What is the equation of axis of symmetry of the given quadratic equation? * y = x2 – 8x - 9
1. What is the equation of axis of symmetry of the given quadratic equation? * y = x2 – 8x - 9
Jawaban:
x = 4
Penjelasan dengan langkah-langkah:
x = -b/2a
= -(-8)/2(1)
= 4
Jawaban:
x = 4
Penjelasan dengan langkah-langkah:
semoga membantu:)
2. 1) What is the y-intercept of the quadratic equation below? * y = x2 - 6x + 9
Penjelasan dengan langkah-langkah:
titik potong persamaan kuadrat
y = x² - 6x + 9
- titik potong terhadap sumbu y, x = 0
y = 0² + 6(0) + 9
y = 9
titik potongnya (0, 9)
- titik potong terhadap sumbu x, y = 0
x² - 6x + 9 = 0
(x - 3)(x - 3) = 0
x = 3
titik potongnya (3, 0)
3. The roots of the quadratic equation 3x²-17+45=25x-54 are......
• 3x² -17x + 45 = 25x - 54
• 3x² - 17x + 45 - 25x + 54 = 0
• 3x² - 17x - 25x + 45 + 54 = 0
• 3x² - 42x + 99 = 0
------------------------- : 3
• x² - 14x + 33 = 0
• (x-3)(x-11) = 0
~ x¹ → x-3 = 0
~ x¹ → x = 3
~ x¹ = 3
~ x² → x-11 = 0
~ x² → x = 11
~ x² = 11
The roots :
x1 = 3 & x2 = 11
→ x = { 3 , 11 }3x² - 17 + 45 = 25x - 54
3x² + 28 = 25x - 54
3x² - 25x + 82 = 0
Solve it by quadratic formula!
a = 3, b = -25, c = 82
x₁₂ = [-b +- √(b² - 4ac)] / (2a)
= {-(-25) +- √[(-25)² - 4.3.82]} / (2.3)
= (25 +- i√359) / 6
x₁ = 25/6 + (i√359) / 6 or
x₂ = 25/6 - (i√359) / 6
4. Let a and b is the roots of quadratic equation -2x-3x+2=0. The value of ab+ab is
-5x.2+-5x.2 ,this is of ab+ab i hope this answer could help you
5. 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)
6. 5. Given that m and n are the roots of equation x² – 3x + 1 = 0. Write a new quadratic equation that the roots are 5m and 5n. (Tolong bantu ya kak harus dikumpulkan 7 menit lagi)
Jawab:
[tex]x^2-15x+25=0[/tex]
Penjelasan dengan langkah-langkah:
Since m and n are the roots of [tex]x^2-3x+1=0[/tex], we have
[tex]m^2-3m+1=0[/tex] and [tex]n^2-3n+1=0[/tex].
Now, notice that
[tex]m^2-3m+1=0\\\iff 25(m^2-3m+1)=0\\\iff 25m^2-(25)(3m)+25=0\\\iff (5m)^2-15(5m)+25=0[/tex],
i.e., 5m is one of the roots of the equation [tex]x^2-15x+25=0[/tex].
In pretty much the same way, we can also show that 5n is one of the roots of this new equation. Therefore, the answer is [tex]x^2-15x+25=0[/tex]. [tex]\blacksquare[/tex]
7. Given quadratic equation y = -×2-x+20a. Find what is the zero value
Using the quadratic formula
[tex] \frac{ - b \: ± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex]x = \frac{ - ( - 1)± \sqrt{( - 1 {)}^{2} - 4( - 1)(20)} }{2( - 1)} = [/tex]
[tex] x = \frac{1± \sqrt{81} }{ - 2} = [/tex]
[tex]x1= \frac{1 + 9}{ - 2} = - 5[/tex]
[tex]x2 = \frac{1 - 9}{ - 2} = 4[/tex]
ANSWER:
X1=(-5)
X2=4
8. solve the quadratic equation below
Step by step explanation
_________
Nomor 1
_________
[tex]\begin{aligned}\rm \frac{5x+12}{3x}&=\rm x\\\rm 5x+12&=\rm 3x^2\\0&=\rm 3x^2-5x-12\\0&=\rm (3x+4)(x-3)\\&\bf x=-\frac{4}{3}~atau~x=3\end{aligned}[/tex]
_________
Nomor 2
_________
[tex]\begin{aligned}\rm \frac{20-8k}{k-5}&=\rm 3k\\\rm 20-8k&=\rm 3k^2-15k\\0&=\rm 3k^2-15k+8k-20\\0&=\rm 3k^2-7k-20\\0&=\rm (3k+5)(k-4)\\&\bf k=-\frac{5}{3}~atau~k=4\end{aligned}[/tex]
9. 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
10. the roots of the quadratic equation 2x^2+px+1=0 are α and β.Given α^2+β^2= 8 find the possible values of p.
2x² + px + 1 = 0
a = 2
b = p
c = 1
α + β
= -b/a
= -p/2
α.β
= c/a
= 1/2
α² + β² = 8
(α + β)² - 2.α.β = 8
(-p/2)² - 2(1/2) = 8
p²/4 - 1 = 8
p²/4 = 8 + 1
p²/4 = 9
p² = 9 x 4
p² = 36
p = √36
p = ± 6
p = 6
or
p = -6
11. Given one of the roots of the quadratic equation px2- 4x + 3p -8 =0 is 1 . Calculate the value of p
Jawab:
p = 3
Penjelasan dengan langkah-langkah:
salah satu akar = 1
persamaan nya= p[tex]x^{2}[/tex]-4x+3p-8 = 0
masukkan angka 1 ke persamaan:
p[tex](1^{2})[/tex] -4(1) +3p -8 = 0
p-4+3p-8 = 0
4p = 12
p=3
12. The quadratic equation ( 1 + k) xkuadrat 4kx + 9 = 0 has two distinct real number roots. The range of values of k is....
syarat memuliki 2 akar real yang berbeda adalah D > 0
D = b² - 4ac
(1 +k)x² + 4kx + 9
D > 0
(4k)² - 4(1+k)(9) > 0
16k² - 36 - 36 k > 0
4k² - 9k - 9 > 0
(4k + 3)(k - 3) > 0
k = -3/4 ATAU k = 3
_+__|__-__|__+__
-3/4 3
karena kurang dari, maka daerah yang negatif jawabannya -3/4 < x < 3
Maaf kalau salah^^
13. Given one of the roots of the quadratic equation x 2 + kx – 3 = 0 is 3. Find the value of k.
Jawaban:
x²+kx-3=0
3²+3k-3=0
9+3k-3=0
3k+6=0
3k=-6
k=-2
barangkali ada yg ditanyalan dm dan follow ig @alwi_dj
14. How to solve this question?Given that a(alpha) and B(beta) are the roots of the quadratic equation x^2-5x+4=0.Form a new quadratic equation with root 2a(alpha) and 2b(beta) [x^2-10x-16=0]
Semoga membantu dan bermanfaat.
15. What are the causes of global warming and solutions for our earth.
Jawaban:
Global warming is caused by the increase of greenhouse gases in the Earth's atmosphere. These gases, such as carbon dioxide, methane, and water vapor, trap heat from the sun, causing the Earth's temperature to rise.There are several main causes of this increase in greenhouse gases. One is the burning of fossil fuels, such as coal and oil, for energy. This releases large amounts of carbon dioxide into the air. Deforestation and land use changes, such as the conversion of forests to agricultural land, also contribute to the increase in carbon dioxide by reducing the number of trees that can absorb the gas.
To solve these issues, we can take several actions. One solution is to switch to renewable energy sources, such as solar and wind power, which do not produce greenhouse gases. We can also implement policies to reduce our reliance on fossil fuels and encourage the use of electric vehicles.
Planting trees and protecting forests can also help to absorb carbon dioxide from the atmosphere. In agriculture, we can adopt practices that reduce methane emissions from livestock, such as changing their diet and improving manure management. Overall, to solve the problem of global warming, it is important for individuals, communities, and governments to work together to reduce greenhouse gas emissions and adopt sustainable practices.
16. What are the solutions to face challenges in the era of globalization of education?
Jawaban:
We need to reinvest in dislocated communities, lower the costs and barriers to trade, match smaller firms with foreign markets, match communities with foreign investors, ensure unfettered access to cross-border digital platforms, provide greater safety net measures, update our system of unemployment insurance, provide .
17. 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)
18. what are the solutions to prevent the racism in our country ?
Jawaban:
ignored and do not be served
Penjelasan:
19. write a quadratic equation for the area of the floor in terms of w
What are the measurements?
20. given that 2 is the only root of the quadratic equation px2 + qx - 8 =0, fibd the value of p and q
PERSAMAAN KUADRAT
X SMA
It means
x1 + x2 = 4
-q / p = 4
-q = 4p
and
x1x2 = 4
-8/p = 4
p = -2
Hence,
q = -4p
q = 8
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