Answer:
30
Step-by-step explanation:
To find the determinant of a parallelogram given points (a, b), (c, d), and (e, f), we can use
and calculate the determinant of that. Three points on the parallelogram are (-1,1), (-1, -5), and (4, 5). Plugging these into the matrix, we get
. The determinant is equal to
![-1 *det \left[\begin{array}{ccc}-5&1\\5&1\end{array}\right] \\- 1 * det \left[\begin{array}{ccc}-1&1\\4&1\end{array}\right] \\\\+ 1 * det \left[\begin{array}{ccc}-1&-5\\4&5\end{array}\right] \\= -1 * (-5*1 - (1*5))- 1 * (-1 * 1 - (4*1)) + 1 * (-1 * 5 - (-5*4)) \\= -1 *(-5-5) -1 * (-1 - 4) + 1 * (-5 - (-20))\\= -1 * (-10) -1 * (-5) +1 * (15)\\= 10 + 5 + 15\\=30](https://tex.z-dn.net/?f=-1%20%2Adet%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%261%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C-%201%20%2A%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%261%5C%5C4%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%2B%201%20%2A%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-5%5C%5C4%265%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D%20-1%20%2A%20%28-5%2A1%20-%20%281%2A5%29%29-%201%20%2A%20%28-1%20%2A%201%20-%20%284%2A1%29%29%20%2B%201%20%2A%20%28-1%20%2A%205%20-%20%28-5%2A4%29%29%20%5C%5C%3D%20-1%20%2A%28-5-5%29%20-1%20%2A%20%28-1%20-%204%29%20%2B%201%20%2A%20%28-5%20-%20%28-20%29%29%5C%5C%3D%20-1%20%2A%20%28-10%29%20-1%20%2A%20%28-5%29%20%2B1%20%2A%20%2815%29%5C%5C%3D%2010%20%2B%205%20%2B%2015%5C%5C%3D30)
Answer:
m = 4
Step-by-step explanation:
The complete question is:
Given:
6.33 x 10
⁹ / 1.79 x 10⁵ ≈ 3 x 
To find:
To best estimate the quotient in scientific notation. what number should replace m?
Solution:
The equation is:
6.33 x 10
⁹ / 1.79 x 10⁵ = 3 x 
Let x = 9 and y = 5 then the above equation becomes:
6.33 x
/ 1.79 x
= 3 x 
Since we know that the exponent property is:
quotient 
Now converting the given equation in the form above we get:
6.33 / 1.79 x
6.33 / 1.79 x 
Now the quotient is 6.33/1.79 ≈ 3.536313
quotient x 
3.536313 x 
Since 9-5 = 4 So
3.536313 x 
3.536 x 
Hence
6.33 x 10
⁹ / 1.79 x 10⁵ ≈ 3.5 x 
Hence m = 4
Answer:
6x ≥ 500
Step-by-step explanation:
I took the test but also it means that in six months, you have to save that amount of money to get exactly or more than 500, so this would be the correct answer!
Answer:
Below
Step-by-step explanation:
(2x/x+3) + (x+3/x-5)
Transform: 2x(x-5) + (x+3)^2 / (x+3)(x-5)
Remove brackets and expand : 2x^2 - 10x + x^2 + 6x + 9 / x^2 - 5x + 3x - 15
Collect like terms : 3x^2 - 4x + 9 / x^2 - 2x - 15
Final answer: 3x^2 - 4x + 9 / x^2 - 2x - 15