https://peda.net/id/c9637422c17 2018-09-26T13:34:45+03:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/b3338674c22 2018-09-27T10:26:50+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7Bx%7D%7Bx%2B1%7D%3D%5Cfrac%7B3x%7D%7B2x%2B1%7D" alt="\frac{x}{x+1}=\frac{3x}{2x+1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cleft(2x%2B1%5Cright)%3D3x%5Cleft(x%2B1%5Cright)" alt="x\left(2x+1\right)=3x\left(x+1\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2%2Bx-3x%5E2-3x%3D0" alt="2x^2+x-3x^2-3x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%5E2-2x%3D0" alt="-x^2-2x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%5Cleft(x%2B2%5Cright)%3D0" alt="-x\left(x+2\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0" alt="x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%2B2%3D0" alt="x+2=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-2" alt="x=-2"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B2x%7D%7B1%2Bx%7D%3D%5Cfrac%7Bx%7D%7B1-x%7D" alt="\frac{2x}{1+x}=\frac{x}{1-x}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5Cleft(1-x%5Cright)%3Dx%5Cleft(1%2Bx%5Cright)" alt="2x\left(1-x\right)=x\left(1+x\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x-2x%5E2-x-x%5E2" alt="2x-2x^2-x-x^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3x%5E2%2Bx%3D0" alt="-3x^2+x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cleft(-3x%2B1%5Cright)%3D0" alt="x\left(-3x+1\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0" alt="x=0"/><!--filtered attribute: style="display: inline;"--><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3x%2B1%3D0" alt="-3x+1=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3x%3D1" alt="3x=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B1%7D%7B3%7D" alt="x=\frac{1}{3}"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7Bx%7D%7Bx%2B1%7D%3D%5Cfrac%7Bx%2B2%7D%7Bx%7D" alt="\frac{x}{x+1}=\frac{x+2}{x}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D%5Cleft(x%2B1%5Cright)%5Cleft(x%2B2%5Cright)" alt="x^2=\left(x+1\right)\left(x+2\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3Dx%5E2%2B2x%2Bx%2B2" alt="x^2=x^2+2x+x+2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-x%5E2-3x-2" alt="x^2-x^2-3x-2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3x-2%3D0" alt="-3x-2=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%2B%5Cfrac%7B2%7D%7B3%7D%3D0" alt="x+\frac{2}{3}=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-%5Cfrac%7B2%7D%7B3%7D" alt="x=-\frac{2}{3}"/> 2018-09-27T10:26:50+03:00 https://peda.net/id/3aaa2ba0c22 2018-09-27T10:16:18+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3%5Cleft(x-1%5Cright)%5Cleft(x-7%5Cright)%3D0" alt="3\left(x-1\right)\left(x-7\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(3x-3%5Cright)%5Cleft(x-7%5Cright)%3D0" alt="\left(3x-3\right)\left(x-7\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3x-3%3D0" alt="3x-3=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D1" alt="x=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-7%3D0" alt="x-7=0"/><!--filtered attribute: style="display: inline;"--><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D7" alt="x=7"/><!--filtered attribute: style="display: inline;"--><br/> nollakohdat x=1 ja x=7<br/> b) 1&lt;x&lt;7 2018-09-27T10:16:18+03:00 https://peda.net/id/d5855574c22 2018-09-27T10:13:29+03:00 a) 3<br/> nollakohdat on x=0 ja x=-2<br/> b) 2<br/> nollakohdat on x=0 ja x=2<br/> c) 1<br/> nollakohdat on x=-2 ja x=2 2018-09-27T10:13:29+03:00 https://peda.net/id/6ce31bb4c18 2018-09-26T15:05:36+03:00 a)<br/> nollakohdat:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-8x%3D0" alt="x^2-8x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cleft(x-8%5Cright)%3D0" alt="x\left(x-8\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0" alt="x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D8" alt="x=8"/><br/> huipun x:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B0%2B8%7D%7B2%7D%3D4" alt="\frac{0+8}{2}=4"/><br/> huipun y:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4%5E2-8%5Ccdot4%3D16-32%3D-16" alt="4^2-8\cdot4=16-32=-16"/><br/> huipun koordinaatit: (4, -16)<br/> b)<br/> samalla tavoin kuin a-kohta huipun y asti:<br/> nollakohdat:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-8x%3D0" alt="x^2-8x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cleft(x-8%5Cright)%3D0" alt="x\left(x-8\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0" alt="x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D8" alt="x=8"/><br/> huipun x:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B0%2B8%7D%7B2%7D%3D4" alt="\frac{0+8}{2}=4"/><br/> huipun y:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4%5E2-8%5Ccdot4%2B7%3D16-32%2B7%3D-9" alt="4^2-8\cdot4+7=16-32+7=-9"/><br/> huipun koordinaatit (4, -9)<br/> <br/> 2018-09-26T15:05:14+03:00 https://peda.net/id/97bc0838c18 2018-09-26T14:59:50+03:00 a) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3%5Cleft(x-1%5Cright)%5Cleft(x-7%5Cright)%3D0" alt="3\left(x-1\right)\left(x-7\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(3x-3%5Cright)%5Cleft(x-7%5Cright)%3D0" alt="\left(3x-3\right)\left(x-7\right)=0"/><br/> nollakohdat:<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3x-3%3D0" alt="3x-3=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3x%3D3" alt="3x=3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D1" alt="x=1"/><!--filtered attribute: style="display: inline;"--><br/> tai<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-7%3D0" alt="x-7=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D7" alt="x=7"/><!--filtered attribute: style="display: inline;"--><br/> v: x=1 tai x=7<br/> <a href="https://peda.net/p/oskari.lahtinen/mpjy/2-2/230/sieppaa-png#top" title="Sieppaa.PNG"><img src="https://peda.net/p/oskari.lahtinen/mpjy/2-2/230/sieppaa-png:file/photo/2515663ab125e7127ab6da0752ff3252275699ee/Sieppaa.PNG" alt="" title="Sieppaa.PNG" class="inline" loading="lazy"/></a><br/> b) 1&lt;x&lt;7 2018-09-26T14:59:16+03:00 https://peda.net/id/ca153ff4c18 2018-09-26T14:48:02+03:00 a) x=3<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cleft(x%2B3%5Cright)" alt="f\left(x\right)=\left(x+3\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%2B3%3D0" alt="x+3=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-3" alt="x=-3"/><br/> x-3=0<br/> b) x=2 tai x=-5<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cleft(x-2%5Cright)%5Cleft(x%2B5%5Cright)" alt="f\left(x\right)=\left(x-2\right)\left(x+5\right)"/>=0 2018-09-26T14:46:21+03:00 https://peda.net/id/381784e0c18 2018-09-26T14:42:17+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cleft(x%2B2%5Cright)%5Cleft(x-3%5Cright)" alt="f\left(x\right)=\left(x+2\right)\left(x-3\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-3x%2B2x-6" alt="x^2-3x+2x-6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-x-6" alt="x^2-x-6"/><br/> b)<br/> nollakohdat x=-1 ja x=4<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cleft(x%2B1%5Cright)%5Cleft(x-4%5Cright)" alt="f\left(x\right)=\left(x+1\right)\left(x-4\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-4x%2Bx-4" alt="x^2-4x+x-4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-3x-4" alt="x^2-3x-4"/><br/> c) 2018-09-26T14:42:17+03:00 https://peda.net/id/39e3bee8c18 2018-09-26T14:35:10+03:00 a) 2x+4 <br/> =2(x+2)<br/> b) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2%2B4x" alt="2x^2+4x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5Cleft(x%2B2%5Cright)" alt="2x\left(x+2\right)"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x%5E2-9x" alt="6x^2-9x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3x%5Cleft(2x-3%5Cright)" alt="3x\left(2x-3\right)"/> 2018-09-26T14:35:10+03:00