<ol>
<li><p>R is the midpoint of line segment PT, and Q is the midpoint of line segment PR. If S is a point between R and T such that the length of segment QS is 10 and the length of segment PS is 19, what is the length of segment ST ?</p></li>
<li><p>If 0 ≤ x ≤ y and (x + y)^2 − (x − y)^2 ≥ 25, whats the least possible value of y ?</p></li>
</ol>
<p>thankss!!</p>
<ol>
<li>17</li>
<li>2.5</li>
</ol>
<p>how? as in plz give the explanations!!</p>
<p>for #1:</p>
<p>It gives you a midpoint so you know that PQ and PR are equal AND PR and RT are equal.
PS is given as 19 and QS is ten therefore PQ is 9, which means QR is 9. 9 + 9 = 18, so PR is 18; therefore, RT is 18. To find the value of RS, you must subtract PS from PR = 1.
Then to find the value of ST, you must subtract 1 from RT (18) which yields 17.</p>
<p>Not sure about #2. I’m having trouble trying to set it up.</p>
<p>To get the lowest possible values, we must view everything in terms of being equal (hence why they used the greater than or equal to signs). So factor out the equation to get (x+y)(x+y)-(x-y)(x-y) which completely factors into 4xy = 25. This means xy = 6.25, and since x and y are equal in our scenario, take the square root of 6.25 to get y = 2.5. </p>
<p>Notice (2.5+2.5)^2 - (2.5-2.5)^2 is 5^2 which is 25.</p>