For a 7 1/2 hour day, Ed makes $90. How much does he make in 1 hour?

Hello, please consider the following.

When you have a complex number in the denominator you need to multiply by its conjugate to eliminate the imaginary component.

The conjugate of 4 - 3i is 4 + 3i, right?

So, let's do it!

[tex]\dfrac{5-7i}{4-3i}=\dfrac{(5-7i)(4+3i)}{(4-3i)(4+3i)}\\\\=\dfrac{5(4+3i)-7i(4+3i)}{4^2-(3i)^2}\\\\=\dfrac{20+15i-28i-21i^2}{16+9}\\\\=\dfrac{20+21-13i}{25}\\\\\large \boxed{=\dfrac{41}{25}-\dfrac{13}{25}i\\}[/tex]

Thank  you.

Complex numbers are numbers with real and imaginary parts.

The expression in standard form of a complex number is: [tex]\mathbf{\frac{41}{25}-\frac{13}{25}i}[/tex]

The expression is given as:

[tex]\mathbf{\frac{5 - 7i}{4 - 3i}}[/tex]

Rationalize

[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{5 - 7i}{4 - 3i} \times \frac{4 + 3i}{4 + 3i}}[/tex]

[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{20 +15i -28i - 21i.i}{(4)^2 - (3i)^2}}[/tex]

[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{20 +15i -28i - 21(-1)}{16 - 9(-1)}}[/tex]

[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{20 +15i -28i + 21}{16 + 9}}[/tex]

Collect like terms

[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{20 + 21+15i -28i }{16 + 9}}[/tex]

[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{41-13i }{25}}[/tex]

Split

[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{41}{25}-\frac{13i }{25}}[/tex]

[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{41}{25}-\frac{13}{25}i}[/tex]

Hence, the expression in standard form of a complex number is: [tex]\mathbf{\frac{41}{25}-\frac{13}{25}i}[/tex]

Read more about complex numbers at:

https://brainly.com/question/12806985

Answer:

The equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex].

Step-by-step explanation:

We are given the following table representing the two quantities below;

x        y

2       3

4       4

6       5

8       6

Firstly, we will find the two-point slope here, that is;

Consider two points; ([tex]x_1,y_1[/tex]) = (2, 3) and ([tex]x_2,y_2[/tex]) = (4,4)

Now, the formula for finding slope is;

Slope =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          =  [tex]\frac{4-3}{4-2}[/tex]  =  [tex]\frac{1}{2}[/tex]

Similarly, finding the slope for the points (6,5) and (8,6);

Slope =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          =  [tex]\frac{6-5}{8-6}[/tex]  =  [tex]\frac{1}{2}[/tex]

Now, the linear equation of the line having slope is given by;

[tex]y-y_1=m\times (x-x_1)[/tex]  ; where m = slope and consider ([tex]x_1,y_1[/tex]) = (2, 3)

So, the equation of the line is;

[tex]y-3=\frac{1}{2} \times (x-2)[/tex]

[tex]y-3=\frac{1}{2}x-1[/tex]

[tex]y=\frac{1}{2}x+2[/tex]

Hence, the equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex].

Answer:

y = -1/2x + 11

Answer:

58-(14)2

58-28

30

Step-by-step explanation:

Answer:

D={3,9}

The numbers are 3 and 9

Step-by-step explanation:

The set A

={,,,,,,,,,}

Let B be the sub set of A containing odd numbers

B={1,3,5,7,9}

Let C be the sub set of A containing multiply of 3

C= {3,6,9}

Now let D be the be the sub set of A containing both odd numbers and multiples of 3

D={3,9}

The value of x will be 50 degrees. The correct option is B.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The opposite angles of the parallelogram are equal and the sum of the adjacent angles of the parallelogram is 180 degrees.

Angle A is 130 degrees then angle F will also be 130 degrees. The angle E will be calculated as below:-

∠F + ∠ E = 180

130 + ∠E = 180

∠E = 180 - 130

∠E = 50

Therefore, the value of x will be 50 degrees. The correct option is B.

To know more about parallelogram follow

https://brainly.com/question/331095

#SPJ2

Answer:

  5 pounds

Step-by-step explanation:

The only thing added or removed from the container was heat, which has no weight. The water has the same weight regardless of its chemical phase (solid, liquid, gas, plasma).

  5 pounds

Answer:

The question is not complete, but I found a similar question (image) that applies to this case:

The correct answer is:

Point N ( or where the arc cuts the horizontal line)

Step-by-step explanation:

From the figure attached to this answer, to copy angle  in the first image on the left onto the inage in the right, Kendric first of all places tha centre of the compass at point M, and extends it to point N, to draw the first arc, which has already been done.

1. Next, the center of the compass should be placed at point N, and extended to the point where the arc touches the inclined line.

2. This measurement is then transferred to the new line, and the center of the compassed placed at point D, and a second arc drawn to cut the first arc.

3. Finally a line is drawn through the point where the two arcs meet to touch point C.

Answer:

No

It could be purely due to chance.

Step-by-step explanation:

A population is defined as the whole group which has the same characteristics. For example a population of the college belongs to the same college . But a sample may be an element of a population.

So it is not necessary for a population to have the same characteristics as the sample.

But it is essential for the sample to have at least one same characteristics as the population.

So we would not be correct in inferring that such a relationship also exists in the population.

It is a hypothesis which can be true or false due to certain conditions or limitations as the case maybe.

For example in a population of smokers some may be in the habit of taking cocaine. But a sample of cocaine users does not mean the whole population uses it.

It could be purely due to chance if we find out that there is a relationship between parents’ and children’s party identification in the population.

Answer:

8x−14

Step-by-step explanation:

3x - 4 + 5x - 10

=3x+−4+5x+−10

Combine Like Terms:

=3x+−4+5x+−10

=(3x+5x)+(−4+−10)

Answer:

x - 6 = 0

Step-by-step explanation:

The only lines that have undefined slopes are vertical lines. Vertical lines are found in the form x = c where c is a constant. With vertical lines, it doesn't matter what the y value is because x will always be c. In this case, c = 6 because the x-coordinate of (6, -1) is 6. Therefore, our equation is x = 6. In standard form, that would be x - 6 = 0.

Answer:

[tex]\huge \boxed{x-6=0}[/tex]

Step-by-step explanation:

Vertical lines have undefined slopes.

The line crosses (6, -1), x = 6.

The equation of the vertical line is x = 6.

The equation of the line in standard form would be x - 6 = 0.

Answer:

The cost of a chicken shawarma wrap = $10.99

The cost of an order of spiced potatoes=$4.99

Equations needed

3x+2y =42.95

5x + 4y=74.91

Step-by-step explanation:

x = the cost of a chicken shawarma wrap

y = the cost of an order of spiced potatoes

Ms. Ironperson

3x+2y =42.95

Mr. Thoro

5x + 4y=74.91

3x+2y =42.95 (1)

5x + 4y=74.91 (2)

Multiply (1) by 2

6x + 4y=85.9 (3)

5x + 4y=74.91. (2)

Subtract (2) from (3)

6x - 5x= 85.9 - 74.91

x=$10.99

Substitute the value of x into (1)

3x+2y =42.95 (1)

3(10.99) + 2y =42.95

32.97 + 2y = 42.95

2y = 42.95 - 32.97

2y=9.98

Divide both sides by 2

y=9.98/2

=4.99

y=$4.99

Therefore,

The cost of a chicken shawarma wrap = $10.99

The cost of an order of spiced potatoes=$4.99

Answer:

Work done = 3750 Joules

Step-by-step explanation:

The force acting in the body should be resolved to it's horizontal component before we can use ut to solve for the problem

Horizontal component= 150 * cos 60

Horizontal component= 150*0.5

Horizontal component= 75N

Work done= Force * distance

Work done= 75*50

Work done= 3750 Nm

Work done = 3750 Joules

Answer:

2n+2

Step-by-step explanation:

-n + (-3) +3n + 5 -3

       (-3+5)  =2  

-n +2+n+3n

3n-n =  2n

2n+2

Answer:

last option from the left

Step-by-step explanation:

To find the price of one water bottle, we can calculate 6 / 24 because 24 bottles cost $6. Now, to find the price of 10 bottles, we can multiply the price of 1 bottle by 10 so the answer is 6 / 24 * 10.

Answer:

310%

Step-by-step explanation:

310% can be expressed as a mixed number because 150% would be 1 1/2.

310% would be 3 1/10.

Answer:

Future amount (A) = $1,258.77 (Approx)

Step-by-step explanation:

Given:

Amount deposit (p) = $693

Rate of interest monthly (r) = 4.9% / 12 = 0.003833

Number of month (n) = 13 × 12 = 156

Find:

Future amount (A)

Computation:

[tex]A = p [1+r]^n \\\\ A = 693 [1+0.003833]^{156}\\\\ A= 693[1.8163]\\\\ A = 1258.77[/tex]

Future amount (A) = $1,258.77 (Approx)

Answer:

I may be incorrect but these are my answers

A) −400≤x≤3,400 and −1≤y≤11 NO

B) −1≤x≤11 and −400≤y≤3,400 YES

C) −1≤x≤11 and −1≤y≤321 YES

D) −400≤x≤3,400 and −400≤y≤321 YES

Step-by-step explanation:

The last three equations, B, C ,D all include the points needed to graph the total number of bricks he can lay in 0 to 10 days.

Answer:

Don't delete my answers!

No

Yes

Yes

Yes

I was doing the QUIZ!

Step-by-step explanation:

Answer:

[tex]$ \frac{2187 \pi}{4}$[/tex]

Step-by-step explanation:

Using Stoke's theorem, we get

[tex]$ \int \int_S curl F.dS = \int_C F.dr$[/tex]

Now parametrize C

r(t) = ( 3 cos t, 3 - 3 sin t )     where, t in [0 2π]

[tex]$ \int_C F. dr= \int_0 ^{2 \pi}F ( 3 \cos t, 3 - 3 \sin t). r'(t)dt$[/tex]

            [tex]$= \int_0^{2 \pi}(( 9 \cos^2 t)(27)(-3\sin t), \sin t \times (-27 \cos t \sin t)) . (-3 \sin t, 0 - 3 \cos t) dt $[/tex]

           [tex]$ = 27 \int_0^{2 \pi} 81 \cos ^2 t \sin ^2 t + 3 \cos ^2 t \sin tdt $[/tex]

           [tex]$ = 27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2t+27 [ - \cos^3 t]_0^{2 \pi}$[/tex]

           [tex]$ = 27 \times \frac{81}{4} \int_0^{2 \pi} \frac{(1- \cos 4t)}{2} $[/tex]

           [tex]$= \frac{2187}{8}[t-\frac{1}{4} \sin 4t]_0^{2 \pi} $[/tex]

           [tex]$= \frac{2187 \pi}{4}$[/tex]

By using Stokes Theorem the required S curl F.ds is [tex]\dfrac{2187\pi }{4}[/tex].

Given that,

Function F(x, y, z) = (x^2y^3z)i + sin(xyz)j + xyzk,

S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y =3, oriented in the direction of the positive y-axis.

We have to determine,

Use Stokes' Theorem to evaluate S curl F·dS.

According to the question,

By using Stokes Theorem to evaluate S curl F .dS.

[tex]\int\ \int _s curlF.ds = \int _c F.dr\\\\[/tex]

Now parametrize C

r(t) = ( 3 cos t, 3 - 3 sin t ) ,

Where, t in [0 2π]

Then,

[tex]\int_c F.dr = \int^{2\pi }_0 F(3cost, 3-3sint).r'(t)dt\\\\[/tex]

[tex]= \int^{2\pi }_0 ((9cos^2t)(27)(-3sint),(sint) \times (-27cost.sint). (-3sint,0-3cost)dt\\\\= 27 \int^{2\pi }_0 81cos^2t .\ tsin^2t + 3 cos^2t. t sintdt\\\\= 27 \int^{2\pi }_0 \dfrac{81}{4}sin^22t+ 27[-cos^3t]^{2\pi }_0\\\\= 27 \times \dfrac{81}{4} \int^{2\pi }_{0} (\dfrac{1-cos4t}{2})\\\\= \dfrac{2187}{8}[t-\dfrac{1}{4}sin4t]^{2\pi }_0\\\\= \dfrac{2187}{8}[2\pi -\dfrac{1}{4}sin4(2\pi )- 0-\dfrac{1}{4}sin4(0 )]\\\\= \dfrac{2187\pi }{4}[/tex]

Hence, By using Stokes Theorem the required S curl F.ds is [tex]\dfrac{2187\pi }{4}[/tex].

To know more about Integration click the link given below.

https://brainly.com/question/17207150

Answer:

8.9375

Step-by-step explanation:

2.75×3.25=8.9375

According to the question it said increase to and that is why I only multiplied but if the question said increase by then I would have to add my product (8.9375) to the original height of the photo.

Answer:

It shows for each gallon consumed, we multiply by 30 to get the amount of miles

This applies for the three questions

Step-by-step explanation:

10 gallons and 300 miles are related in such a way that you divide the number if miles by number of gallons.

300/10 = 30 miles per gallon.

It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.

5 gallons ad 150 miles related in such a way that you divide the number if miles by number of gallons.

150/5 = 30 miles per gallon.

It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.

1 gallon and 30 miles related in such a way that you divide the number if miles by number of gallons.

30/1= 30 miles per gallon.

It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.

Answer:

Hey there!

We don't have enough information. 7(n+5) can be written as either the 7 times the sum of n+5, or 7 multiplied by n+5.

Let me know if this helps :)

Answer:

[tex]\sqrt{11.5} =w[/tex] (Width)

[tex]4\sqrt{11.5}= Length[/tex]

Step-by-step explanation:

Area of a rectangle: 46 = w(L)

L = 4w

Substitute

46 = 4[tex]w^{2}[/tex]

Divide both by 4

[tex]11.5=w^{2}[/tex]

[tex]\sqrt{11.5} =w[/tex] (Width)

[tex]4\sqrt{11.5}= Length[/tex]

Answer:

nxjhbfhbfwihsfnjkfdbjbshcxbdbjibebfhdhwhhdhdhffvnfnjehrhffbfgnfjrjhhfrj

Step-by-step explanation:

Step-by-step explanation:

-6x - 12 - 16 + 16x + 52

10x + 24

Answer:1,-8

Step-by-step explanation: -2,5( add 7) 5,-4(sub 9),-4,3(add 7), 3,-6(sub 9)

Pattern of +7,-9,+7,-9

-6+7=1 and 1-9=-8

Answer:

zev=15/100*56=9.6 pages

Answer:

y=3/2x-2

Step-by-step explanation:

Find the slope first:

[tex]m=\frac{y_{2-y_{1} } }{x_{2}-x_{1} } =\frac{1-(-2)}{2-0}=\frac{3}{2}[/tex]

Then solve for y-intercept:

[tex]y=\frac{3}{2}x+b\\-2=\frac{3}{2}(0)+b\\-2=b[/tex]

Now, write out your complete equation:

y=3/2x-2

Answer: There will be 12 engineers remaining in the product development department.

Step-by-step explanation:

So the givens are:

60 employees and 1/3 are engineers and if 40% of engineers are moved to another division and how many engineers will remain in the product development department?

So what we need to do:

60 * 1/3 = 60 / 3 = 20

There are 20 engineers.

20 * 40% = 8

There are 8 engineers that are going to be moved to another division.

20 - 8 = 12

12 engineers will remain in the development department.

Hence, your answer.

By calculations, 12 engineers will remain in the development department.

A companys product development division has 60 employees. Of these, [tex]\frac{1}{3}[/tex] are engineers.

The third part of a number is obtained by dividing a number by three, or what is the same, multiplying by a third ([tex]\frac{1}{3}[/tex]), thus dividing the number into a total of three equal parts.

In this case:

[tex]\frac{1}{3}[/tex]×60= 20

So, a companys product development division has 20 engineers.

40% of engineers are moved to another division.

The percentage is a way of referring to a proportion taking the number 100 as a reference. To calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100.

In this case:

40% of engineers= 40%×20=[tex]\frac{40x20}{100}[/tex]= 8

8 engineers are moved to another division.

The number of engineers who remain in the department is calculated by subtracting the total number of engineers in the department and the number of engineers who move to another division:

20 - 8= 12

12 engineers will remain in the development department.

Learn more about percentage with this examples:

https://brainly.com/question/16083614

brainly.com/question/1301322?referrer=searchResults

Image

Step-by-step explanation:

It's actually called Translation but image is the same thing as translation