Recent questions tagged parallel

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How do you identify which lines are parallel?
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What is the role of machine learning in identifying causal relationships in learning analytics?
295
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On a graph, what is an y-coordinate?
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Determine the values of \(m\) for which \(y=m x-1\) is a tangent to \(y=x^2-2 x+3\).
233
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What is the equation of the line that is parallel to the line $y = 2x+1$ and passes through the point $(3,5)$?
444
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How do you solve the equation $ax^2 + bx + c = 0$ using the quadratic formula?
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The function \(f: x \rightarrow \log _a x\) passes through the point \((4 ;-2)\).(a) Determine the value of \(a\) and hence the equation of \(f\).(b) Write down the equat...
242
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A specific tree grows \(1,5 \mathrm{~m}\) in the 1st year. Its growth each year thereafter is \(\frac{2}{3}\) of its growth in the previous year. What is the greatest hei...
613
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Determine the equation of the line through the points $(1,2)$ and $(3,4)$ in the form $ax + by + c = 0$.
264
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In the \(x y\)-coordinate plane, the \(x\)-axis and the line \(y=x\) are mirrors. If you shoot a laser beam from the point \((126,21)\) toward a point on the positive \(x...
279
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A mustache is created by taking the set of points \((x, y)\) in the \(x y\) coordinate plane that satisfy \(4+4 \cos (\pi x / 24) \leq y \leq 6+6 \cos (\pi x / 24)\) and ...
248
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Across the face of a rectangular post-it note, you idly draw lines that are parallel to its edges. Each time you draw a line, there is a \(50 \%\) chance it'll be each di...
493
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How can we use machine learning algorithms to automatically discover patterns and relationships in large datasets?
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A plane passing through the point \((3,1,1)\) contains two lines whose direction ratios are \(1,-2,2\) and \(2,3,-1\) respectively. If this plane also passes through the ...
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The plane passing through the points \((1,2,1),(2,1,2)\) and parallel to the line, \(2 x=3 y, z=1\) also passes through the point:
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What is \(6.4-y=62 / 5\)?
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Find the standard equation of the circle with center at \((1,-2)\) and passing through the point \((7,4)\).
419
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Describe geometrically the family of lines \(y=3 x+b\).
527
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Describe geometrically the family of lines \(y=m x+2\).
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Use two inequalities to describe the set of all points above the line \(L: 4 x+3 y=9\) and below the line \(M\) : \(2 x+y=1\)
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Determine whether the lines \(3 x+6 y=7\) and \(2 x+4 y=5\) are parallel.
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Does the point \((-1,-2)\) lie on the line \(L\) through the points \((4,7)\) and \((5,9)\) ?
689
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If the point \((2, k)\) lies on the line with slope \(m=3\) passing through the point \((1,6)\), find \(k\).
377
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Find an equation of the line through \((2,3)\) and parallel to the line with the equation \(y=5\).
601
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Find an equation of the line through \((2,3)\) and parallel to the line with the equation \(4 x-2 y=7\).
422
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Find an equation of the line \(L\) through \((-1,4)\) and parallel to the line \(M\) with the equation \(3 x+4 y=2\).
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A circle centered at the incenter \(I\) of a triangle \(A B C\) meets all three sides of the triangle: side \(B C\) at \(D\) and \(P\) (with \(D\) nearer to \(B\) ), side...
301
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Three given rectangles cover the sides of a given triangle completely and each rectangle has a side parallel to a given line. Show that the rectangles also cover the inte...
354
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In a trapezoid \(A B C D\) sides \(A B\) and \(C D\) are parallel and \(E\) is a fixed point on the side \(A B\). Define a point \(F\) from a side \(C D\) so that the int...
537
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A finite set \(S\) of integer points in the coordinate plane is called a two-neighbor \(s e t\) if for each point \((p, q) \in S\), exactly two of the points \((p \pm 1, ...
232
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In a trapezoid \(A B C D\) sides \(A B\) and \(C D\) are parallel and \(E\) is a fixed point on the side \(A B\). Define a point \(F\) from a side \(C D\) so that the int...
245
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Find all real numbers \(a, b, c\), and \(d\) such that\[a^2+b^2+c^2+d^2=a(b+c+d)\]
281
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A line parallel to \(y=4 x+\) 6 passes through \((5,10)\). What is the \(y\) coordinate of the point where this line crosses the \(y\)-axis?
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A pair of ladders whose lengths are \(4.2 \mathrm{~m}\) and \(5.6 \mathrm{~m}\) are leaned onto a wall such that they reach the same height. The base of the longer ladder...
290
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Is it true that, if three items in parallel each having a reliability of 0.90 then they have an overall system reliability of 0.729?
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A system is to be composed of 5 identical components in series. What is the lowest reliability component that can be used in order to have an overall system reliability o...
256
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A system consists of 6 components connected. Find the overall reliability of the system, given that the reliabilities of \(A, B, C, D, E\), and \(F\) are, respectively, \...
870
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A system consists of 5 identical components connected in parallel. Determine the reliability of each component if the overall reliability of the system is to be \(0.96\) ...
506
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An electric circuit consists of 7 transistors connected in parallel. Determine the reliability of each transistor if the overall reliability of the circuit is to be \(0.9...
301
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In a circle, a finite set \(S\) of chords (segments connecting two points on the circle) is given, with a property that each of the chords from \(S\) passes through a mid...
287
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Find the number of ordered quadruples \((a, b, c, d)\) of real numbers such that\[\left(\begin{array}{ll}a & b \\c & d\end{array}\right)^{2}=\left(\begin{array}{ll}c & a ...
542
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Three noncollinear points and a line \(\ell\) are given in the plane. Suppose no two of the points lie on a line parallel to \(\ell\) (or \(\ell\) itself). There are exac...
477
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A line parallel to \(y=4 x+6\) passes through \((5,10)\). What is the \(y\)-coordinate of the point where this line crosses the \(y\)-axis?
737
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In the circult diagram below, the battery has nogligible internal resistance. The resistance of the ammeter and wires may also be ignored The reading on voltmeter \(V_{3...
382
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Prove that \(\hat{G}=\hat{J} ; \hat{H}=\hat{K}\) and \(\hat{I}=\hat{L}\) if the corresponding sides of two triangles are in proportion, then the corresponding angles are ...
488
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Given that If the corresponding angles in two triangles are equal, then the corresponding sides are in proportion (AAA) and \(\triangle G H I\) and \(\triangle J K L, \ha...
408
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Given \(KL \parallel IJ\), calculate \(x\)
501
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Prove that \(\frac{D P}{P E}=\frac{D Q}{Q F}\) given that A line drawn parallel to one side of a triangle cuts the other two sides in proportion. (Proportion Th. or side ...
589
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Determine the value(s) of \(x\) and \(y\) :
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Determine the value of \(x\) :
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