The answer is: "3" .
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Use the Pythagorean theorem (for right triangles):
a² + b² = c² ;
in which "a = "side length 1" (unknown; for which we which to solve);
"b" = "side length 2" = "√3" (given in the figure) ;
"c" = "length of hypotenuse" = "2√3" (given in the figure);
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a² + b² = c² ;
a² = c² − b² ;
Plug in the known values for "c" and "b" ;
a² = (2√3)² − (√3)² ;
Simplify:
(2√3)² = 2² * (√3)² = 2 * 2 * (√3√3) = 4 * 3 = 12 .
(√3)² = (√3√3) = 3 .
a² = 12 − 3 = 9 .
a² = 9
Take the "positive square root" of EACH SIDE of the equation; to isolate "a" on one side of the equation; & to solve for "a" ;
+√(a²) = +√9 ;
a = 3 .
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The answer is: "3" .
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When we want to find the roots of a one-variable function, we look for where its graph intersects the x-axis. In this case, the graph intersects the x-axis at 
The vertex of a parabola is the highest or lowest point on it, depending on whether the leading coefficient of the quadratic function is negative or positive. In this case, we see that the lowest point is 
For the y-intercept, just look for where the graph intersects the y-axis; in this case, that point is 
Using this information, the vertex-form equation of the parabola is
so the factors are two copies of
In this case, the value of
in the equation
was conveniently 1; if that's not the case, you'll want to plug in
to solve for the value of a that gives the correct y-intercept.
Does that help clear things up?
Answer:
it is underfined because if you look closely there is no slope in the graph
Answer:
Parallel
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts. If you multiply the top equation by 2, you get:
2(12x + 4y = 16)
24x + 8y = 32
This shows that both lines have the same slope, but then you find the y-intercepts, they are different:
1st equation y-int = 4
2nd equation y-int = 9/2 or 4.5

By the quadratic formula,

Then


Multiply numerator and denominator by the denominator's conjugate:
