Triangle ABC is shown on the grid. What is the perimeter of triangle ABC? A(-1,5) B (4, 5) C (-1,1). A 9+ sqr21 units. B 9+sqt29
1 answer:
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Answer:
(x, y, z) = (3, -2, 4)
Step-by-step explanation:
The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...
z = 5 -(3 +(-2)) = 4
The solution is (x, y, z) = (3, -2, 4).
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Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:
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If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:
-3x -4y +4(5 -x -y) = 15 ⇒ -7x -8y = -5
(-3x -4y +4z) +(2x -y -4z) = (15) +(-8) ⇒ -x -5y = 7
This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...
-7(-5y -7) -8y = -5 ⇒ 27y = -54 ⇒ y = -2
x = -5(-2) -7 = 3
z = 5 -(3) -(-2) = 4
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<em>Additional comment</em>
If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.
Answer:
23
Step-by-step explanation:
Given:
The sequence of numbers is given as:
4 2
9 8
15 15
22 ?
Let the unknown number be 'x'.
Now, if we observe the numbers that are on the left or right side, we conclude that the difference between two numbers is increasing by 1 .
Right side: Left side:
8 - 2 = 6 9 - 4 = 5
15 - 8 = 7 ( 6 + 1) 15 - 9 = 6
22 - 15 = 7
Therefore, the next difference will also increase by 1 and will be equal to 8. So,
Adding 15 both sides, we get:
Therefore, the unknown number will be 23.