find the equation of the straight line which has a gradient of 2 and which passes through the point (2,1).
1. find the equation of the straight line which has a gradient of 2 and which passes through the point (2,1).
y-y1=m(x-x1)
y-1=2(x-2)
y=2x-4+1
y=2x-3
mungkin gitu(?)
2. Let p; q be the solutions of the quadratic equation x^2 - 2mx - 5n = 0 and let m; n be the solutions of x^2 - 2px - 5q = 0. If p 6= q 6= r 6= s, then the value of p + q + m + n is ....
pembahasan terlampir
3. Let p; q be the solutions of the quadratic equation x^2 - 2mx - 5n = 0 and let m; n be the solutions of x^2 - 2px - 5q = 0. Then the value of p + q + m + n is ....
p + q = -b/a = -(-2m)/1 = 2m
m+n = -b/a = -(-2p)/1 = 2p
p + q + m + n = 2m + 2p = 2(m + p)
4. Equation & Different of cinderella and rapunzel?
Equation : They both has a stepmother
They both are isolated
They both married to a prince
Different : Cinderella is actually not a princess, Rapunzel is a princess
Rapunzel has no step sisters, Cinderella has step sisters
Cinderella saved by her shoes, Rapunzel saved by her hair
5. If the equation 4x2 - 12x + c = 0, where c is a constant, has two equal roots, find the value of c and the roots of the equation.
Jawaban:
(2x-3)(2x-3)
4x²-6x-6x+9
4x²-12x+9
c=9
6. the quadractic equation 2x²+hx-6k=0 has roota a and B. The quadractic equation 3x²+1=h+12x also has roots a and B. Find the value h and k
GATAU LAH CARI SENDIRI
7. Suppose (x^2 + x − 1)^x−2 = 1 , the number of solutions of the equation is .... (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
(x²+x-1)^(x-2)=1
(x²+x-1)^(x-2)=(x²+x-1)^0
x-2=0
x=2
(B)2
8. There are 3 types of solutions based on their concentration; hypotonic, isotonic, and hypertonic. Take salt-water for example, hypotonic salt-water has less than 0,45% salt concentration. Isotonic salt-water has 0,9% concentration of salt. Hypertonic salt-water has more than 0,9% concentration of salt. Explain what happen to an animal cell inside each of those solutions!
Jawaban:
pohon-pohon zoo di go ko
9. |3x + 5) = 8. Find all values of x which make this equation true.
Jawaban:
1, -13/3
Penjelasan dengan langkah-langkah:
|3x + 5| = 8
if 3x + 5 positive:
3x + 5 = 8
3x = 8 - 5 = 3
Hence x = 1
if 3x + 5 negative:
-3x - 5 = 8
-3x = 8 + 5 = 13
Hence x = -13/3
10. The line equation which is trough point (-3,7) and having gradient -2 is
(y-y1) = m (x-x1)
(y-7) = -2 (x-(-3))
y-7 = -2 (x+3)
y-7 = -2x -6
y+2x = -6 +7
y+2x = 1 atau -2x-y = -1
11. An object has a position equation of 2t²+4t-8 the equation of the velocity sector for the object is
Kinematics.
x = 2t² + 4t - 8
v = dx / dt
= 4t + 4
12. Find the value of m which the equation x^2+ (m – 3)x + 4 = 0 has two real roots.
• Persamaan Kuadrat
-
Nilai m agar x² + (m - 3)x + 4 = 0 memiliki 2 akar - akar real adalah m ≤ -1 atau m ≥ 7
• Pembahasan •
D ≥ 0 → Memiliki dua akar - akar reaL
x² + (m - 3)x + 4 = 0
a = 1
b = m - 3
c = 4
0 ≤ b² - 4ac
0 ≤ (m - 3)² - 4(1)(4)
0 ≤ m² - 6m + 9 - 16
0 ≤ m² - 6m - 7
0 ≤ (m + 1)(m - 7)
HP = { m ≤ -1 atau m ≥ 7 }
•••
-AL
Jawab:
m ≥ 7 atau m ≤ - 1
Penjelasan dengan langkah-langkah:
akan memiliki akar akar bilangan real jika D ≥ 0
bentuk umum persamaan kuadrat adalah ax² + bx + c = 0, maka dari soal diperoleh
a = 1
b = m - 3
c = 4
karena D ≥ 0, maka
D ≥ 0
b² - 4ac ≥ 0
(m-3)² - 4.1.4 ≥ 0
m² - 6m + 9 - 16 ≥ 0
m² - 6m - 7 ≥ 0
(m - 7)(m + 1) ≥ 0
maka didapat m ≥ 7 atau m ≤ -1
jadi, HP = {m | m ≥ 7 atau m ≤ - 1}
13. If x and y are the solutions of equation system: 7x + 2y = 19 and 4x − 3y = 15, the value of 3x − 2y is.... * A. -9 B. -3 C. 7 D. 11
Jawaban:
D.11
Penjelasan dengan langkah-langkah:
7x+2y=19 (×3) → 21x+6y=57
4x-3y=15 (x-2) → -8x+6y=-30
Eliminasi
29x=87
x=3
Substitusi
12-3y=15
-3y=3
y=-1
3(3)-2(-1)
9+2
11
Jawab:
Penjelasan dengan langkah-langkah:
(Terlampir)
14. Different & Equation of cinderella and rapunzel?
different: #Cinderella have 2 sisters, but Rapunzel don't have sister or sibling
#Cinderella's parent is not king and queen, but Rapunzel's parent is king and queen.
Equation: #Cinderella and rapunzel's hair is blonde
# Cinderella and Rapunzel was meet with them true love
15. The equation mx^2+nx+2n=8x+4 has the roots n and 1/m, m≠0. (a) Find the value of m and of n. (b) Hence, using the value of m and of n in (a),find the quadratic equation that has the roots 2m and - 1/n. .
Penjelasan dengan langkah-langkah:
It's known that:
f(x) → mx² + nx + 2n = 8x + 4
f(x) → mx² + nx - 8x + 2n - 4 = 0
f(x) → mx² + x(n-8) + (2n - 4), has roots:
x1 = n x2 = 1/m
it's also known that there is a formula for a quadratic equation f(x) → ax² + bx + c = 0 which has roots x1 and x2, so it can be applies:
x1 + x2 = -b/a
x1 × x2 = c/a
in the question:
a = m b = (n-8) c = (2n-4)
a. x1 + x2 = -b/a
n + 1/m = -((n-8)/m)
(nm+1)/m = -((n-8)/m)
nm+1 = -n+8
nm+n = 7 ..................... (1) 4m + 4 = 7 → m = ¾
x1 × x2 = c/a
n×1/m = (2n-4)/m
n = 2n-4
4 = n
b. x1 = 2m = 2.¾ = 3/2
x2 = -1/4
x1 + x2 = -b/a x1 × x2 = c/a
3/2 - ¼ = -b/a 3/2 × (-¼) = c/a
5/4 = -b/a -⅜ = c/a
10/8 = -b/a
b= -10
a = 8
c = -3
g(x) = 8x² - 10x - 3
16. make an equation of the line that has a gradient in the middle and through (3,-4)
The equation of the line that has a gradient in the middle and through (3 , -4) is y = [tex]\tt - \dfrac {4}{3} x[/tex]
MoreExplanation:Gradient is a straight line that shows how steep the straight line is. The gradient is usually symbolized as m.
Gradient formula :
• through one coordinate, m = [tex]\tt \dfrac {y}{x}[/tex]
• through two coordinates, m = [tex]\tt \dfrac {y_2 - y_1}{x_2 - x_1}[/tex]
Equationofastraightlinethathasagradientformula:
• through one coordinate, [tex]\tt y - y_1 = m\ (x - x_1)[/tex]
• through two coordinates, [tex]\tt \dfrac {y - y_1}{y_2 - y_1} = \dfrac {x - x_1}{x_2 - x_1}[/tex]
• through two parallel lines, [tex]\tt m_1 = m_2[/tex]
• through two perpendicular lines, [tex]\tt m_1 \times m_2 = -1[/tex]
Tobeknown:
a line has a gradient in the middle and through (3 , -4)
Tobeasked:
The equation of the line = . . . . ?
Tobeanswered:
Because the straight line is through one coordinate,
m = [tex]\tt \dfrac {y}{x}[/tex]
m = [tex]\tt - \dfrac {4}{3}[/tex]
Equation :
[tex]\tt y - y_1 = m(x - x_1)[/tex]
y - (-4) = [tex]\tt - \dfrac {4}{3}[/tex] (x - 3)
y + 4 = [tex]\tt - \dfrac {4}{3} x - \dfrac {4}{3} \times -3[/tex]
y + 4 = [tex]\tt - \dfrac {4}{3} x + 4[/tex]
y = [tex]\tt - \dfrac {4}{3} x + 4 - 4[/tex]
y = [tex]\tt - \dfrac {4}{3} x[/tex]
Conclusion:
The equation of the line that has a gradient in the middle and through (3 , -4) is y = [tex]\tt - \dfrac {4}{3} x[/tex]
LearnMore:how to find the equation in which the gradient is known and through one coordinate https://brainly.co.id/tugas/25571198how to find the equation in which the gradient is known and through two coordinates https://brainly.co.id/tugas/25559882how to find the equation in such two parallel lines and through one coordinate https://brainly.co.id/tugas/25544954Detail:Subject : Math
Class : VIII (National School) or IX (Integrated School)
Chapter : Straight Lines Equation
Code : 8.2.3.1
Key Words : gradient, straight lines, equation
17. Which equation represents the standard enthalpy change of formation of water .....
Jawaban:
equation represents the standard enthalpy change of formation of water
is 2H2(g)+O2(g)→2H2O(l)
18. The number of solutions for the following equation: |x+1|+|x—2| = 4 is .... (A) 6 (B) 5 (C) 4 (D) 3 (E) 2
|x + 1| + |x - 2| = 4
Ix + 1 + x - 2 = 4
2x - 1 = 4
2x = 5
x = 5/2
IIx + 1 + x - 2 = -4
2x - 1 = -4
2x = -3
x = -3/2
19. (i) If x = 5 is a solution of the equation x^2 - qx + 10 = 0, find the value of q.(ii )Hense, find the other solutions of the equation.(i) q =(ii) x =
Penjelasan dengan langkah-langkah:
x²-qx+10=0
5²-5q+10=0
25+10=5q
35 = 5q
q = 7
x²-7x+10 = (x-5)(x-2)
x=5 atau x=2
20. Help asap.find the equation of line is thatline passes the point A -3,67 and hasgradient 1/2
pgl
-
I think the line passes point A (-3 , 6) with gradient 1/2 !
here your answer :
y - y₁ = m (x - x₁)
y - 6 = 1/2 (x + 3)
2y - 12 = x + 3
x - 2y + 15 = 0
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