<span>
You can write the equation in point-slope form, which has the format <em>y-y</em>subscript1=<em>m</em>(<em>x-x</em>subscript1), with <em>y</em>subscript1 and <em>x</em>subscript1 being the y and x coordinates for a point on the line, and <em>m</em> being the slope. </span>
<span /><span>Substitute a y and x coordinate into the equation so you have <em>y</em>-6=<em>m</em>(<em>x</em>-2)</span>
<span /><span><span>Then find the slope so you can replace <em>m</em>. The slope formula is <em />(<em>y</em>subscript2-<em>y</em>subscript1)/(<em>x</em>subscript2-<em>x</em>subscript1). </span><span>Substitute the coordinates in so you have <em>m</em>=(16-6)/(4-2), which simplifies to 10/2 and then 5.</span></span>
<span><span /></span><span>Now the equation is <em>y</em>-6=5(<em>x</em>-2)</span>
<span />If you want a different form, for example slope-intercept form, you can change it to that:
<span><em>y</em>-6=5(<em>x</em>-2)</span>
<span><em>y</em>=5x-4</span>
The answer is (3, -7). If the function is written in the form y = a(x –
h)^2 + k, the vertex will be (h, k). Let's write the function 8x^2 – 48x
+ 65 in the form of a(x – h)^2 + k. g(x) = 8x^2 – 48x + 65. g(x) = 8x^2
– 48x + 72 - 72 + 65. g(x) = (8x^2 – 48x + 72) - 7. g(x) = (8 * x^2 – 8
* 6x + 8 * 9) - 7. g(x) = 8(x^2 - 6x + 9) - 7. g(x) = 8(x - 3)^2 - 7.
The function is now in the form a(x – h)^2 + k, where a = 8, h = 3, and k
= -7. Thus, the vertex is (3, -7).
Use the the double angle formula:
sin(2A)=2sin(A)cos(A)
substitute 2x for A, then
20sin(2x)cos(2x)=10(sin(2(2x))cos(2(2x))=10sin(4x)
That means she need to buy 2 packs of 100.
Its E...........................................
