Geometry!! Please help!! What is the value of x?

Mathematics

2 answers:

forsale [732]3 years ago

7 0

The answer is: " x = 75 units ".
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Explanation:
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Set up the follow ratios, or proportions, as fractions:

x/ 63 = 50/42; Solve for "x" ;
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→ Reduce the "50/42" ; " 50/42" = (50÷2) / (42÷2) = 25/21 .

Rewrite: " x / 63 = 25 / 21 " .

Cross multiply: Given: "a/b = c/d " ; "ad = bc" ;

Thus, "21x = (63) * (25) ;

Divide each side of the equation by "21" ; to isolate "x" on one side of the equation; and to solve for x" ;

" 21x / 21 = [ 63 * 25 ] / 21 " ;

Note: "63/21 = 3 " ;

So: x = 3 * 25 ;
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x = 75 .
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The answer is: " x = 75 units ".
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swat323 years ago

7 0

Answer:

Step-by-step explanation:

75 units

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Using a directrix of y = −3 and a focus of (2, 1), what quadratic function is created?

Lelechka [254]

Answer:

$y=\dfrac{1}{8}(x-2)^2-1$

Step-by-step explanation:

The distance between the focus and the directrix is the vertical distance from the point to the line:

1 -(-3) = 4

The vertex is half that distance between the point and the line, so is at x=2 and ...

y = (-3 +1)/2 = -1

The vertical scale factor of the quadratic is 1/(4p) where p is the distance from vertex to focus. Here, that distance is 2, so the equation in vertex form is ...

y = (1/(4·2))(x -2)² -1

y = (1/8)(x -2)² -1

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Check

Any point on the parabola is equidistant from the focus and directrix. This is easily checked at the vertex, which is halfway between focus and directrix, and at the points having the same y-value as the focus. Those two points are (-2, 1) and (6, 1), both of which are 4 units from the focus and 4 units from the directrix.