For what values of h and k does the linear system have infinitely many solutions?

Mathematics

1 answer:

Sophie [7]3 years ago

7 0

Answer:

h=-32 and k=-24

Step-by-step explanation:

$4x_1 + 3x_2 = -1:a_1x_1 + b_1x_2=c_1\\hx_1 +kx_2=8:a_2x_1+b_2x_2=c_2$

For infinitely many solutions, lines must be same; $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\\\\=\frac{4}{h}=\frac{3}{k}=\frac{-1}{8}\\\\h=-32, k=-24$

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Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at

Anna007 [38]

Answer:

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84

Step-by-step explanation:

Loan payment per month=Amount to pay÷discount factor

Mathematically P=A÷D

where D is the discount factor calculated using the formula;

$\frac{(1+i)^n-1}{i(1+i)^n}$

where i=periodic interest rate=annual rate divided by number of payment periods

A is the amount to pay after downpayment

P is the loan monthly payment amount

n=number of periodic payments=payments per year times number of years

⇒In this question you find the discount factor then divide the amount remaining to pay with the discount factor to get monthly payments

Given;

Cost of boat=$32000

Down payment=$14000

Loan to pay=$32000-$14000=$18000

Annual rate=5.5%=i=5.5%÷12=0.458%⇒0.00458

Periodic payments, n=4×12=48

Finding the discount factor D;

$D=\frac{(1+i)^n-1}{i(1+i)^n} \\\\\\D=\frac{(1+0.00458)^{48} -1}{0.00458(1+0.00458)^{48} } \\\\\\D=\frac{1.2455-1}{0.005703} \\\\\\D=\frac{0.2455}{0.005703} =43.05$