Someone, please help me with this.

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]

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a = 85 10cent coins

b = 117 20cent coins

a = 10c coins

b = 20c coins

$31.90 = c3190

a + b = 202 => a = 202 - b

10a + 20b = 3190

10(202 - b) + 20b = 3190

2020 - 10b + 20b = 3190

10b = 3190 - 2020

10b = 1170

b = 117 (20cent coins)

a = 202 - 117

= 85 (10cent coins)

Answer:

ray

Step-by-step explanation:

ray is the answer because it starts with a startline but has no endpoint so it goes on for infinity.

Hello, please consider the following.

[tex]\displaystyle \lim_{x\rightarrow3}~\dfrac{2x^2-18}{x^2-3x} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x^2-3^2)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x-3)(x+3)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x+3)}{x} \\ \\ \\=\dfrac{2(3+3)}{3}\\ \\ \\=\dfrac{2*3*2}{3} =\Large \boxed{\sf \bf \ 4 \ }[/tex]

Thank you

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2x^2-18}{x^2-3x}[/tex]

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x^2-9)}{x^2-3x}[/tex]

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x^2-3^2)}{x^2-3x}[/tex]

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x+3)\cancel{(x-3)}}{x\cancel{(x-3)}}[/tex]

[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2x+6}{x}[/tex]

[tex]\\ \tt\longmapsto \dfrac{2(3)+6}{3}[/tex]

[tex]\\ \tt\longmapsto \dfrac{6+6}{3}[/tex]

[tex]\\ \tt\longmapsto \dfrac{12}{3}=4[/tex]

Problem 6, part c)

The tickmarks indicate the sides are the same length. This triangle is isosceles.

The two base angles are always opposite the congruent sides. One base angle is 25, so the other base angle must be 25 as well (base angles are congruent for isosceles triangles).

The three angles of this triangle are

25, 25 and 4x+2

Add those three angles up, set the result equal to 180, and solve for x

4x+2+25+25 = 180

4x+52 = 180

4x = 180-52

4x = 128

x = 128/4

====================================================

Problem 7, part a)

We use the same idea as with the last problem above. This works because this triangle is also isosceles (due to the tickmarks).

The three angles of this triangle are

(4x+1), (4x+1) and (5x-4)

note how (4x+1) shows up twice because it is a base angle

Add up those angles and set it equal to 180 to solve for x

(4x+1) + (4x+1) + (5x-4) = 180

13x - 2 = 180

13x = 180+2

13x = 182

x = 182/13

x = 14

Using this x value, we can find angle F

angle F = 5x-4

angle F = 5*14-4

angle F = 70-4

====================================================

Problem 7, part b)

We'll use the x value found back in part a) above.

angle D = 4x+1

angle D = 4*14+1

angle D = 56+1

Angle E is also 57, since D and E are congruent base angles

note how D+E+F = 57+57+66 = 180 to help confirm our answers

Answer:

49 and 118

Step-by-step explanation:

Let the two numbers be x and y

x+y = 167

y = 3x-29

Substitute into the first equation

x+ 3x-29 = 167

Combine like terms

4x - 29 = 167

add 29 to each side

4x = 167+29

4x = 196

Divide by 4

4x/4 = 196/4

x = 49

x+y = 167

49+y = 167

y = 167-49

y =118

Answer:

[tex]\Huge \boxed{\mathrm{49 \ and \ 118}}[/tex]

Step-by-step explanation:

Let the first number be [tex]x[/tex]

Let the second number be [tex]y[/tex]

[tex]x+y=167[/tex]

[tex]y=3x-29[/tex]

Applying substitution method.

[tex]x+3x-29=167[/tex]

Combining like terms.

[tex]4x-29=167[/tex]

Adding 29 to both sides.

[tex]4x=196[/tex]

Dividing both sides by 4.

[tex]x=49[/tex]

Substituting x = 49 for the second equation.

[tex]y=3(49)-29[/tex]

Multiplying the numbers.

[tex]y=147-29[/tex]

Subtracting.

[tex]y=118[/tex]

The two required numbers are 49 and 118.

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.

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Answer:

$87,461

Step-by-step explanation:

Given that the dimensions or sides of lengths of the triangle are 119, 147, and 190 ft

where S is the semi perimeter of the triangle, that is, s = (a + b + c)/2.

S = (119 + 147 + 190) / 2 = 456/ 2 = 228

Using Heron's formula which gives the area in terms of the three sides of the triangle

= √s(s – a)(s – b)(s – c)

Therefore we have = √228 (228 - 119)(228 - 147)(228 - 190)

=> √228 (109)(81)(38)

= √228(335502)

=√76494456

= 8746.1109071 * $10

= 87461.109071

≈$87,461

Hence, the value of a triangular lot with sides of lengths 119, 147, and 190 ft is $87,461.

Answer:

YES

Step-by-step explanation:

For example, in the figure displayed in the attachment, the length of [tex] YM = MS + SY [/tex]

[tex] MS = 3 [/tex]

[tex] SY = 10 [/tex]

Therefore, [tex] YM = 3 + 10 = 13 [/tex].

The lengths of segments MS and SY sums up to give you the length of YM.

Answer:

[tex](x+8)^2 = 86[/tex]

Step-by-step explanation:

Given

[tex]x^2 + 16x = 22[/tex]

Required

Determine an equivalent equation

[tex]x^2 + 16x = 22[/tex]

Get the coefficient of x

[tex]Coefficient = 16[/tex]

Divide this by 2

[tex]Result = \frac{16}{2}[/tex]

[tex]Result = 8[/tex]

Take its square

[tex]Result = 8^2[/tex]

[tex]Result = 64[/tex]

Add this to both sides of the equation

[tex]x^2 + 16x + 64 = 22 + 64[/tex]

[tex]x^2 + 16x + 64 = 86[/tex]

Expand the expression on the right hand side

[tex]x^2 + 8x + 8x + 64 = 86[/tex]

Factorize

[tex]x(x+8)+8(x+8) = 86[/tex]

[tex](x+8)(x+8) = 86[/tex]

[tex](x+8)^2 = 86[/tex]

Hence, the equivalent equation is [tex](x+8)^2 = 86[/tex]

Answer:

The values of r = -3/2 ,7

Step-by-step explanation:

2r2 - 11r - 21 = 0.

The is a quadratic equation in the form

2r²-11r -21= 0

Let's determine the value of r using factorization method

2r² -14r +3r -21= 0.

2r(r-7)+3(r-7)= 0

(2r+3)(r-7)= 0

2r+3= 0

2r= -3

r= -3/2

And

r-7= 0

r= 7

The values of r = -3/2 ,7

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.

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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:

value of the variable: 3/2

perimeter: 84 feet

Step-by-step explanation:

Let's find the value of the variable first:

It is a square, so all 4 sides are the same (have the same length)

This means, 3(2f + 4) = 12f + 3

Simplify it,

6f + 12 = 12f + 3

6f = 9

f = 3/2

So, the variable f = 3/2!

Let's find the perimeter:

First, we find the value of one side of the square

12f + 3 is a side

because f = 3/2, we know that the one side of a square is 18 + 3 ft, which is 21 ft

Like I said, all 4 sides are the same in a square, so we can just calculate the length of 1 side, and multiply it by 4!

so 21 * 4 = 84!

The perimeter of this square is 84 feet!

I hope this helps! Please tell me if I did anything wrong, thank you and have a great day =D

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:

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: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:

hello your question is incomplete attached is the complete question

answer : 25/2 ( A )

Step-by-step explanation:

using Stokes' Theorem to calculate

F = 5yi + 7xj  + [tex]z^3 k[/tex]

line y = 5 - 2x

attached below is the remaining part of the solution to the question

Answer:

Step-by-step explanation:

[tex]a_n=\frac{1}{3} a_{n-1}[/tex]

Answer:

99,595

Step-by-step explanation:

We are looking at division and remainders. What do you do when a remainder is present? You usually add it when multiplying to get the final number, but since we are doing this backwards, we have to subtract the numbers divided by the remainder.

25 - 20 = 5

30 - 25 = 5

40 - 35 = 5

Look for the LCM (Least Common Multiple) for 20, 30, and 40 :

600

Now for the equation :

n + 5 = Multiple of all numbers and LCM =

n + 5 = 166 * 600 = 99,600

n = 99,600 - 5 = 99,595

The greatest 5 digit number which when divided by 25, 30 and 40 has a remainder of 20, 25, and 35 is 99,595

The reason why the above value arrived at is correct is as follows:

The required parameter;

To find a 5 digit number that with remainder of 20, remainder of 25 and a remainder of 35, when divided by 25, 30, and 40 respectively

Strategy;

Find the LCM of the divisor, then find the highest common multiple of the

LCM that is a 5 digit number, equate the expression for the required 5 digit

number to the highest common multiple of LCM of the divisors by adding

a value that will give a factor of the divisor as follows;

Let x represent the 5 digit number, from the question, we get;

x = 25·a + 20

x = 30·b + 25

x = 40·c + 35

x < 99,999

The 5 digit number is not a multiple of 25, 30, and 40, therefore, the number is not a multiple of the LCM of 25, 30, and 40 which is 600

The highest multiple of 600 which is a 5 digit number = 99,600

Therefore, we can write;

25·a + 20 + 5 = 30·b + 25 + 5 = 40·c + 35 + 5 = 99,600

However;

25·a + 20 + 5 = x + 5

By transitive property, we get

x + 5 = 99,600

∴ x = 99,600 - 5 = 99,595

The 5 digit number, x = 99,595

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Answer:

8

Step-by-step explanation:

Jason = 22

Taylor = x

Taylor is 8

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:

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:

2n+2

Step-by-step explanation:

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

       (-3+5)  =2  

-n +2+n+3n

3n-n =  2n

2n+2

Answer:

11.5 cm²

Step-by-step explanation:

We know that the triangle has a base of 3 + 4 = 7 and a height of 3 + 2 = 5. Therefore, the area of the triangle is 7 * 5 / 2 = 17.5. The area of the 3 by 2 rectangle is 3 * 2 = 6 so the shaded area is 17.5 - 6 = 11.5 square cm.

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:

12

Step-by-step explanation:

144 chairs in total.

the room is square, this means that the number must be multiplied by the same number

12x12= 144

there are 12 chairs on the first row.

Answer:

EA, or s

Step-by-step explanation:

The line AE could also be named any of the following:

AC, EC, CE, CA, EA

If you’re only looking at the line segment AE, the only option is:

EA

Since I don’t know whether you need the line or line segment, you might want go with EA since it’s on both lists. It could also be line s.

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:

135°

Step-by-step explanation:

Because the lines are parallel, <1 and <3 are the same.