# 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?
379
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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?
777
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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...
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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 views 0 answers 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 \%$$ chance it'll be each di...
493
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How can we use machine learning algorithms to automatically discover patterns and relationships in large datasets?
604
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A plane passing through the point $$(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$$?
559
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Find the standard equation of the circle with center at $$(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$$.
311
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Use two inequalities to describe the set of all points above the line $$L: 4 x+3 y=9$$ and below the line $$M$$ : $$2 x+y=1$$
503
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Determine whether the lines $$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$$.
194
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A circle centered at the incenter $$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$$ so that the int...
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A finite set $$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 views 0 answers 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}$$ are leaned onto a wall such that they reach the same height. The base of the longer ladder...
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Is it true that, if three items in parallel each having a reliability of 0.90 then they have an overall system reliability of 0.729?
580
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A system is to be composed of 5 identical components in series. What is the lowest reliability component that can be used in order to have an overall system reliability o...
256
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A system consists of 6 components connected. Find the overall reliability of the system, given that the reliabilities of $$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 views 0 answers 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$$ passes through a mid...
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Find the number of ordered quadruples $$(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?
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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 views 1 answers Prove that \(\hat{G}=\hat{J} ; \hat{H}=\hat{K}$$ and $$\hat{I}=\hat{L}$$ if the corresponding sides of two triangles are in proportion, then the corresponding angles are ...
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Given that If the corresponding angles in two triangles are equal, then the corresponding sides are in proportion (AAA) and $$\triangle G H I$$ and $$\triangle J K L, \ha... 408 views 1 answers 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$$ :
376
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Determine the value of $$x$$ :