the sum of the squares of two consecutive even integers is 340 find the two numbers
1. 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
2. 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
3. The sum of two consecutive positive integers is greater than 26 and less than 37. Find all possible values of the smaller of the two integers
Jawab:
Penjelasan dengan langkah-langkah:
4. the sum of two consecutive even numbers is 38.find the smallest number of the even numbers. tolong saya kesulitan
x = smallest number
x + x + 2 = 38
2x × 2 = 38
2x = 36
x= 18
5. 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
6. the sum of integers is 82,and the different is 26.the multiplication of those integers is
A + B = 82
A - B = 26
A = [tex] \frac{(82 + 26)}{2} [/tex] = 54
B = 54 - 26 = 28
A x B = 54 x 28 = 1512
7. the areas of two squares are 64 cm² and 16 cm².what is the difference between the lengths of the squares ?
Penjelasan dengan langkah-langkah:
area of square = side x side
64cm2 = side x side
side( length) = 8cm x 8cm
the length of 64cm2 square is 8cm
16cm2 = 4cm x 4cm
the length of 16cm2 square is 4cm
The difference = 8cm - 4cm = 4cm
8. ________ are numbers that represents the products of consecutive positive integers.
Jawabannya: zero (nol)
Pesan: maaf kalau salah, semoga membantu
9. 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
~CrystalMeth@brainly.co.id
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. Suppose that the sum of n consecutive integers (included positive integers, 0 and negative integers) is 55, find the largest value of n.
1+2+3....m=½m(m+1)
-1-2-3....-k=-½k(k+1)
m=54
k=54
sm+sk=0
max n
-54-53-...-3-2 -1+0 1+2+3...54= 0
-54-53-...-3-2 -1+0+1+2+3...54 +55=55
n=2*54+2=110
12. the sum of consecutive odd numbers is 56 .Find the greatest of the 4 numbers pakai cara y jgn asal
Jawaban:
Let first number be x
Then second odd number = x + 2
Third odd number = x + 4
Fourth odd number = x + 6
Adding them all
x + (x +2) + (x +4) + (x + 6) = 56
4x + 12 = 56
4x = 44
x = 11
Greatest odd number is x + 6.
So, answer is 11 + 6 = 17
Thank you.
13. 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
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. What is the greatest number of consecutive integers whose sum is 45 ?
Jawaban:
49
47 + 48 + 49 = 144
The greatest number = 49
16. If the sum of 5 different positive integers is 100, what is the greatest possible value for the median of the 5 integers? jawab pake cara yes thanks
let the numbers are a, b, c, d , and e with a < b < c < d < e
obvious, c as the median. to get the greatest median, then the first of 2 numbers must be minimum ((a,b) = (1,2) , (1,3), ... etc)) and the 3 last numbers (c,d, and e) are consecutive positive integers.
just trials :
if a = 1 and b = 2, then supposed c = x , d = x+1, and e = x + 2
give us :
1 + 2 + x + x + 1 + x + 2 = 100
3x + 6 = 100
3x = 94
x = 94/3 = 31.33 (it is not an integer)
others :
if a = 1 and b = 3, then let c = x, d = x+1, and e = x+2,
give us :
1 + 3 + x + x + 1 + x + 2 = 100
3x + 7 = 100
3x = 100 - 7
3x = 93
x = 93/3 = 31
therefore, the greatest possible value as the median is 31
17. 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.
18. the sum of 2 consecutive positive integers and their product is 271. Find the intergers
x + (x+1) + x(x+1) = 271
2x + 1 + x^2 + x = 271
x^2 + 3x - 270 = 0
(x+18) (x-15)
x = -18 or x = 15
(x+1) = - 17 or x = 16
SEMOGA MEMBANTU
MAAF APABILA ADA KESALAHAN
19. Find three consecutive odd integers such that the sum of the first, two times of the second, and three times of the third is 70.
Jawab:
PenjelasanTemukan tiga bilangan bulat ganjil yang berurutan sehingga jumlah dari yang pertama, dua kali yang kedua, dan tiga kali yang ketiga adalah 70. dengan langkah-langkah:
MAAF HANYA INI SAJA YANG BISA SAYA BANTU:)
20. There are 3 consecutive even integers. Let x be the smallest number. i. Express the other two integers in terms of x ii. If the sum of these 3 integers is 66, find the integers.
(x) + (x+2) + (x+4) = 66
3x + 6 = 66
3x = 66 - 6
3x = 60
x = 60 ÷ 3
x = 20
x = 20
x + 2 = 22
x + 4 = 24
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