I became a tutor and idk how to do this
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The statement " <span>y </span>varies directly as <span>x </span>," means that when <span>x </span>increases,<span>y </span>increases by the same factor. In other words, <span>y </span>and <span>x </span>always have the same ratio:
<span>where </span><span>k </span>is the constant of variation.
<span>We can also express the relationship between </span><span>x </span><span>and </span><span>y </span>as:
<span><span>y = kx</span> </span>
<span>where </span><span>k </span>is the constant of variation.
Since <span>k </span>is constant (the same for every point), we can find <span>k </span>when given any point by dividing the y-coordinate by the x-coordinate. For example, if <span>y </span>varies directly as <span>x </span>, and <span>y = 6</span> when <span>x = 2</span> , the constant of variation is <span>k = = 3</span> . Thus, the equation describing this direct variation is <span>y = 3x </span>.
Example 1: If <span>y </span>varies directly as <span>x </span>, and <span>x = 12</span> when <span>y = 9</span> , what is the equation that describes this direct variation?
<span>k = = </span>
<span>y = x</span>
Example 2: If <span>y </span>varies directly as <span>x </span>, and the constant of variation is <span>k = </span>, what is <span>y </span>when <span>x = 9</span> ?
<span>y = x = (9) = 15</span>
As previously stated, <span>k </span>is constant for every point; i.e., the ratio between the <span>y </span>-coordinate of a point and the <span>x </span>-coordinate of a point is constant. Thus, given any two points <span>(x 1, y 1)</span> and <span>(x 2, y 2)</span> that satisfy the equation, <span> = k </span>and <span> = k </span>. Consequently, <span> = </span>for any two points that satisfy the equation.
Example 3: If <span>y </span>varies directly as <span>x </span>, and <span>y = 15</span> when <span>x = 10</span> , then what is <span>y </span>when <span>x = 6</span> ?
<span> = </span>
<span> = </span>
<span>6() = y </span>
<span>y = 9</span>
In a kite, there is always an angle that is not right, otherwise, it would have a rectangular shape.
The diagonals are not of the same length because that would mean it would have a rectangular shape as well.
The sides are not equal, because that would mean it would have a rhomboid shape, to which a square belongs to.
The top edges are congruent with each other, as well as the bottom ones. This is because you can turn one into the other by reflecting them using an isometry, so D is true.
