23. Q23
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Similar Question 1
<p>Find the <code class='latex inline'>4</code> integers <code class='latex inline'>a, b, c</code> and <code class='latex inline'>d</code> that satisfy the following conditions:</p> <ul> <li>the sum of <code class='latex inline'>b</code> and <code class='latex inline'>c</code> is 30</li> <li>the sum of <code class='latex inline'>a</code> and <code class='latex inline'>d</code> is 35</li> <li>the numbers <code class='latex inline'>a < b < c < d</code> are in geometric sequence</li> <li>the sum of the squares of the 4 numbers is 1261</li> </ul>
Similar Question 2
<p>Find the <code class='latex inline'>4</code> integers <code class='latex inline'>a, b, c</code> and <code class='latex inline'>d</code> that satisfy the following conditions:</p> <ul> <li>the sum of <code class='latex inline'>b</code> and <code class='latex inline'>c</code> is 30</li> <li>the sum of <code class='latex inline'>a</code> and <code class='latex inline'>d</code> is 35</li> <li>the numbers <code class='latex inline'>a < b < c < d</code> are in geometric sequence</li> <li>the sum of the squares of the 4 numbers is 1261</li> </ul>
Similar Question 3
<p>If the interior angles of a pentagon form an arithmetic sequence and one interior angle is <code class='latex inline'>90^o</code>, find all possible values of the largest angle in the pentagon.</p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>The sum of the first <code class='latex inline'>n</code> terms of a sequence is <code class='latex inline'>S_n = 3^n -1</code>, where <code class='latex inline'>n</code> is a positive integer.</p><p>Prove that <code class='latex inline'>\displaystyle \frac{t_{n + 1}}{t_n} </code> is constant for all values of <code class='latex inline'>n</code></p>
<p>A sequence <code class='latex inline'>t_1, t_2, t_3</code> is formed by choosing <code class='latex inline'>t_1</code> at random from the set {1, 2, 3}, <code class='latex inline'>t_2</code> at random from the set {4, 5, 6}, and <code class='latex inline'>t_3</code> at random from the set {7, 8, 9}. What is the probability that <code class='latex inline'>t_1, t_2, t_3</code> is an arithmetic sequence?</p>
<p>Find the <code class='latex inline'>4</code> integers <code class='latex inline'>a, b, c</code> and <code class='latex inline'>d</code> that satisfy the following conditions:</p> <ul> <li>the sum of <code class='latex inline'>b</code> and <code class='latex inline'>c</code> is 30</li> <li>the sum of <code class='latex inline'>a</code> and <code class='latex inline'>d</code> is 35</li> <li>the numbers <code class='latex inline'>a < b < c < d</code> are in geometric sequence</li> <li>the sum of the squares of the 4 numbers is 1261</li> </ul>
<p>Consider the following system of equations.</p> <ul> <li> <code class='latex inline'>x_1 + x_2 =120</code></li> <li> <code class='latex inline'>x_2 + x_3 =160</code></li> <li> <code class='latex inline'>x_3 + x_4 =140</code></li> <li> <code class='latex inline'>x_4 + x_5 =125</code></li> <li> <code class='latex inline'>x_1 + x_3 + x_5 =215</code></li> </ul> <p>What is the value of <code class='latex inline'>x_1 + x_5</code>?</p>
<p>For the family of lines with equations of the form <code class='latex inline'>px + qy = r</code>, and which all pass through the point <code class='latex inline'>(-1, 2)</code>, prove that <code class='latex inline'>p, q</code>, and <code class='latex inline'>r</code> are consecutive terms of an arithmetic sequence.</p>
<p>If <code class='latex inline'>t_{n} = m</code>, and <code class='latex inline'>t_{m} = n</code> in a arithmetic sequence, (<code class='latex inline'>m \neq n</code>) then find the value for <code class='latex inline'>t_{m + n}</code>. </p>
<p>If the interior angles of a pentagon form an arithmetic sequence and one interior angle is <code class='latex inline'>90^o</code>, find all possible values of the largest angle in the pentagon.</p>
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