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GenaCL600 [577]
2 years ago
13

Which of the following expressions represents

Mathematics
1 answer:
KatRina [158]2 years ago
5 0

Answer:

3k (m + \frac{1}{3}n)

Step-by-step explanation:

Sum of m and one - third of n is :

                                     = m + \frac{1}{3}n

Product of 3k to  the sum is :

                                     =3k \times (m + \frac{1}{3}n)

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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

To get the amount to pay monthly divide the loan to pay with the discount factor

=\frac{18000}{43.05} =418.14

Monthly payments=$418.14

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

$14000+$20070.84=$34070.84

8 0
3 years ago
HELP PLEASE!!! IM DOING A QUIZ!
Marat540 [252]

Answer:

equivalent = 30w 30(w) 30*w

the rest are non equivalent

8 0
3 years ago
Rewrite the polynomial in the form ax^2+bx+c and then identify the values of a, b, and c. 6+9x^2
Ulleksa [173]

Answer:

see below

Step-by-step explanation:

6+9x^2

Rewriting in decreasing powers of x

9x^2 +0x + 6

ax^2+bx+c

a = 9

b =0

c = 6

5 0
3 years ago
Find the roots of:
Elena-2011 [213]

\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \  2x^3-7x^2+8x-3=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

  | 2  -7    8  -3

<u>1 |      2   -5   3</u>

  | 2   -5    3  0

<u> 1 |      2     -3   </u>

    2   -3     0

So the factorization is (x-1)² (2x-3)=0. So:

                     \bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2}  }

\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \  x^3-x^2-4=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

      |  1  -1  0  -4

  <u>2  |     2  2     </u>

         1  2  2  0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

                   \bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }

\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \  6x^3+7x^2-9x+2=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

   | 6    7       9      2

<u>-2 |      -12    10     -2</u>

     6    -5     1       0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

         \bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}

                     \large\displaystyle\text{$\begin{gathered}\sf  \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}

6 0
2 years ago
A man gave half of his welfare allowance to his wife,1/5 to each of his two sons the rest to his daughter. Find the fraction giv
vichka [17]

Answer:

1/10.

Step-by-step explanation:

Total allowance=1

Half to wife so 1-1/2=1/2(Left from total)

1/5 to each son so 2/5 to both(Total for sons).

Left for daughter 1/2-2/5=1/10(Ans)

8 0
2 years ago
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