Answer:
<h2>x = 6.5 cm</h2>Step-by-step explanation:
The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.
Use the Pythagorean theorem:
We have
Substitute:
<em>use (a + b)² = a² + 2ab + b²</em>
<em>subtract x² from both sides</em>
<em>subtract 216.09 from both sides</em>
<em>divide both sides by 29.4</em>
Answer:
option 3
Step-by-step explanation:
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.
