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3 years ago

Complete the synthetic division problem below.

Mathematics

1 answer:

rewona [7]3 years ago

4 0

Answer:

Step-by-step explanation:

- 2 | 2 2 - 2 4

↓ - 4 4 - 4

--------------------------

2 - 2 2 0 ← remainder

Since the remainder = 0 then (x + 2) is a factor

quotient = 2x² - 2x + 2

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What is the value of x in 2.5(6x-4)=10+(1.5+0.5)

Alecsey [184]

Answer:

x = 22/15

Step-by-step explanation:

2.5(6x-4)=10+(1.5+0.5)

Combine like terms

2.5(6x-4)=10+(2)

2.5(6x-4)=12

Divide each side by 2.5

6x-4 = 4.8

Add 4 to each side

6x = 8.8

Divide by 6

6x/6 = 8.8/6

x = 88/60

x = 22/15

5 0

3 years ago

A certain college graduate borrows 7864 dollars to buy a car. The lender charges interest at an annual rate of 13%. Assuming tha

White raven [17]

Answer:

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = =$1573.17

Step-by-step explanation:

Consider A represent the balance at time t.

A(0)=$ 7864.

r=13 % =0.13

Rate payment = $k

The balance rate increases by interest (product of interest rate and current balance) and payment rate.

$\frac{dB}{dt} = rB-k$

$\Rightarrow \frac{dB}{dt} - rB=-k$ .......(1)

To solve the equation ,we have to find out the integrating factor.

Here p(t)= the coefficient of B =-r

The integrating factor $=e^{\int p(t) dt$

$=e^{\int (-r)dt$

$=e^{-rt}$

Multiplying the integrating factor the both sides of equation (1)

$e^{-rt}\frac{dB}{dt} -e^{-rt}rB=-ke^{-rt}$

$\Rightarrow e^{-rt}dB - e^{-rt}rBdt=-ke^{-rt}dt$

Integrating both sides

$\Rightarrow \int e^{-rt}dB -\int e^{-rt}rBdt=\int-ke^{-rt}dt$

$\Rightarrow e^{-rt}B=\frac{-ke^{-rt}}{-r} +C$ [ where C arbitrary constant]

$\Rightarrow B(t)=\frac{k}{r} +Ce^{rt}$

Initial condition B=7864 when t =0

$\therefore 7864= \frac{k}{r} - Ce^0$

$\Rightarrow C= \frac{k}{r} -7864$

Then the general solution is

$B(t)=\frac{k}{r}-( \frac{k}{r}-7864)e^{rt}$

To determine the payment rate, we have to put the value of B(3), r and t in the general solution.

Here B(3)=0, r=0.13 and t=3

$B(3)=0=\frac{k}{0.13}-( \frac{k}{0.13}-7864)e^{0.13\times 3}$

$\Rightarrow- 0.48\frac{k}{0.13} +11614.98=0$

⇒k≈3145.72

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = ${(3145.72×3)-7864}

=$1573.17

4 0

4 years ago

Solve the proportion below. 7/x=19

alexgriva [62]

Answer:

The value of x is approximately 0.3684.

Step-by-step explanation:

Given:

$\frac{7}x}=19$

We need to solve the proportion.

Solution:

Now we can see that;

In given equation one number is fraction and other number is whole number.

Now To make whole number into fraction we will divide by 1.

hence the whole number will be equal to;

$19=\frac{19}{1}$

Now the new equation will be;

$\frac{7}{x}=\frac{19}{1}$

Now by cross multiplication we get;

$7\times1=19\times x\\\\7=19x$

Now dividing both side by 19 we get;

$\frac{7}{19}=\frac{19x}{19}\\\\x\approx0.3684$

Hence the value of x is approximately 0.3684.

6 0

4 years ago

What are the square number factors of 56?

balandron [24]

Answer:

2,4,7,8,14,and 28

7 0

2 years ago

Determine whether the following system of equations has one solution, no solution, or an infinite number of solutions. Explain y

expeople1 [14]

A) 2x - 4y = 10
B) 7x - 9y = 12
Multiplying equation A by -3.5
A) -7x +14y = -35 then adding B
B) 7x - 9y = 12
5y = -23
y = -4.6

2x -4*-4.6 = 10
2x + 18.4 = 10
2x = -8.4
x = -4.2
It has one solution (-4.2, -4.6)

6 0

3 years ago