<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:
2
Step-by-step explanation:
To solve this equation, you need to convert 2 1/2 into an improper fraction:
2 1/2 = 5/2
Then, you convert this into 6ths:
5/2 = 15/6
Next, you divide 15/6 by 5/6:
15/6 / 5/6 = 3
Because Jamal wouldn't make a stop at the end (it wouldn't be considered a stop because he is done), you subtract 1:
3-1=2
The answer is 2 (hope this helps, sorry if i got it wrong)
Answer:
Step-by-step explanation:
Given
Required
Find y when 
We have:
Express as equation
Solve for k
When
When , we have:
Answer: First option.
Step-by-step explanation:
It is important to remember the definition of "Translation".
A Translation is defined as a transformation that moves every point of an object a determine distance in a given direction. In Translation, the shape and the size of the object do not change.
Then, given a point:
Where "x" is the x-coordinate and "y" is the y-coordinate.
And given the following translation:
We can notice that:
- 2 units are added to the original x-coordinate. This indicates that the object must be moved 2 units to the right.
- 4 units are subtract from the original y-coordinate. This indicates that object must be moved 4 units down.
Answer: 21
Step-by-step explanation: 3 x 7 = 21
