Two students in Mrs. Albring’s preschool class are stacking blocks, one on top of the other. Reece’s blocks are 6 cm high, and M
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Answer:
x = 0; y = -6; z = 1
Step-by-step explanation:
You want to find the solution to the system of equations ...
- 9x+y-3z=-9
- 10x-y+2z=8
- -10x-y+4z=10
This set of equations is conveniently solved using the matrix row-reduction features of a scientific or graphing calculator, spreadsheet, or any of a number of apps or on-line calculators.
The attachment shows the solution to be ...
(x, y, z) = (0, -6, 1)
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<em>Additional comment</em>
Solving a system of three or more equations "by hand" often can be done by an ad hoc process. It can be done in systematic fashion using Gauss-Jordan reduction techniques, but that often gets messy. Similarly, Cramer's Rule can be used, but that math tends to involve more arithmetic operations than are really necessary.
Adding the first equation to the other two eliminates the y-variable and reduces the system to two equations in two unknowns.
(9x +y -3z) +(10x -y +2z) = (-9) +(8) . . . . adding [1] and [2]
19x -z = -1 . . . . simplified
(9x +y -3z) +(-10x -y +4z) = (-9) +(10) . . . . adding [1] and [3]
-x +z = 1 . . . . simplified
At this point, we could graph the two equations, or we can proceed algebraically.
Adding these two equations gives ...
(19x -z) +(-x +z) = (-1) +(1)
18x = 0 ⇒ x = 0
Using the second of the reduced equations, we find ...
-x +z = 1
0 +z = 1 ⇒ z = 1
And using the second of the original equations, gives us ...
10(0) -y +2(1) = 8
-y = 6 . . . . . subtract 2
y = -6 . . . . multiply by -1
Then the solution is (x, y, z) = (0, -6, 1), as above.
- Zero Product Property: if a × b = 0, then either a or b = 0 or both a and b = 0.
(Make sure to set f(x) to zero)
So for this equation, I will be factoring by grouping. Firstly, what two terms have a product of -5x^2 and a sum of 4x? That would be 5x and -x. Replace 4x with 5x - x:
Next, factor 5x^2 + 5x and -x - 1 separately. Make sure that they have the same quantity on the inside:
Now you can rewrite the equation as:
Now apply zero product property to the factors to solve for x:
<u>The x-intercepts are (1/5 ,0) and (-1,0).</u>
As in each table can seat 8 people and the probability you need to find is about the first person you can ignore this data.
Probability that the first person to enter the room will be randomly seated at a maple table:
#maple tables: 9
# total tables: 9 +10 +5 +7=31