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ページ1:
SISTEM Persamaan 1. Dua Variabel (SPLDV) • Eliminasi 2x + y 3 x 1 X = 8 1x1 2x+y=8 = 1 1x2 2x-24-2. g = 3 LINEAR 12x+214 = -3 112x + 204 = 12 y=-1511 3x+5(-5)=3 39=6 y=2 3x-75 = 3 ca + 3 = 5 1 0 = 2 X 211 b 1 = 2 4) 3 2x+5y+3 3x-2y-2 3 = 1- 2x+5y+3 3x-2y-2. • Subtitusi 2x+4=8 x = 4 = 1 x = 1+y 2(179)+y=8 2+2y+y=8 3y =6 y =2 Eliminasi Subtitusi 2x+2-8 2x = 6 XX = 26 3x=78 × => =2611 y = -15 $ 11 misala = 1 2x+54 +3 x = 3. 2) 1×11/14 = 11 x 6 b = 2x+y=8 x-4=1+ 3x=9 x = 3 HP = (312) 3-y=1 2=y 12x78y = 24 9x-8y = 60 + 21X =84 ✗ = = " 3(4)+29 = 6 +36 = 1 36 = 2x-4 = 5 x12 3x+2y=6 9x-8y =60 1×4 9 +39 = 1 30-66- 29+66=2 59- = 2 3x-2y-2 39-66= = 2 2 + 2x+y=8x04 (0,8) 480 (410) x-4-1×10/0 X0-1 (0,1) (-1,0) 6. 4- > HP (3.2) 2- 246 = Grafik Contoh 1) 4x + 7y+1=0 ×3 3x + Sy-3=0 1 x 4 X 12724 = 6 2y= =-b y=-311 (4-3) 3) ½ + ½ = 5 + 13 = -5 onisal: a.b b == a = → 1 = 2x+54+3 2x+5y+3=2 =2x+5y=-11x3 b = 6 = y j = a+b=5 ×2 29- -36=-5 XI 29 +26=10 2a-3b=-5 sb = 15 b=3 <- 1 3x-2y-2 3x-2y-2=6 =3x-2y=81×2 6x+5y=-3 6x-44=16 194-19 y=-1 2x+5(-1)=-1 2x-5=-1 2x = 4 => x=2/1
ページ2:
12. TIGA VARIABEL (SPLTV) # 9. 2 39-404) 30 20 P&P 2x + 34-2-5 *+ 4+2 = 9 3. 39 + =0 4) 2x+4y-6-32 x-3y=-7-27 × = 24 +2 = -5 = 3 4 J 2x +44 +32=6 2x + 3(3) =2 22 x-3y+22=-7 2x + 1 = 2 X- 2y+2=-5 + 3x + 4y P&P = 14 - Y 2x =1 X = x-3y+22=-7 x + y + z = 9 31 X3 x-24+ z = -5 -y+z --2 x-24-2 =-7 + 2x-y =3 P&Ps 3x+44 = 14 x1 2x-9 = 2 x4 3x + 4y = 14 8x-49 = 8 IX ✗ 212) - =22 = 211 2 = 2 4-4 y = 211 x + y + z = 9 2+2+2=9 4+2=9 z=511 Hp (2,2,5) 2) 2x + 3y = 2 ... 1 -x + 4 + + misal a D 2x +44 +32=6 2x - by +62 =-14 109-32 = 20 -3y+32=-6 -104-32 = 20 a = x, b = 1/1, c = /== + = 14 y = 2 29 +26+30 = 4 × 9 +4b-4c = 0x21x3 39 +36 +20=1 20+2b+3c=4 29+0b-8c=0 - 74 +2+2 = -2 × 1 2 bb + c = 4 1×3 39 +12b-12C = 0 3a+3b+20=1 9b-14c = -1 1x2 -18b433c=12 18b-28 C = -2 SC = 10 C = 211 + 1 z = " x-2(2)+1=-5 ✗- 4 +1 =-5 x-3=-5 x= -2 x + 2z = 1 2 3y +8=3 3 -bb + 11 (22) = 4 -6b+22 2x+3y = 21×1 x+27=1x2 2x + 3y = 2 2x + 42 =2 34-42=0.4 3y+87=3 3y+42=0 122=3 2 = 1 =4 -6b=-18 b = 311 at 4(3) 4(2) = 0 9+12-8=0 a+4=0 a = -4 -> = a = -411 1 - b = 3 -> C = 2 = C C C C
ページ3:
A (27) -> 7-a (2)²+b.2+c 7=4a+ab+c... (1) B(-67) 7 = 9 (-6)²+ b (-6)+c 7-360-6b+ C ... (ii) c (10) > 0 = a()" + b (1)+c o= a+b+c... ii) Tentukan persamaan parabola mempunyai nilai b untuk x = 0 dan x = -2 dan nilai max = 8 0+ (0)9+ (0)109 <- (910) (i) 7 7=4a+ab+c) 7=3(1)+b 7=369 +66 +C 7=3+b b = c (-2,6) -> 6 = a(-2)+ b(-2)+6 0-49-2b2 0=29-b 0 = -320 +86 :8 4-b11 0 1 -qa+b (iv) Yp = b²-4ac 8 0=1+4+c ya b=29 -21-2) i 7 = 40+2b+c fff 0 = a + b + c ==411 v 7 = 3a+b (V) 0=5+0 -5=4 y=ax fbx+c =(1)x+(4)x+(-5) x2+4x-511 [V 0=-49+b 7 = 39+ b -7--79 1 = a, + P(xp.Up) yp = nilai max/min (α<0) (a>0) -b Xp Sumbu Simetr = →>> 20 == Contoh 1) Tentukan Persamaan Parabola melalui (0,5) (2-3) dan Sumbu simetri 3 (0.5) -> 5 = 9 (0) + 6 (0) +c 5=C1 (2,-3)-3=a (2)+6(2)+5 -3=4a+2b 15 -8-49+26 = 2a+b : 2 -4= Xp. b. = 3 20 b =-69 -> b=-6(1) b = -6. -4=29-6a -4=-49 1=91 Y = 1.x + (-6)x+5 =x-6x+511 (201)-4 (9, (6)-8 -4(a) 4a-249 =-320 (4=(-2)x+(-4)x+6 4a² + 8a=0 4ȧ (a+2) = 0 C = O (TM) 9=-211 Menggambar Kurva 4 = -2x²-4x+6 = -2x-4x+b1 Cari titik potong sbx -> y=0 0 = -2x²-4x+6 x2+2x-3 (x+3)(x-1) x ==3->(-3,0711 x = -1 -> (10) // :(-2) ii) Cari titik potong 864 → x = 0 = -2(0)2-4(0)+6 y = 4-6 1016111 iii) Can titik puncak (Xp, Yp) Xp = -1-4) 4 = 2(-2) -2 -1 Yp=-(-4)-4(-2)(6)= 16-198 -4(-2) 1 8 41-118) 64 = 8, iv) Titik Banky > misal; ctnhik -45×52 X-4-228 (-4,-10) d (2,-10). 4-106-108 (-2,6) (-4) - y=-2(-4)2-4(-4)+6 =-32+16+6 = -10
ページ4:
| (11) > y = -2(-2)+4(-2). (2) Kurva 19 = 8+8+6 →>9=-2(2)-4(2)+6 E -8-8+6 9==10 19 6 -10 2 -4≤x 10 -4<x 0 Bentuk umum x = ay² + by +c axo (-) 970 (4) > cccc c c c c
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bantu ya kak..
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hallo guyss,boleh ga minta rangkuman atau materi apa aja matematika kelas 10 semester 2 ?? pliss bantu yahh butuh bangett,bagi yg berbaik hati🥹
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buatkan grafik dari 1.y=sin x 2.y=sin (x+30°) 3.y= -2 sin(x-30°)
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gusyyy adaaa anak inten enggak disiniii??? plisss butuh teman anak inten ajarin donggg mtkk buat tka soalnyaa
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jawablah dengan benar dan tepat, hitung melalui langkah langkah
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