26%20-2%20%5Cend%7Bmatrix%7D%20%5Cright%5D%20%2B%20%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%20b%20%26%204%20%5C%5C%20-2%20%26%201%20%5Cend%7Bmatrix%7D%20%5Cright%5D)
This addition of matrices can be combined into one matrix.
To add matrices, add the corresponding components of each matrix.
After adding, we'll have the following
![\left[ \begin{matrix} 2+b & a+4 \\ -3 & -1 \end{matrix} \right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%202%2Bb%20%26%20a%2B4%20%5C%5C%20-3%20%26%20-1%20%5Cend%7Bmatrix%7D%20%5Cright%5D%20)
This matrix should be equal to the matrix on the right-hand side of the equation. This means that each corresponding component of this matrix and the other matrix should be equivalent.
This means that

AND

Solving these one-step equations will give the values of a = -4 and b = -1. That's answer choice D.
Answer:
68%
Step-by-step explanation:
We observe that the mean of the sample is (61+71)/2 = 66 mph which means the standard deviation of the sample is 5 because 66-5=61 and 66+5=71. The Empirical Rule states that for data observed in a normal distribution, 68% of data will fall within one standard deviation of the mean. Therefore, approximately 68% of vehicles travel between 61 miles per hour and 71 miles per hour.
1000 x 5 = 5000
Lana's dad would take about 5000 steps.
5000 x 2 = 10,000
Lana would take about 10,000 steps.
Glad I could help, and good luck!