1. 2 soal dan jawaban tentang, Menyusun Persamaan Kuadrat Baru, jika diketahui akar-akarnya (X1 dan X2 ) 2. 2 soal dan jawaban , Jumlah dan Hasil Kali akar-akar persamaan kuadrat. tolong kakak, jngn ngasal yaaa, thanks
Answer (3)
The required down payment is $13,500, and the total monthly payment for a 30-year loan at 10.0% interest rate is approximately $773.75.
To find the required down payment, we first calculate 15% of $90,000:
Down payment = 15% × $90 , 000 = 0.15 × $90 , 000 = $13 , 500
Albert Tilman needs to make a down payment of $13,500.
Next, to find the total monthly payment for a 30-year loan, we'll use the formula for the monthly payment on a fixed-rate mortgage:
M = P × ( 1 + r ) n − 1 r ( 1 + r ) n
Where:
M is the monthly payment
P is the principal loan amount (original loan amount minus down payment)
r is the monthly interest rate (annual rate divided by 12)
n is the number of payments (number of years times 12)
First, we calculate the monthly interest rate ( r ):
r = 12 × 100 10.0%
= 12 0.1
= 0.008333333
Now, we calculate the total number of payments ( n ):
n = 30 × 12
= 360
Substituting these values into the formula:
M = P × ( 1 + 0.008333333 ) 360 − 1 0.008333333 ( 1 + 0.008333333 ) 360 M = P × ( 1.008333333 ) 360 − 1 0.008333333 ( 1.008333333 ) 360
Since P = $90 , 000 − $13 , 500 = $76 , 500 , we plug this into the equation:
M = $76 , 500 × ( 1.008333333 ) 360 − 1 0.008333333 ( 1.008333333 ) 360
First, calculate (1.008333333)^{360} \
( 1.008333333 ) 360 ≈ 5.715578
Now, substitute this value back into the equation:
M = $76 , 500 × 5.715578 − 1 0.008333333 × 5.715578 M ≈ $76 , 500 × 4.715578 0.047630814 M ≈ $76 , 500 × 0.01011157 M ≈ $773.7477
So, the total monthly payment for a 30-year loan with a 10.0% mortgage rate is approximately $773.75.
Albert Tilman needs a down payment of $13,500 for a $90,000 house. His total monthly mortgage payment for a 30-year loan at a 10% interest rate is approximately $773.75.
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Jawaban:bahas bikin contoh soal dan jawaban tentang menyusun persamaan kuadrat baru dan mencari jumlah serta hasil kali akar-akar persamaan kuadrat. 1. Menyusun Persamaan Kuadrat Baru - Konsep: Jika akar-akar persamaan kuadrat baru adalah x₁ dan x₂, maka persamaan kuadratnya adalah:x² - (x₁ + x₂)x + x₁x₂ = 0 Soal 1: Susunlah persamaan kuadrat yang akar-akarnya 3 dan -5. Jawaban: 1. Identifikasi Akar:- x₁ = 3- x₂ = -52. Hitung Jumlah Akar:- x₁ + x₂ = 3 + (-5) = -23. Hitung Hasil Kali Akar:- x₁x₂ = 3 * (-5) = -154. Susun Persamaan Kuadrat:- x² - (x₁ + x₂)x + x₁x₂ = 0- x² - (-2)x + (-15) = 0- x² + 2x - 15 = 0 Jadi, persamaan kuadratnya adalah x² + 2x - 15 = 0 Soal 2: Susunlah persamaan kuadrat yang akar-akarnya 2 + √3 dan 2 - √3. Jawaban: 1. Identifikasi Akar:- x₁ = 2 + √3- x₂ = 2 - √32. Hitung Jumlah Akar:- x₁ + x₂ = (2 + √3) + (2 - √3) = 43. Hitung Hasil Kali Akar:- x₁x₂ = (2 + √3)(2 - √3) = 4 - 3 = 14. Susun Persamaan Kuadrat:- x² - (x₁ + x₂)x + x₁x₂ = 0- x² - (4)x + (1) = 0- x² - 4x + 1 = 0 Jadi, persamaan kuadratnya adalah x² - 4x + 1 = 0 2. Jumlah dan Hasil Kali Akar-akar Persamaan Kuadrat - Konsep: Untuk persamaan kuadrat ax² + bx + c = 0, jumlah akar-akarnya (x₁ + x₂) adalah -b/a, dan hasil kali akar-akarnya (x₁x₂) adalah c/a. Soal 1: Tentukan jumlah dan hasil kali akar-akar persamaan kuadrat 2x² - 5x + 3 = 0. Jawaban: 1. Identifikasi Koefisien:- a = 2- b = -5- c = 32. Hitung Jumlah Akar:- x₁ + x₂ = -b/a = -(-5)/2 = 5/23. Hitung Hasil Kali Akar:- x₁x₂ = c/a = 3/2 Jadi, jumlah akar-akarnya adalah 5/2 dan hasil kali akar-akarnya adalah 3/2. Soal 2: Tentukan jumlah dan hasil kali akar-akar persamaan kuadrat x² + 4x - 7 = 0. Jawaban: 1. Identifikasi Koefisien:- a = 1- b = 4- c = -72. Hitung Jumlah Akar:- x₁ + x₂ = -b/a = -4/1 = -43. Hitung Hasil Kali Akar:- x₁x₂ = c/a = -7/1 = -7 Jadi, jumlah akar-akarnya adalah -4 dan hasil kali akar-akarnya adalah -7.
