<u>Answer:</u>
The solution set of given equations -x-y-z = -8 and - 4x + 4y + 5z = 7 and 2x + 2z = 4 is (3, 6, -1)
<u>Solution:</u>
Given, set linear equations are
-x – y – z = -8 ⇒ x + y + z = 8 → (1)
-4x + 4y + 5z = 7 ⇒ 4x – 4y – 5z = -7 → (2)
2x + 2z = 4 ⇒ x + z = 2 → (3)
We have to solve the above given equations using substitution method.
Now take (3), x + z = 2 ⇒ x = 2 – z
So substitute x value in (1)
(1) ⇒ (2 – z) + y + z = 8 ⇒ 2 + y + z – z = 8 ⇒ y + 0 = 8 – 2 ⇒ y = 6.
Now substitute x and y values in (2)
(2) ⇒ 4(2 – z) – 4(6) – 5z = - 7 ⇒ 8 – 4z – 24 – 5z = -7 ⇒ -9z – 16 = -7 ⇒ 9z = 7 – 16 ⇒ 9z = -9 ⇒ z = -1
Now substitute z value in (3)
(3) ⇒ x – 1 = 2 ⇒ x = 2 + 1 ⇒ x = 3
Hence, the solution set of given equations is (3, 6, -1).
Answer:
C) A histogram because the class organizes the data into different ranges or intervals.
Step-by-step explanation:
A histogram is a graphical representation of numerical data. It is an approximate approach that groups a set of data into ranges on the x axis and having their match frequencies on the y axis.
A histogram makes it possible to represent a large amount of data and frequency in just one graph because of the interval/range option.
Because Mariner Middle school has a large number of students (550) and their height organized into equal intervals, the histogram is the best option.
Answer:
-6
Step-by-step explanation:
y intercept is -6 because formula of gradient is y=mx+c.......c is the y intercept
Variance is the answer.
Explanation:
The variance is the average of the squared differences from the mean. To figure out the variance, first calculate the difference between each point and the mean; then, square and average the results.
Acceleration is the derivative of velocity, so it is a measure of the change in velocity over time. Dimensional units reflect this as fps (feet per second) for velocity and fps^2 (fps per second). Here, acceleration is simply given as the change in velocity divided by the time.
This works as long as all your units are equivalent (i.e. if time was in minutes and velocity was in f/s, you would need to convert first).
