5

A straight line through the origin $O$ meets the parallel lines $4 x+2 y=9$ and $2 x+y+6=0$ at points $P$ and $Q$, respectively. The point $O$ divides the segment $...

Question

A straight line through the origin $O$ meets the parallel lines $4 x+2 y=9$ and $2 x+y+6=0$ at points $P$ and $Q$, respectively. The point $O$ divides the segment $P Q$ in the ratio(A) $1: 2$(B) $3: 4$(C) $2: 1$(D) $4: 3$

A straight line through the origin $O$ meets the parallel lines $4 x+2 y=9$ and $2 x+y+6=0$ at points $P$ and $Q$, respectively. The point $O$ divides the segment $P Q$ in the ratio (A) $1: 2$ (B) $3: 4$ (C) $2: 1$ (D) $4: 3$



Answers

Which of the following equations represents a line
that is parallel to the line with equation
$y=-3 x+4 ?$
$$\begin{array}{l}{\text { A) } 6 x+2 y=15} \\ {\text { B) } 3 x-y=7} \\ {\text { C) } 2 x-3 y=6} \\ {\text { D) } x+3 y=1}\end{array}$$

Okay, so for this one, it's us. Two different points of the number line are both three units from the point with coordinate negative four. He's let's draw door number line. So here is negative, for we know that it's both three units from that point. So three to the left because this negative seven and three to the right gives us negative one. So we want to find a way that we can plug in these two points as our X and still get the same thing on the other side of the equation. Well, so let's go and try plugging it in. So if we plug in the negative seven seven plus for the opposite value of that is three, that one works negative one plus before the opposite value of that is also three sound works. So is probably our answer, but let's check through the rest. So if we have negative seven minus four, that absolutely becomes eleven, so that does not work already. See negative seven plus three. The absolute value of that is for so that one works. But then the negative one plus three becomes absolutely have to sew. That does not work for D neg. A seven minus three is negative is going to be an absolute value of ten. So that one false does not work. So is our answer.

So this problem We're given the coordinates of A and B, and we need to find a point. Be such that we have this ratio a p to P. B is equal to fourth to three Now, we could just plot these points and draw line and have some partitions. So shall we have this ratio? But can we do this and more mathematical way? Now you're looking from voting for prom 43. I draw it out the partitions, but to induce with just numbers Here, it's our time to draw anything but one thing that wicked nose here is that we can tackle each of the coordinates independently. Wanna look the ex cornets here Sunny ex Cornet survey here Ace of X is one and B so X is equal to eight. So if I take a piece of X on its face of X here I get seven. Yeah, right. So I So the difference is second. So for one to divide the partitions evenly right into forced to re show Here. Done. I want to break those seven into four through Asia, right? Somebody goes four plus three here. So and we get to a the pee here. I need one plus four. And if I need to get from B to pee, I need you eight minus three. Here. So one plus four here is equal to eight months. Three here. Right? Way to visualize this is that Let's say, have 70 partitions. The 43 ratio happens here. All right, so it's a society. So let's say this is red are missing a toupee. Blew your present will be two, um p and have a pee right here. Okay, then if I want this for the three ratio here, right, Four evens, least based partitions. Three evenly spaced politicians here. Right now, we need to find an evenly spaced partition or some way to divide it up into a ratio for the three here. In that case, here it's evenly spaced partitions One. Therefore, I could split seven, Chief, because four plus three here something of a d. P i ad for be the P s. A track three. My three are at least in terms of number, evenly spaced partitions. And I get this in that case here, these equations should balance. Fight was five. Therefore, the ex Queen Yippie is you go to five. Let's look at the white quartets. A little trickier for this one. So, like a is needed to and D'You record B is 12 year. If I look the difference here, that's equal to 14. So can a partition 14 in such a way that have two numbers here, right? Like me, Auntie Angie a 14 year and have a ratio of 4 to 3. Well, about April 6 here is since I don't know seven, actually 14. Therefore, I should double for 3 to 8 to six. Right. You contract this reassured by how I look at a over six foot four or three. So this partition works. So here I have nave to a starting point and I add the partition for app for that. So that would be eight. So negative plus eight is equal to 2 12 minus six Theseus. Number should be equal into one of them, and they are Safety Eagle six. So that is D Y coordinates of P. It's really know the expo in a penal Micanopy soapy should be five six

Right. So here, on problem number 27 we've been given six different lines. We want to know which ones are parallel to each other, which ones are perpendicular to each other. So it means we need to identify the slope on all these. So on a we've got white was three experts three. And so our slope is three. B X equals negative one. Well, that's a vertical line, so that would have an undefined slope. Why minus five equals 1/2 times X minus two. Well, that's in Point Slope form. So that 1/2 there's your so why it was three. That's a horizontal line. And so that has a slope of zero. Why plus for it goes native to times, actually six. That's also in Point Slope form. It's or slope. Here's negative, too. The last of the state sector. Figure out what our soap is on. This last one. It's in standard form, so we need to put it in soap intercept form and find it. So So it's a track. Nine acts on each side. We get negative. Three is equal to negative nine X plus five. Divide by negative three and so we get wise equal to nave. Nine. Vibe I 93 deposit three X minus 5/3. So that's what that line is. And soap intercept form. That's our soap. Here is three. Let's backtrack here, this one. This last night then we just found, has a slope of three. It's the spirit of all this. This one has a slope, but three. So now it's from Paris. We want to know, right? So now we have the slopes. Let's start by identifying which lines are parallel. So latrines have the exact same slope. Well, the only ones that have the exact same slope or a and F so a and F for parallel. And those were the only ones because those were the only ones that have the same slope. Right now. Perpendicular two lines are perpendicular. If their slopes are opposite reciprocal, well, see an E si has a slope of 1/2 if you flip 1/2 over and change its sign that make it negative, too. So seeing E have have opposite reciprocal slopes, and so those are perpendicular to each other. Be in dear, also perpendicular to each other. It's a little harder to sell their when you're talking about slopes, but B is a vertical line and X equals lines of vertical line. De is a horizontal line. Wyffels line is a horizontal, and vertical and horizontal lines are perpendicular to each other. S O, B and D are also perpetrated. And then that's everything. There's no other pair there where the soldier opposite reciprocal. And so those are all of the perpendicular.

The flight A says three y minus four X is equal to three. Online B is three y is equal to negative for X Plus nine. I'm going to get them into still intercept form and compared the slopes. So if a divide line B by three, I get why is equal to negative for over three X plus three and then if I move this to the other side, I've got three. Y is equal to four X plus three. If I divide both sides by three, why is 4/3 X plus one so you can see that these are not parallel because one is a negative for over three slope and one is a positive for over three slopes. It's close but not close.


Similar Solved Questions

5 answers
Give the structures of compounds throughCanc HBr(gas)heat1) Hg(OAch CHJOHMg ether2) NaBHAHzSO4OHMCPBAheat2) HyotGive the products of the following reactionsSec- butyl isopropyl ether= excess conc. HBr; heatb) di-n-butyl cther +hot = conc NaOHethoxybenzene conc. HI; heatdi-n-butyl ether Na metalpropylene oxide (2-methyl oxirane) CH;NHzf) potassium tert-butoxide n-butyl bromideg) I-methyl-[,2-epoxycyclohexane methanol in acidic solution
Give the structures of compounds through Canc HBr (gas) heat 1) Hg(OAch CHJOH Mg ether 2) NaBHA HzSO4 OH MCPBA heat 2) Hyot Give the products of the following reactions Sec- butyl isopropyl ether= excess conc. HBr; heat b) di-n-butyl cther +hot = conc NaOH ethoxybenzene conc. HI; heat di-n-butyl eth...
5 answers
Opehb Provious Ansutrs LCACCon5 3.3.005 An underground gasoline storage tank Icaking: The tank currently contains 600 gallons gasoline value of the stored gasoline changing? Per dayMhnDtaur nitlosinggallons per day: If the value the gasoline 52.57 per gallon, how qulckly theNeed Help?
Opehb Provious Ansutrs LCACCon5 3.3.005 An underground gasoline storage tank Icaking: The tank currently contains 600 gallons gasoline value of the stored gasoline changing? Per day Mhn Dtaur nit losing gallons per day: If the value the gasoline 52.57 per gallon, how qulckly the Need Help?...
5 answers
Question 135 ptsThe following table gives the approximate amount of emissions, E of nitrogen oxides in millions of metric tons per year in the US. Let t be the number of years since 1985 and EYear E1985 11.61990 1995 5,0 16.92000 6.42005 14.12010 13.72015 20.82020 38.6Using right endpoints and 7 rectangles, estimate the integral f(t) dtYou must enter the exact numerical decimal answer in reduced form:
Question 13 5 pts The following table gives the approximate amount of emissions, E of nitrogen oxides in millions of metric tons per year in the US. Let t be the number of years since 1985 and E Year E 1985 11.6 1990 1995 5,0 16.9 2000 6.4 2005 14.1 2010 13.7 2015 20.8 2020 38.6 Using right endpoint...
5 answers
That rust '094011 Calculato 1
that rust '0940 1 1 Calculato 1...
5 answers
! Gnal percene Oline 1 A blologlst measured the Ienathns {tlcedod 7U 22.75 WH 1 24,75-25,75 Si 1 ~20,75 1 thalone 8 1 = ' 10.7 1 1 1 ! 1 relative Trequency Ong ul Ics: districution 1 1 1chac tollou
! Gnal percene Oline 1 A blologlst measured the Ienathns {tlcedod 7U 22.75 WH 1 24,75-25,75 Si 1 ~20,75 1 thalone 8 1 = ' 10.7 1 1 1 ! 1 relative Trequency Ong ul Ics: districution 1 1 1 chac tollou...
5 answers
[ExplanatonnudodExhanatoryEanlanalen
[ Explanaton nudod Exhanatory Eanlanalen...
3 answers
2 = In(z?+yP) points) At the point Po(O, 1,,0), find an equation for the tangent plane to the surface
2 = In(z?+yP) points) At the point Po(O, 1,,0), find an equation for the tangent plane to the surface...
5 answers
Why ' I5 be following structure not = CHO meso compound?HO-HO~HCH;OH
Why ' I5 be following structure not = CHO meso compound? HO- HO ~H CH;OH...
5 answers
Altha = crew will not return alive Froblcm i8^ J chance that some member ) retutning Alive drop t0 suppase that 1 Each spsce shuttk (ligh Ihere probablity of all thc crew members Aucr how r4ua 'Onsecutave Ruccesstul flghts docs the
altha = crew will not return alive Froblcm i8^ J chance that some member ) retutning Alive drop t0 suppase that 1 Each spsce shuttk (ligh Ihere probablity of all thc crew members Aucr how r4ua 'Onsecutave Ruccesstul flghts docs the...
5 answers
Hide VmerhtemConstrntsDoriano tho Danity 0n objuct Ihat innt mun 4524 and whon placed Injo . grhou Ilad Crunaot; (ha wator lovul naou Itom 10 ; mLo 227m1Poz} *Konu Inebo124 Qnl15,6 QrmL OUiuu WinLSubrutAenueat AnaweProvido Fooqbuck
Hide Vmer htem Constrnts Doriano tho Danity 0n objuct Ihat innt mun 4524 and whon placed Injo . grhou Ilad Crunaot; (ha wator lovul naou Itom 10 ; mLo 227m1 Poz} * Konu Inebo 124 Qnl 15,6 QrmL O Uiuu WinL Subrut Aenueat Anawe Provido Fooqbuck...
5 answers
Multiply.$$(30 x+12) 3$$
Multiply. $$(30 x+12) 3$$...
5 answers
Identlfy the data set's level ot measurement:Ilst of 1240 social securlty numbersratlonominaordinalIntervalDetermlne whether the numerical value i5 parameter or a statistic: Explain vour reasoningThe average salary of all assembly-line employees at a certain car manufacturer Is 530,000Font FamilyAA-
Identlfy the data set's level ot measurement: Ilst of 1240 social securlty numbers ratlo nomina ordinal Interval Determlne whether the numerical value i5 parameter or a statistic: Explain vour reasoning The average salary of all assembly-line employees at a certain car manufacturer Is 530,000 F...
5 answers
2F.For the plana A4pa ihowatin Eienoey detinmninl thellec atunanlahbm Kmntmali Oe 2 ehe); Su suImHolonG(5,8 19)G (4.6.83)665. 8 3)0( 93)
2F.For the plana A4pa ihowatin Eienoey detinmninl thellec atunanlahbm Kmntmali Oe 2 ehe); Su su Im Holon G(5,8 19) G (4.6.83) 665. 8 3) 0( 93)...
5 answers
QuestionFind the expectaton and the variance for a uniform random variable U defined on the unit interval [0,1] (b)IfUis uniform on [0,1], and Y =a +bU_ find E(Y), Var(y) and Standard Deviation (Y)_
Question Find the expectaton and the variance for a uniform random variable U defined on the unit interval [0,1] (b)IfUis uniform on [0,1], and Y =a +bU_ find E(Y), Var(y) and Standard Deviation (Y)_...
5 answers
Pb(s) Pb +2 (be) = Fe+3 (be) 2 (s)IH 3 & 8 standard 75 2 ceher the potential: eaciont [ ion many concentration is moles 0.050 electrons 2 3 and taadspeoduct ion
Pb(s) Pb +2 (be) = Fe+3 (be) 2 (s) IH 3 & 8 standard 75 2 ceher the potential: eaciont [ ion many concentration is moles 0.050 electrons 2 3 and taadspeoduct ion...
5 answers
The time required between generation and disappearance of free electrons is calledNONEbarrier potentialholesSettling time
The time required between generation and disappearance of free electrons is called NONE barrier potential holes Settling time...

-- 0.020909--