The sum of the squares of two consecutive positive numbers is 1105. Find the numbers.Help meee
1. 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.
Pelajari lebih lanjutMateri tentang Soal Cerita Persamaan Kuadrat (Menentukan Ukuran Kebun yang Berbentuk Persegi Panjang) pada https://brainly.co.id/tugas/33272145
#BelajarBersamaBrainly
#SPJ1
2. 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.
3. 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
4. Ans: 48 The average of 5 numbers is 12.8. What is the sum of the numbers?
Jawab:
64
Penjelasan dengan langkah-langkah:
For knowns,
Average = 12.8Have 5 numbersSum =
5 Numbers = 12.8, 12.8, 12.8, 12.8, 12.8 = 64
5. There are five positive numbers. The sum of the first and the fifth number is 15. the second number is ⅓ of the sum of these five numbers, the third number is ¼ of this sum and the fourth number is 1/5 of this sum. What is the value of the largest number? (Pakai cara)
example : the five positive numbers are a, b, c, d, and e,, the sum = x
a + e = 15
b = 1/3 x
c = 1/4 x
d = 1/5 x
otomatis a = 1/2 x dan e = 1/6 x
1/2 x + 1/6 x = 4/6 x = 2/3 x
a + e = 15
2/3 x = 15
x = 15 : 2/3
= 45/2
the value of the largest number is
a = 1/2 x = 1/2 ( 45/2 ) = 45
=>> 45
maaf kl salah
6. The sum of three numbers x, y, and z is 180. If sum of x and y is 130, sum of x and z is 110 then y+z-x equal to ....
Z =50
Y = 70
X =60
Jawabannya 60
7. 1.the average of the 4 number is 56 the first numbers is 5 more than the second .The third numbers is the half of the second and the fourth number is three time the sum of the first and second numbers Find the numbers?2.the sum of three consecutive odd numbers is 135 . Find the largest odd numbers
Jawaban :
1.
a = 29
b = 24
c = 12
d = 159
2.
47
Pembahasan :
1.
[tex]\frac{a+b +c +d}{4}[/tex] = 56
a + b + c + d = 4(56)
a + b + c + d = 224
a = 5 + b
c = [tex]\frac{b}{2}[/tex]
d = 3( a + b )
a + b + c + d = 224
5 + b + b + [tex]\frac{b}{2}[/tex] + 3(a + b) = 224
5 + b + b + [tex]\frac{b}{2}[/tex] + 3(b + 5 + b) = 224
5 + b + b + [tex]\frac{b}{2}[/tex] + 3(2b + 5) = 224
5 + b + b + [tex]\frac{b}{2}[/tex] + 6b + 15 = 224
8b + [tex]\frac{b}{2}[/tex] + 20 = 224
8b + [tex]\frac{b}{2}[/tex] = 224 - 20
8b + [tex]\frac{b}{2}[/tex] = 204
8b + [tex]\frac{b}{2}[/tex] = 204
____________ ×2
16b + b = 408
17b = 408
b = 24
a = 5 + b
a = 5 + 24
a = 29
c = [tex]\frac{b}{2}[/tex]
c = [tex]\frac{24}{2}[/tex]
c = 12
d = 3( a + b )
d = 3( 29 + 24)
d = 3(53)
d = 159
2.
a + b + c = 135
a = b - 2
c = b + 2
a + b + c = 135
b - 2 + b + b + 2 = 135
3b = 135
b = 45
c = b + 2
c = 45 + 2
c = 47
Detail Jawaban :
Mapel : Matematika
Kelas : 6
Materi : Aljabar
#AyoBelajar #BelajarBersamaBrainly
8. the sum of 4 consecutive even numbers is 68. find greatest of the 4 numbers
Jawaban:
the sum of 4 consecutive even numbers is 68. find greatest of the 4 numbers
9. the sum of three numbers a, b, and c is 240. if sum of a and b is 160 , sum of a and c is 170 then b+c-a equal to
Diketahui :
a + b + c = 240
a + b = 160
a + c = 170
Ditanya :
b + c - a = ??
Dijawab :
a + b = 160
160 + c = 240
c = 240 - 160
c = 80
a + c = 170
a + 80 = 170
a = 170 - 80
a = 90
a + b = 160
90 + b = 160
b = 160 - 90
b = 70
Jadi b + c - a = 70 + 80 - 90 = 60
10. two consecutive even numbers are such that the sum of their squares is 146. Find the two numbers
Jawaban:
dua bilangan genap berurutan sehingga jumlah kuadratnya adalah 146. Tentukan kedua bilangan tersebut
Penjelasan dengan langkah-langkah:
x+(x+2)= 146
2x = 144
x = 72
bilangan genap terbesar = x+2
= 72 +2 = 74
11. 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
12. 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]
13. There are two numbers such that their difference is 7 and the difference of their squares is 175, sum of the numbers = ?
Jawab:
a+b = 25
Penjelasan dengan langkah-langkah:
Dik:
a-b = 7
[tex]a^{2} -b^{2} = 175[/tex]
Dit? a+b
(a+b)(a-b) = 175
(a+b)(7) = 175
a+b = 175/7
a+b = 25
14. 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 ???
15. If the sum of three consecutive numbers is 72, what is the largest number? *this is algebra word problem
X+x+1+x+2=72
3x=72-2-1
3x=69
X=23
Largest number :
X+2
23+2
25
16. Three numbers are in the ratio of 5: 6: 7. What is the smallest number if the sum of the three numbers is 72? pls help thanks ❤
Jawab:
the smallest number is 20.
Penjelasan dengan langkah-langkah:
cmiiw
17. the sum of three numbers in a row is 90. Find the three numbers!
misal
angka pertama = a
angka kedua= a+1
angka ketiga = a+2
maka
a+a+1+a+2= 90
3a+3=90
3a=87
a=29
angka pertama =a = 29
angka kedua=a+1=29+1=30
angka ketiga=a+2=29+2=31
coba cek . 29+30+31=90
itu menurutku, kalau salah mohon koreksinya ya
18. =QUIZ=On each of the three separate pieces of paper there is a three-digits number. The sum of the three numbers is 826. What is the sum of the two hidden digits?
243 + 157 + 426 = 826
So the answer is 5 + 4 = 9
19. the sum of 3 odd numbers is 45. find the three numbers
Jawaban:
Odd numbers artinya angka ganjil.
3 odd numbers artinya 3 angka ganjil.
Penjumlahan 3 angka ganjil yg hasilnya 45, maka bilangan tersebut adalah 15.
45/3=15 → 15+15+15=45#sejutapohon20. The sum of three consecutive odd numbers is 111. Find the product of the 3 numbers.
Because they're only odd numbers, the gap is 2.
n + (n+2) + (n+4) = 111
3n + 6 = 111
n = 105 / 3
n = 35
--
The numbers are 35, 37, and 39 (n, n+2, and n+4)
<3
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