Answer:
<u>Option b. (x = 3, y = 20, z = -14)</u>
Step-by-step explanation:
Given:
2x + 2y + 3z = 4
5x + 3y + 5z = 5
3x + 4y + 6z = 5
Solve using Cramer’s rule
∴ ![\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] =\left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%263%5C%5C5%263%265%5C%5C3%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
∴A = ![\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] = -1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%263%5C%5C5%263%265%5C%5C3%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20-1)
Ax = ![\left[\begin{array}{ccc}4&2&3\\5&3&5\\5&4&6\end{array}\right] = -3](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%262%263%5C%5C5%263%265%5C%5C5%264%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20-3)
Ay = ![\left[\begin{array}{ccc}2&4&3\\5&5&5\\3&5&6\end{array}\right] =-20\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%264%263%5C%5C5%265%265%5C%5C3%265%266%5Cend%7Barray%7D%5Cright%5D%20%3D-20%5C%5C)
Az = ![\left[\begin{array}{ccc}2&2&4\\5&3&5\\3&4&5\end{array}\right] = 14](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%262%264%5C%5C5%263%265%5C%5C3%264%265%5Cend%7Barray%7D%5Cright%5D%20%3D%2014)
∴ x = Ax/A = -3/-1 = 3
y = Ay/A = -20/-1 = 20
z = Az/A = 14/-1 = -14
<u>So, the answer is option b. (x = 3, y = 20, z = -14)</u>
Answer: 2/3
Cathy rolls a number cube that is labeled from 1 to 6.
Total outcomes = {1,2,3,4,5,6}
she rolls an even number or a multiple of 3
Outcomes of an even number = {2,4,6}
Outcomes of multiple of 3 = {3,6}
so favorable outcomes of even number or a multiple of 3 = {2,3,4,6}
Probability ( any event) =number of favorable outcomes divide by total number of outcomes
probability(even number or a multiple of 3) = 
I believe the fastest way to solve this problem is to take any two of the given points and to find the slope and y-intercept of the line connecting those two points.
Let's choose the 2 given points (-3,16) and (-1,12).
Going from the first point to the second, the increase in x is 2 and the increase in y is actually a decrease: -4. Thus, the slope of the line connecting these two points is m = -4/2, or m = -2.
Now use the slope-intercept formula to find the y-intercept, b.
One point on the line is (-3,16), and the slope is m = -2.
Thus, the slope-intercept formula y = mx + b becomes 16 = -2(-3) + b.
Here, b comes out to 10.
So now we have the slope and the y-intercept. Write the equation:
y = mx + b becomes y=-2x+10. Which of the four given answer choices is the correct one?
Answer:
omg
I
1. 3×3×3×3 = 81
2. 2²a³
3. (-5)³ (-5×-5×-5) = -125
4. 1
5. a^m-n
II
1. 1.6807× 10⁴
2. (7×7×7) × (2×2×2×2×2×2) = 21952
3. 32²
4. 2187
5. 803025
3(1,000,000)=3,000,000
3(100,000)=300,000
2(100)=200
3,300,200
