The basic wage earned by a truck driver for a 40-hour week is $560.00
(i) Calculate his hourly rate
For overtime work, the driver is paid one and a half times the basic hourly rate.
(ii) Calculate his overtime wage for 10 hours overtime.
(iii) Calculate the TOTAL wages earned by the truck driver for a 55-hour week.​

Combine the fractions on the left with a common denominator:

[tex]\dfrac a{x+1} + \dfrac b{x-1} + \dfrac c{(x+1)^2} = \dfrac{a(x+1)(x-1) + b(x+1)^2 + c(x-1)}{(x-1)(x+1)^2}[/tex]

It follows that

[tex]3x^2+3x-2 = a(x+1)(x-1) + b(x+1)^2 + c(x-1)[/tex]

Expand the right side and collect like powers of x :

[tex]3x^2+3x-2 = a(x^2-1) + b(x^2+2x+1) + c(x-1)[/tex]

[tex]3x^2+3x-2 = (a+b)x^2 + (2b + c)x -a +b - c[/tex]

Then we have the system of equations

[tex]\begin{cases}a+b=3\\2b+c=3\\-a+b-c=-2\end{cases}[/tex]

or in matrix form,

[tex]\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix} \begin{bmatrix}a\\b\\c\end{bmatrix} = \begin{bmatrix}3\\3\\-2\end{bmatrix}[/tex]

Compute the determinant of the coefficient matrix:

[tex]\det\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix} = -4[/tex]

Then the inverse of the coefficient matrix is equal 1/det times the adjugate of the coefficient matrix (a.k.a the transpose of the cofactor matrix):

[tex]\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix}^{-1} = \dfrac1{-4} \begin{bmatrix}-3 & -1 & 2 \\ 1 & -1 & -2 \\ 1 & -1 & 2\end{bmatrix}^\top = -\dfrac14 \begin{bmatrix}3&-1&-1\\1&1&1\\-2&2&-2\end{bmatrix}[/tex]

Multiply both sides of the equation by the inverse :

[tex]\begin{bmatrix}a\\b\\c\end{bmatrix} = -\dfrac14 \begin{bmatrix}3&-1&-1\\1&1&1\\-2&2&-2\end{bmatrix} \begin{bmatrix}3\\3\\-2\end{bmatrix} = \begin{bmatrix}2\\1\\1\end{bmatrix}[/tex]

So, we have a = 2 and b = c = 1, and the partial fraction decomposition is

[tex]\dfrac{3x^2+3x-2}{(x+1)^2(x-1)} = \dfrac 2{x+1} + \dfrac 1{x-1} + \dfrac 1{(x+1)^2}[/tex]

Answer:

Step-by-step explanation:

One can solve for a, b, c a little more directly than using a system of 3 equations.

If we multiply the rational expression by (x+1)², we get ...

  (3x² +3x -2)/(x -1) = (x+1)²(a/(x+1) +b/(x-1)) +c

Evaluating this for x = -1 gives ...

  (3(-1)² +3(-1) -2)/(-1 -1) = c

  -2/-2 = 1 = c

Similarly, multiplying by (x -1) gives ...

  (3x² +3x -2)/(x +1)² = (x -1)(a/(x +1) +c/(x +1)²) + b

Evaluating this for x = 1 gives ...

  (3·1² +3·1 -2)/(1 +1)² = b

  4/4 = 1 = b

Now, we need to find the value of 'a'. The identity will hold true for any value of x, so we can see what happens when we substitute x=0. We can use the values of 'b' and 'c' that we found above.

  (3·0² +3·0 -2)/((0 +1)²(0 -1)) = a/(0 +1) +1/(0 -1) +1/(0 +1)²

  -2/-1 = a -1 +1   ⇒   a = 2

_____

System of equations solution

When the terms of the right-side expansion are combined, the numerator of the result is ...

  a(x +1)(x -1) +b(x +1)^2 +c(x -1) = (a+b)x² +(2b+c)x +(-a+b-c) ≡ 3x² +3x -2

Equating the coefficients gives the system of equations whose augmented matrix is:

  [tex]\left[\begin{array}{ccc|c}1&1&0&3\\0&2&1&3\\-1&1&-1&-2\end{array}\right][/tex]

Transforming this to reduced row-echelon form using any of a variety of available tools gives ...

  [tex]\left[\begin{array}{ccc|c}1&0&0&2\\0&1&0&1\\0&0&1&1\end{array}\right][/tex]

which tells you the solution is (A, B, C) = (2, 1, 1).

Answer:

y= 4/1x +1

Step-by-step explanation:

the number on the y axis is the b and you do rise over run to find m you rise (so you go up or down) 4 times and run( go to the sides) once.

rise 4

-------- = -----

run 1

Answer:

y = 3x + 1

Step-by-step explanation:

Slope: As it rises 3, it runs 1

Slope = Change in y/change in x

Slope = 3/1

y - intercept = 1 ,the point of intersection

Equation : y = mx + b

m = slope

b = y-intercept

Equation : y = 3x + 1

-Chetan K

[tex]\left(\dfrac{5}{n+1}\right) \left( \dfrac{n+1}{n+3} \right)\\\\\\=\dfrac{5(n+1)}{(n+1)(n+3)} \\\\\\=\dfrac{5}{n+3}[/tex]

Answer:

there are 12 boys

Answer:

It is either 4 or 9.

Step-by-step explanation:

because you have to subtract or divide

Answer:

I believe its d

Step-by-step explanation:

168 hours I guess

have a food day

Step-by-step explanation:

This is point-slope form:

[tex]y-y1=m(x-x1)[/tex]

in this case:

[tex]y-3=-\frac{2}{3} (x+6)[/tex]

Looking at the structure of point slope form up top, you can find the slope and one point.

[tex]m=-\frac{2}{3} \\x1=-6\\y1=3\\(-6,3)[/tex]

Now, just find the graph with a slope of [tex]-\frac{2}{3}[/tex] that passes through (-6, 3). It's hard to see on the image, but that looks like the top left.

By the way, what's the "no links" thing about? I just came back to this site after a year away

Step-by-step explanation:

4x×y=20

.....

..................................

The expression for four times the product of a number x and a number y is equal to 20 is 4xy = 20.

Given,

Four times the product of a number x and a number y is equal to 20.

We need to write the expression.

- 2 times M = 2 x M

- Product of M and N = M x N

- 3 more than M = M + 3

- 3 less than M = M - 3

Find the expression.

We have,

Four times the product of a number x and a number y is equal to 20.

Here,

The product of a number x and a number y can be written as:

= (x) x y

Four times the product of a number x and a number y can be written as:

= 4 x [ (x) x y ]

- is equal to 20 can be written as:

= 20

Now,

We get,

4xy = 20

Thus the expression for Four times the product of a number x and a number y is equal to 20 is 4xy = 20.

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Answer:

Find out the value of x.

To prove

Definition of mid- segment

It is a segment connecting the midpoints of two sides of a triangle.

It is always parallel to the third side, and the length of the midsegment is half the length of the third side.

As shown in the triangle given below.

As given

DE = 5x and BC = 11x – 15

Thus

15 = 11x - 10x

15 = x

Therefore the value of x is 15 .

Step-by-step explanation:

Answer:

34800, 350000, 300000

Step-by-step explanation:

5>=5

34800

7>=5

350000

4<=5

300000

[tex] \huge \bf \color{gold} \frac{3}{5} \div \frac{2}{6} = [/tex]

[tex] \tt \frac{3}{5} \times \frac{6}{2} = [/tex]

[tex] \tt \frac{18 \div 2}{10 \div 2} = [/tex]

[tex] \tt \frac{9}{5} = [/tex]

[tex] \boxed {\color{blue}{ 1 \frac{4}{5}}}[/tex]

THE RESULT IS 1 4/5

Answer:

The solution is 9/5 and 1/5

Step-by-step explanation:

3/5÷2/6

= 3/5×6/2

= 3/5×3

= 9/5

3/5÷6/2

= 3/5×2/6

= 3/5×1/3

= 1/5

[tex](7 + 17 - 14 - 8)q = 14[/tex]

[tex](24 - 22)q = 14[/tex]

[tex]2q = 14[/tex]

Divide both sides by 2

[tex] \frac{2q}{2} = \frac{14}{2} \\ [/tex]

[tex]q = 7[/tex]

There u go...

Have a great day ❤

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{2}{3}[/tex] ← is in slope- intercept form

with y- intercept c = - [tex]\frac{2}{3}[/tex] → A

Answer: If Percentage decrease % = 20%, (1 - Percentage decrease %) = 1 - 20% = 100/100 - 20/100 = 80/100 = 0.8 => Percentage decreased number = 0.8 × Initial value

Step-by-step explanation: Number 100 decreased by 20% (20 percent) of its value (percentage decrease) and calculated absolute change (actual difference)

Answer:

60 degrees

Step-by-step explanation:

Because line ED exists, the sum of 100, 20, and x must be 180. So, just solve for x in the equation 100 + 20 + x = 180

20 + x = 80

x = 60

Answer:

{ - 5, 19, 31 }

Step-by-step explanation:

Substitute the values from the domain ( input) into f(x) to obtain range (output )

f(- 3) = 2(- 3) + 1 = - 6 + 1 = - 5

f(9) = 2(9) + 1 = 18 + 1 = 19

f(15) = 2(15) + 1 = 30 + 1 = 31

range is { - 5, 19, 31 }

Answer:

(B) 25, 36

Step-by-step explanation:

1 = 1²

4 = 2²

9 = 3²

16 = 4²

25 = 5²

35 = 6²

Answer:

1. acute

2. obtuse

3. right

4. acute

5. straight

6. obtuse

7. acute

8. obtuse

9. straight

10. ∠ EAD , ∠ CED , ∠ BCE , ∠ BEA  , ∠EBC

11. ∠CDA  , BCD

12. ∠AED ,∠BEC

13. ∠ AEC, ∠ BED

14. ∠ EAU , ∠EUI , ∠IUO , ∠OAE

15. ∠ EUO , ∠IUA

16. ∠AUO , ∠EIO

Answer:

Step-by-step explanation:

1

Answer:

the scale diagram is 9.12

We have that for the Question, it can be said that

The amount of money Janine will have to accumulate in her company’s 401(k) plan over the next 40 years is

From the question we are told

Janine is 25 and has a good job at a biotechnology company.

Janine estimates that she will need $875,000 in her total retirement nest egg by the time she is 65 in order to have retirement income of $20,000 a year. (She expects that Social Security will pay her an additional $15,000 a year.) She currently has $5,000 in an IRA, an important part of her retirement nest egg. She believes her IRA will grow at an annual rate of 8 percent, and she plans to leave it untouched until she retires at age 65. How much money will Janine have to accumulate in her company’s 401(k) plan over the next 40 years in order to reach her retirement income goal? Use Exhibit 1-A.

Generally the equation for the IRA Amount  at Retirement  is mathematically given as

IAR= 5000 * 1.08^(40)

=  108622.6

Since estimate is at

$875,000  

Therefore

Accumulation in 401,000 = 875000 - 108622.6

Accumulation in 401,000 = 766377.4

Hence

The amount of money  Janine will have to accumulate in her company’s 401(k) plan over the next 40 years is

$ 766377.4

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Answer:

z> 5/4

To graph, use the open dotted line and put it at point 5/4 aka 1.25 going towards the right because it is greater than.

Step-by-step explanation:

Isolate your variable (z) by multiplying both sides of the equation by 5/3.

z> 5/4

Answer:

x=12; y=138.

Step-by-step explanation:

1. 4x+(3x+6)=90 - to calculate 'x';

3x+6+y=180 - then to calculate 'y';

2. 7x+6=90; ⇒ x=12;

3. 3*12+6+y=180; ⇒ y=138°.

Using linear system of equations, the cost tie is £7.43.

In everyday life, we can utilize linear equations to compare prices, make predictions, create budgets, and more. When all of the variables have a highest power of one, an equation is considered to be linear. Each variable is reliant on the others. A one-degree equation is another name for this kind of equation. Continue reading to learn how to solve a linear equation in one or two variables using its standard form, formula, graph, and rules.

Given,

Haala buys 13 identical shirts and 22 identical ties for £363.01 the cost of the shirt is £15.35,

According to question,

let cost of shirt = x

cost of tie = y

Now putting it in the equation,

13x + 22y = 363.01

given x = 15.35

⇒ y = 363.01 - 13(15.35) / 22

y = 363.01 - 199.55 / 22

y = 7.43

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