the sum of two numbers is 8. determine the two numbers such tat the sum of their squeres is minimized
1. the sum of two numbers is 8. determine the two numbers such tat the sum of their squeres is minimized
what do you want to ask ???
2. The sum of two numbers is 20. Their difference is 4. Find the two numbers.
Jawab:
Hari/Tanggal: Rabu, 15 Desember 2020
Jam: 08.57 WIB
____________________________________
a + b = 20
Difference is 4 (a - b)
So,
Elimination~
a + b = 20
a - b = 4
_________-
b + b = 16
2b = 16
b = 16/2
b = 8
Subtitution~
a - b = 4
a - 8 = 4
a = 4 + 8
a = 12
a = 12
b = 8
12 - 8 = 4
and
12 + 8 = 20
it's right :^
May Be Useful ^^
The two numbers are 12 and 8 .
PembahasanDiketahui :
The sum of two numbers is 20. Their difference is 4.
Ditanya :
Find the two numbers.
Jawab :
[tex]\text{Let two numbers are} \: \: x \: \: \text{and} \: \: y \: . \\ \\[/tex]
The sum of two numbers is 20.
[tex]x + y = 20 \\ \\ [/tex]
Their difference is 4.
[tex]x - y = 4 \\ \\ [/tex]
[tex]\text{Eliminate} \: \: y \: \: \text{to find} \: \: x \: .\\ \\ [/tex]
[tex]\begin{aligned}\\&x + y = 20\\ &x - y = 4\end{aligned} \\ \: \: \: \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } + \\ \begin{aligned}\\ \: 2x& = 24 \\ \: x& = 12\end{aligned} \\ [/tex]
Substitute x = 12 to equality x - y = 4
We get
[tex]x - y = 4 \\ \\ 12 - y = 4 \\ \\ y = 12 - 4 \\ \\ \boxed{y = 8} \\ \\ [/tex]
Kesimpulan :
The two numbers are 12 and 8 .
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Detail JawabanKelas : 8
Mapel : Matematika
Materi : Sistem persamaan linear dua variabel
Kode Kategorisasi : 8.2.5
Kata Kunci : SPLDV, eliminate, substitute, sum, difference
3. the sum of two numbers is 138 and their difference is 88.Find the two numbers
x+y=138.....pers 1
x-y=88........pers 2
x=88+y.......pers 3
substitusi pers 3 ke pers 1
x+y=138
88+y+y=138
88+2y=138
2y=138-88
2y=50
y=50/2
y=25 substitusikan ke pers 3
x=88+y=88+25=113
itu caranya. semoga membantu
4. The sum of two numbers is 20 and the sum of their squares is 272. Find the firstnumber
Jawab:
4 or 16
Penjelasan dengan langkah-langkah:
Let the numbers be x and y
x + y = 20
sum of their squares is 272 so x^2 + y^2 = 272
Find the first number,
We know that x^2 + y^2 = (x + y)^2 - 2xy
so 272 = 20^2 - 2xy
272 = 400 - 2xy
2xy = 128
xy = 64
We know that x + y = 20 and xy = 64, so we can make quadratic equation,
let a1 = x and a2 = y
a^2 - 20a + 64 = 0
(a - 16)(a - 4) = 0
a = 16 or a = 4
So the first number can be 4 or 16
If the first number less than the second, the answer is 4
Semoga terbantu :)
IG: @djie.jemmy
Jawab:
4 or 16Penjelasan dengan langkah-langkah:
If the first number is [tex]x[/tex] and the second one is [tex]y[/tex],
we can write:
[tex]x + y = 20[/tex]
[tex]x^{2} + y^{2} = 272[/tex]
Then
[tex]x = 20 - y[/tex]
Substitute [tex]x = 20 - y[/tex] to [tex]x^{2} + y^{2} = 272[/tex]
[tex](20 - y)^{2} + y^{2} = 272[/tex]
[tex]400 - 40y + y^{2} + y^{2} = 272[/tex]
[tex]2y^{2} - 20y + 128 = 0[/tex]
Factorize the equation and we get:
[tex](y-16)(y-4) = 0[/tex]
[tex]y = 16[/tex] ∨[tex]y = 4[/tex]
If we substitute [tex]y = 16[/tex] to [tex]x = 20 - y[/tex], we get [tex]x = 4[/tex]
So, we can conclude that both numbers are 4 and 16.
5. The sum of two numbers is 24. Twice the first number plus the second is 26. What are the two numbers?
Jawab:
first number = 2
second number = 22
Penjelasan dengan langkah-langkah:
first number = x
second number = y
x + y = 24
2x + y = 26
x = 24-y
2(24-y) +y = 26
48 - 2y + y =26
y = 48 - 26
y = 22
x = 24 -22
x = 2
6. The sum of two square numbers is 25².what are the square numbers?
Jawab:
Simplify 25^2 to a real number
25x25= 625
Then, find out which 2 square numbers add to become 625.
625= 20^2+15^2
625= 400+225
So, the square numbers are 20^2 and 15^2
Penjelasan dengan langkah-langkah:
Jawab:
15² and 20²Penjelasan dengan langkah-langkah:
Square number = product of the multiplication of 2 same numbers
The product of 25² =
25 × 25 =
625
The sum of two square numbers = 625
225 + 400 = 625
15² + 20² = 25²
嘉誠
7. the sum of two square numbers is 15². What are the square numbers?
Jawaban:
gambarnya mana?kok gak ada?
8. The difference between two positive numbers is 7 and the square of their sum is 289. Find the two numbers.
a - b = 7
a = b + 7
a² + b² = 289
(b +7)² + b² = 289
b² + b² + 14b + 49 - 289 = 0
2b² + 14b - 240 = 0
(2b + 30)(b - 8) = 0
2b + 30 = 0
2b = -30
b = -30/2
b = -15
a = 15
b - 8 = 0
b = 8
the two numbers are 15 and 8
9. The sum of two numbers is 14 and their differences is 2. Find the numbers!
Penjelasan dengan langkah-langkah:
jumlah dua angka adalah 14 dan perbedaannya adalah 2.temukan nomornya.
number is 8 and number 6
14 bagi 2 : 88-2 : 6
the answer is 6
10. The sum of two numbers is 262. The difference between the two numbers is 22. Find the smaller number
Jawaban:
the smaller number is 120
Penjelasan dengan langkah-langkah:
a + b = 262
a - b = 22
eliminasi b
2 a = 284
a = 284/2 = 142
a + b = 262
142 + b = 262
b = 262-142 = 120
11. The sum of two numbers is 27. One of the numbers exceeds the other by 9. Find the numbers.
Jawaban:
itu jawabannya ya maaf kl salah
Jawaban:
9 and 18
Penjelasan dengan langkah-langkah:
[tex]x = y + 9 \\ \\ x + y = 27 \\ (y + 9) + y = 27 \\ 2y + 9 = 27 \\ 2y = 27 - 9 \\ 2y = 18 \\ y = 9 \\ \\ x = y + 9 \\ x = 9 + 9 \\ x = 18[/tex]
12. The sum of two numbers is 63. The ratio of the two numbers is 4:5. Find the first number and the second number!
• first number :
4 / (4 + 5) x 63 = 28
• second number :
5 / (4 + 5) x 63 = 45
13. The sum of the squares of two consecutive positive numbers is 1105. Find the numbers.Help meee
Terdapat dua bilangan positif berurutan. Jumlah kuadrat kedua bilangan tersebut bernilai 1105. Analisis persamaan kuadrat memberikan solusi bahwa tidak ada dua bilangan positif berurutan yang memenuhi.
Penjelasan dengan langkah-langkahDiketahui:
Terdapat dua bilangan positif berurutan.
Jumlah kuadrat kedua bilangan tersebut bernilai 1105.
Ditanya: kedua bilangan tersebut
Jawab:
PemisalanMisalkan kedua bilangan tersebut termasuk bilangan bulat. Misalkan pula bilangan pertama adalah x, maka bilangan kedua yang lebih besar adalah x+1.
PersamaanJumlah kuadrat kedua bilangan tersebut bernilai 1105, dapat diubah ke dalam persamaan berikut:
x²+(x+1)² = 0
x²+x²+2x+1 = 0
2x²+2x+1 = 0
x²+x+0,5 = 0
DiskriminanKoefisien x² dan x-nya sama-sama bernilai 1, sedangkan konstantanya bernilai 0,5.
D = 1²-4·1·0,5 = 1-2 = -1 < 0
KesimpulanKarena diskriminannya bernilai negatif, maka persamaan kuadrat tersebut tidak memiliki akar real. Jadi, tidak ada dua bilangan positif berurutan yang jumlah kuadratnya bernilai 1105.
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14. two numbers are in the ratio 8 : 7. If the sum of these two numbers is 450, find the numbers.
First number=240
second number=210
15. 1. The sum of two numbers is 154 and their difference is 46. Find the two numbers. please answer
Jawaban:
x + (x + 46) = 154
x + x + 46 = 154
2x + 46 - 46 = 154 - 46
2x = 108
x = 108 ÷ 2
x = 54
x + 46
54 + 46
= 100
The two numbers are 54and 100.
16. The sum of two numbers is 27. One of the numbers exceeds the other by 9. Find the numbers.
Jawaban:
The numbers are 9 and 18
Penjelasan dengan langkah-langkah:
x + y = 27
y = x + 9
x + x + 9 = 27
2x + 9 = 27
2x = 18
x = 9
The first number: x = 9
The second number: y = x + 9 = 18
17. 6. The sum of two numbers is 183 and their difference is 71. Find the two numbers.
The sum of two numbers = 183
The difference of them = 71
Make into algebra :
a + b = 183
a - b = 71
We can use elimination or substitution method , we get :
2b = 112
b = 56
a = 71 + b
a = 71 + 56
a = 127
Then , the numbers are 127 and 56
18. The sum of two numbers is 66.4. One number is 19 times the other number. What are the two numbers?
Jawaban:
Jumlah dari dua angka adalah 66,4. Satu angka sama dengan 19 kali angka lainnya. Apa
dua angka itu?
translate nya
Penjelasan dengan langkah-langkah:
tapi maaf kurang mengerti saya
19. the sum of the squares of two consecutive even integers is 340 find the two numbers
x^2+(x+1)^2 = 85
x^2+x^2+2x+1 = 85
2x^2+2x-84 = 0
(2x - 12)(x+7) = 0
2x = 12 atau x = -7
If x = 6 maka x+1 = 7
If x = -7 maka x+1 = -6
Thus, the numbers are 6 and 7 or -7 and -6
20. he sum of two prime numbers is 85. What is the product of these two prime numbers
Dia jumlah dari dua bilangan prima adalah 85. Apa adalah produk dari dua bilangan prima ini.the prime numbers are 83 and 2
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