1. Solve for x when 16x = 2x + 56. 2. Solve for x when 14 = [tex] \frac{6 + 4x}{5x} [/tex] 3. Solve for x when 45 = 24 + 3x. 4. Solve for x if 5x2 + 20 = 1,000. 5. If q = 560 − 3p solve for p when q = 314.
1. 1. Solve for x when 16x = 2x + 56. 2. Solve for x when 14 = [tex] \frac{6 + 4x}{5x} [/tex] 3. Solve for x when 45 = 24 + 3x. 4. Solve for x if 5x2 + 20 = 1,000. 5. If q = 560 − 3p solve for p when q = 314.
1.
16x = 2x + 56
16x - 2x = 56
14x = 56
x = 56/14
x = 4
2.
[tex]14 = \frac{6 + 4x}{5x} \\ 14 \times 5x = 6 + 4x \\ 70x = 6 + 4x \\ 70x - 4x = 6 \\ 66x = 6 \\ \frac{6}{66} = x \\ \frac{1}{11} = x[/tex]
3.
45 = 24 + 3x
45 - 24 = 3x
21 = 3x
21/3 = x
7 = x
4.
5x² + 20 = 1000
5x² = 1000 - 20
5x² = 980
x² = 980/5
x² = 196
x = √196
x = 14
5.
q = 560-3p
314 = 560 - 3p
3p = 560 - 314
3p = 246
p = 246/3
p = 82
2. Solve for x...good luck
Jawab:
x = 1, x = 3, x = 2, x = -1
Penjelasan dengan langkah-langkah:
Terlampir pada gambar yaa
eksponen
x^(x² - 5x + 6) = 1
kemungkinan 1
x = 1
kemungkinan 2
x² - 5x + 6 = 0 dg syarat x ≠ 0
(x - 2)(x - 3) = 0
x = 2 atau x = 3
memenuhi
kemungkinan 3
x = -1 dg syarat (x² - 5x + 6) adalah genap
(-1)^genap = 1
uji x = -1
(-1)² - 5(-1) + 6 = 1 + 5 + 6 = 12 memenuhi syarat
x = -1
memenuhi
HP={-1,1,2,3}
3. Solve for x + 5 = 13.
Penjelasan dengan langkah-langkah:
x + 5 = 13
x = 13 -5
x = 8
semoga membantu
Jawab:
X + 5 = 13
X = 13 - 5 = 8
Penjelasan dengan langkah-langkah:
4. given the functions f(x) = x^2 - x and g(x) = x^2 - 3x - 12 a. solve the equation f(x) = 6 b. solve the equation f(x) = g(x)
Jawaban:
BSOLVETHEEQUATIONF(X)=6Penjelasan dengan langkah-langkah:
MAAFKALAUSALAH5. solve for x in 2/5x = 8.
~ MathPenyelesaian:
= 2/5x = 8
x = ?
—5 × 2/5x = 8 × 5
2x = 40
2x = 40/2
x = 20
2/5x = 8
x = 5/2 × 8
x = 5 × 4
x = 20
6. solve for x 8(3^(6-3)) = 40
[tex]8(3^{6 - x}) = 40\\3^{6-x} = 5\\^3log5 = 6 - x\\1,5 = 6 - x\\x = 6 - 1,5\\x = 4,5[/tex]
7. solve cosec (x-30°) = 2 for 0°<x<360°pliss bantuu
Himpunan penyelesaian dari [tex] \rm cosec(x-30)^o = 2[/tex] adalah {60°,180°}.
Pendahuluan :[tex]\bf\blacktriangleright Pengertian:[/tex]
Trigonometri adalah ilmu matematika yang mempelajari mengenai sudut. Contoh dari sudut yang akan dipelajari : sinus, cosinus, tangen, cosecan, secan, dan cotangen.
[tex] \\[/tex]
[tex]\bf\blacktriangleright Persamaan~Trigonometri~Umum :[/tex]
•[tex]\rm sin~x = sin~\alpha[/tex]
Kemungkinan 1 : x = α + k.360
Kemungkinan 2 : x = (180-α) + k.360
•[tex]\rm cos~x = cos~\alpha[/tex]
Kemungkinan 1 : x = α + k.360
Kemungkinan 2 : x = -α + k.360
•[tex] \rm tan~x = tan~\alpha[/tex]
Kemungkinan 1 : x = α + k.180
[tex]\\[/tex]
[tex]\bf\blacktriangleright cos(x+\alpha) \pm cos(x-\alpha) = c ~dan~sin(x+\alpha)\pm sin(x-\alpha) = c :[/tex]
•[tex] \rm sin(A+B)+sin(A-B) = 2sin~A.cos~B[/tex]
•[tex] \rm sin(A+B)-sin(A-B) = 2cos~A.sin~B[/tex]
•[tex] \rm cos(A+B)+cos(A-B) = 2cos~A.cos~B[/tex]
•[tex] \rm cos(A+B)-cos(A-B) = -2sin~A.sin~B[/tex]
[tex] \\[/tex]
[tex]\bf\blacktriangleright ax+bx = 0:[/tex]
•[tex] \rm sin~A+sin~B = 2sin\frac{1}{2}(A+B)cos\frac{1}{2}(A-B)[/tex]
•[tex] \rm sin~A-sin~B = 2cos\frac{1}{2}(A+B)sin\frac{1}{2}(A-B)[/tex]
•[tex] \rm cos~A+cos~B = 2cos\frac{1}{2}(A+B)cos\frac{1}{2}(A-B)[/tex]
•[tex] \rm cos~A-cos~B = -2sin\frac{1}{2}(A+B)sin\frac{1}{2}(A-B)[/tex]
[tex] \\[/tex]
[tex]\bf\blacktriangleright acos~x+bsin~x :[/tex]
•[tex] \rm k~cos(x-\alpha)[/tex]
•[tex] \rm k~cos(x+\alpha)[/tex]
•[tex] \rm k~sin(x+\alpha)[/tex]
•[tex] \rm k~sin(x-\alpha)[/tex]
k diperoleh dari :[tex] \rm \sqrt{a^2+b^2}[/tex]
α diperoleh dari : [tex] \rm tan~\alpha =\frac{b}{a}[/tex]
dimana : a adalah koefisien cos dan b koeofisien sin
[tex] \\[/tex]
[tex]\bf\blacktriangleright sin(A\pm B)~dan~cos(A\pm B) :[/tex]
•[tex] \rm sin(A+B) = sinA.cosB+cosA.sinB[/tex]
•[tex] \rm sin(A-B) = sinA.cosB-cosA.sinB[/tex]
•[tex] \rm cos(A+B) = cosA.cosB-sinA.sinB[/tex]
•[tex] \rm cos(A-B) = cosA.cosB+sinA.sinB[/tex]
[tex]\\[/tex]
[tex]\bf\blacktriangleright Tabel~Trigonometri:[/tex]
[tex]\rm{\boxed{ \begin{array}{c|c|c|c|c|c} \underline {{}\alpha} &\underline{\bf 0^o}&\underline{\bf 30^o}& \underline{\bf 45^o}&\underline{\bf 60^o}&\underline{\bf 90^o} \\\\ \bf sin~\alpha & 0 & \frac{1}{2} & \frac{1}{2}\sqrt{2} & \frac{1}{2}\sqrt{3} & 1 \\\\ \bf cos~\alpha & 1 & \frac{1}{2}\sqrt{3} & \frac{1}{2}\sqrt{2} & \frac{1}{2} & 0 \\\\ \bf tan~\alpha & 0 & \frac{1}{3}\sqrt{3} & 1 & \sqrt{3} & \infty \end{array}}}[/tex]
•Kuadran I (0° ≤ α ≤ 90°) = semua +
•Kuadran II (90°≤ α ≤ 180°) = sin +
•Kuadran III (180° ≤ α ≤ 270°) = tan +
•Kuadran IV (270° ≤ α ≤ 360°) = cos +
•Fungsi tetap 180 ± α atau 360 ± α
•Fungsi berubah 90 ± α atau 270 ± α (sin menjadi cos, cos menjadi sin, tan menjadi cotan)
Pembahasan :Diketahui :
[tex] \rm cosec(x-30)^o = 2[/tex] untuk 0° < x < 360°
Ditanya :
HP?
Jawab :
[tex] \rm cosec(x-30)^o = 2[/tex]
[tex] \rm \frac{1}{sin(x-30)^o} = 2[/tex]
[tex] \rm sin(x-30)^o = \frac{1}{2}[/tex]
[tex] \rm sin(x-30)^o = sin~30^o[/tex]
Kemungkinan 1 :[tex] \rm x-30 = 30+k.360[/tex]
[tex] \rm x = 30+30 +k.360[/tex]
[tex] \rm x = 60+k.360[/tex]
[tex] \rm k = 0\rightarrow x = 60^o[/tex] (M)
[tex] \rm k = 1\rightarrow x = 420^o[/tex] (TM)
Kemungkinan 2 :[tex] \rm x-30 = (180-30)+k.360[/tex]
[tex] \rm x-30 = 150+30 +k.360[/tex]
[tex] \rm x = 180+k.360[/tex]
[tex] \rm k = 0\rightarrow x = 180^o[/tex] (M)
[tex] \rm k = 1\rightarrow x = 540^o[/tex] (TM)
Kesimpulan :Jadi, HP = {60°,180°}.
Pelajari Lebih Lanjut :1) Operasi Hitung Trigonometri
https://brainly.co.id/tugas/417528882) Perbandingan Trigonometri
https://brainly.co.id/tugas/417446133) Identitas Trigonometri
https://brainly.co.id/tugas/417634574) Aturan Sinus
https://brainly.co.id/tugas/417845045) Aturan Cosinus
https://brainly.co.id/tugas/417652986) Persamaan Trigonometri Bentuk a cos x + b sin x
https://brainly.co.id/tugas/46598278Detail Jawaban :Kelas : 10Mapel : MatematikaMateri : TrigonometriKode Kategorisasi : 10.2.7Kata Kunci : Cosec, Sin, Persamaan Sederhana8. Solve for x and find the measure of the bold angle
[tex]16x - 6 = 14x + 6 \\ 16x - 14x = 6 + 6 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6 \\ \\ bold \: angle \\ 14x + 6 \\ 14.6 + 6 \\ 84 + 6 \\ 90[/tex]
9. |x-2|+|x+3|<5 solve for x plissss sekarang jugaa
Semoga paham yaa.. :))
10. 4х – 5y = 33х - 4y = 6solve for y and x
For this question, you can use elimination method
[tex]4x - 5y = 3 \\ 3x - 4y = 6 \\ - - - - - - ( - ) \\ x - y = - 3 = = > x = y - 3[/tex]
We get 3rd equation, that is x = y - 3. Substitute x = y - 3 to the 1st equation.
[tex]4(y - 3) - 5y = 3 \\ 4y - 12 - 5y = 3 \\ - y = 15 \\ y = - 15[/tex]
Finally we get the value of y. Now the last step, substitute y to the 2nd equation to get the value of x.
[tex]3x - 4( - 15) = 6 \\ 3x + 60 = 6 \\ 3x = - 54 \\ x = - 18[/tex]
Finally we get the value of x and y, x = -18 and y = -15.
■■■■■■■■■■■■■■■■■■■■﷽■■■■■■■■■■■■■■■■■■■■
4х – 5y = 3
3х - 4y = 6
■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
[tex]\left[\begin{array}{ccc}MATH\end{array}\right][/tex]
[tex]Diketahui:[/tex]
[tex]4(y-3)-5y=3[/tex]
[tex]Ditanya:[/tex]
Substitute x = y - 3[tex]Dijawab:[/tex]
[tex]4(y-3)-5y=3[/tex]
[tex]4y-12-5y=3[/tex]
[tex]-y=15[/tex]
[tex]\left[\begin{array}{ccc}y=-15\end{array}\right][/tex]
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
[tex]\left[\begin{array}{ccc}MATH\end{array}\right][/tex]
[tex]Diketahui:[/tex]
[tex]3x-4(-15)=6[/tex]
[tex]Ditanya:[/tex]
Substitute y = x - 6[tex]Dijawab:[/tex]
[tex]3x-4(-15)=6[/tex]
[tex]3x+60=6[/tex]
[tex]3x=-54[/tex]
[tex]x=-18[/tex]
• • • • • • • • • • • • • • • • • • • • • • • • • • • »Detail JawabanKelas : 9
Mapel : MATIMATEKA - FISIKA
Bab : [Kelas 9 MATIMATEKA - FISIKA Bab 2 - Substitute]
Kode : 9.22.2
Kata Kunci : Substitute x = y
11. solve for x 2^(3-x) = 565
Bab Logaritma
Matematika SMA Kelas X
2^(3 - x) = 565
²log 565 = 3 - x
3 - x = log 565 / log 2
3 - x = 2,752 / 0,301
x = 3 - 9,14
x = -6,14⇒log1023−x=log10 = 565
⇒(3−x)log10.2=2.7520
(3−x)(0.3010)=
2.7520
3−x=2.7520
0.3010=9.143
3.000−9.143=x
x=−6.143
.
12. 3 |2x - 1| + |2x - 1| = 20Solve for xdengan caranya kak, terimakasih
Jawab:
Penjelasan dengan langkah-langkah:
nilai mutlak
misalkan |2x - 1| = a , dengan a ≥ 0
3|2x- 1| + |2x - 1| = 20
3a+ a = 20
4a = 20
a= 5
|2x - 1| = 5
2x - 1 = - 5 atau 2x - 1 = 5
2x= - 4 atau 2x= 6
x= - 2 atau x = 3
13. solve for x if 1/a + x-2 = b-2
1/a + x-2 = b-2
1 + x-2 = a (b-2)
1 + x-2 = ab - 2a
x-2 = ab - 2a - 1
x = ab - 2a - 1 - 2
maka x = ab - 2a - 3
14. Form an equation in x use it to solve for X
(x + 10 + (x+8) + 28) / 4 = 15
2x + 46 = 15 . 4
2x = 60 - 46
2x = 14
x = 7
(x + 10 + x + 8 + 28) / 4 = 15
2x + 46 = 15 × 4
2x = 60 - 46
x = 14/2
x = 7
Kalau boleh jadikan jawaban terbaik yah.
15. Solve the exponential equation for
Jawaban:
x= -4
Penjelasan dengan langkah-langkah:
Itu 1 saat:
(9/8)⁰
3x+12= 0
3x= -12
x= -4
[tex]( \frac{9}{8} ) {}^{3x + 12} = 1 \\ ( \frac{9}{8} ) {}^{3x + 12} = ( \frac{9}{8} ) {}^{0} \\ 3x + 12 = 0 \\ 3x = - 12 \\ x = \frac{ - 12}{3} \\ x = - 4[/tex]
[tex] \: [/tex]
»Detail Jawaban: Mapel: Matematika Kelas: X Materi: Eksponensial#AyoBelajar!
16. Form an equation in x use it to solve for X
4 · 15 = x + 10 + x + 8 + 28
60 = 2x + 46
14 = 2x
x = 7
Sekian,semoga membantu.(x + 10 + x + 8 + 28) / 4 = 15
2x + 46 = 15 × 4
2x = 60 - 46
x = 14/2
x = 7
Kalau boleh jadikan jawaban terbaik yah.
17. 9 Given the functions f(x)= x² - x and g(x)= x² – 3x – 12,asolve the equation f(x) = 6b solve the equation f(x) = g(x).
Penjelasan dengan langkah-langkah:
a.) f(x)=6
=>6=x²-x
x² - x - 6 = 0
(x + 2) (x - 3) = 0
x = -2, and x = 3
b.) f(x) = g(x)
g(x) = 6
=>6=x²-3x-12
=> x² - 3x - 12 - 6
=> x² -3x - 18
(x - 6) (x + 3) = 0
=> x=6,andx=-3
18. Berapakah [tex]\frac{3}{2}x+5 = 6[/tex] Solve for x btw
Jawab:
2/3
Penjelasan dengan langkah-langkah:
19. Given that x = 6 and y = -4, solve 2x^2 - y^3
Answer:
136
Step-by-stepexplanation:
x = 6
y = -4
Substitution x and y
2x² - y³
= 2(6²) - (-4)³
= 2(6 × 6) - (-4 × -4 × -4)
= 2(36) - (16 × -4)
= 72 - (-64)
= 72 + 64
=136-Hope This Help-
20. Solve for x: |x-5|=2|x+1|
(x-5 +2x+2)(x-5 - (2x+2)) = 0
(3x - 3) (-x+3) = 0
x = 1 atau x = 3
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