Multiply the following complex numbers:
(7-3i)(8 + 4i)​

Answer:19.7

Step-by-step explanation:

Sin‐(7.5/22.3) on your calculator

The answer to 3 significant figures is 19.7

Size of angle YZX for the given measurements of triangle YZX is equal to 19.651°( 3 significant figure).

" Angle is defined as when two rays meet at one point known as vertex."

Formula used

[tex]sin\theta = \frac{ opposite side }{Hypotenuse}[/tex]

According to the question,

As shown in the figure,

In triangle YXZ,

Angle X = 90 degrees

Opposite side to ∠YZX , XY = 7.7cm

Hypotenuse ,  ZY = 22.3 cm

Substitute the value in the formula to get the value of size of angle YZX,

[tex]sin YZX = \frac{XY}{ZY}[/tex]

⇒[tex]sin YZX = \frac{7.5}{22.3}[/tex]

⇒[tex]sin YZX = 0.3363[/tex]

⇒ [tex]YZX = sin^{-1} (0.3363)[/tex]

⇒∠YZX = 19.651°

Hence, size of angle YZX for the given measurements of triangle YZX is equal to 19.651°( 3 significant figure).

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Answer:

a = - 3, b = 5

Step-by-step explanation:

To rationalise the denominator multiply the numerator/ denominator by [tex]\sqrt{2}[/tex]

= [tex]\frac{\sqrt{2}(10-\sqrt{18}) }{(\sqrt{2})^2 }[/tex]

= [tex]\frac{10\sqrt{2}-\sqrt{36} }{2}[/tex]

= [tex]\frac{10\sqrt{2}-6 }{2}[/tex]

= 5[tex]\sqrt{2}[/tex] - 3

= - 3 + 5[tex]\sqrt{2}[/tex] ← in the form a + b[tex]\sqrt{2}[/tex]

with a = - 3 and b = 5

Answer:

The first choice.

Step-by-step explanation:

Direct variation is represented by y = kx where k is a constant and the graph passes through the origin.

Here k = 3..

Answer: [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

When any number has a negative exponent, all the negative exponent is doing is flipping the sides.

When we plug -3 in for x we get [tex]-3^{-2}[/tex].

Now just imagine the -3 in fraction form as [tex]\frac{-3}{1}[/tex]. And all you do now is just flip the sides to get [tex](\frac{1}{-3} )^{2}[/tex]

And now apply the exponent 2 to the 1 and negative 3.

1 to the power of 2 is just 1

-3 to the power of 2 is 9.

So your answer is [tex]\frac{1}{9}[/tex]

[tex]\displaystyle\bf\\g^{2x+1}=g^{3x-2}\\\\g=g\\\\3x-2=2x+1\\\\3x-2x=1+2\\\\\boxed{\bf x=3}[/tex]

Answer:

Plot I area= 32.5cm²

Plot II area = 73.09cm²

Plot III area = 35cm²

Plot IV area = 54cm²

Total the area of Field​ = 194.59cm²

Step-by-step explanation:

The field is made up of four plots with different shapes. So we would find the area of the 4 shapes to get the area of the plots.

A question related to this can be found at brainly (question ID: 18861101)

Find attached the diagram

Given:

AC = 13cm

AE = 19cm

CF = DE = 7cm

AD = AE - DE

AD =  19-7 = 12cm

GF = 9cm, EH = 15cm

GH = 17cm

Plot I: A right angle triangle

Area = ½ × base × height

Base = CD, height = AD

Using Pythagoras theorem

CD = √(AC² - AD)²

CD = √(13² - 12²) = √(169-144)

CD = √25 = 5

Area = ½ × 5 ×13= 32.5

Area plot I = 32.5cm²

Plot II: An equilateral triangle

Area of the equilateral triangle = a²/4 ×(√3)

√3=1.73

a = side = AC

Area = (13)²/4 ×(√3) = 42.25 × 1.73 = 73.0925

Area of Plot II = 73.09cm²

Plot III: A rectangle

Area of a rectangle = length × width

length = 7cm

width = 5cm

Area of plot III = 7×5 = 35cm²

Plot IV: A trapezium

Area of trapezium = ½(base 1 + base2) × height

Base 1= FE = CD

Base 2= GH

To get height using diagram 2. When you draw the lines from the two points on base1, you would have 1 rectangle in the middle with the two triangles by the side.

We would apply Pythagoras theorem to find h in the two right angled triangles:

Hypotenuse ² = opposite ²+adjacent ²

1st ∆: 9² = h²+a²

h² = 81-a²

2nd ∆: 15² = h² + (12-a)²

225 = h² +144 - 24a+ a²

225-144 = h²-24a+ a²

Insert value for h² in the 2nd

81 = 81-a² - 24a + a²

24a = 81-81

a= 0

h² = 81-0²

h = √81 = 9

Area of trapezium = ½(5+7) × 9

= 6 × 9

Area of plot IV= 54cm²

Total the area of field​ = area of plot I + area of plot II + area of plot III +area of plot IV

= 32.5 + 73.09 + 35+ 54

Total the area of Field​ = 194.59cm²

Answer:

8.75 km.

Step-by-step explanation:

You can set up a ratio of the map to the actual distance of [tex]\frac{1}{50000}[/tex].

Then, this ratio can be used to cross multiply and divide to get an equivalent ratio for the distance:

[tex]\frac{1}{50000}[/tex]=[tex]\frac{17.5 cm}{x cm}[/tex] By cross-multiplying we have x (in centimeters) = 17.5×50000. This tells us that x = 875,000 cm.

However, the answer asks for the distance in kilometers, so we need to convert it. There are 100,000 centimeters in a kilometer, so by dividing: 875000÷100000=8.75 kilometers.

Answer:

8.5 cm

Step-by-step explanation:

Angles of the triangle:

Right triangle as it has 90° angle

Sides are a, b and 19 cm

Answer:

2nd option: (0.5, 7), maximum; (2, 1) point of inflection; (3.5, -5), minimum.

Step-by-step explanation:

The maximum point, or a point of the graph with the highest y-value, is at

(0.5, 7).

The minimum point, or a point of the graph with the lowest y-value, is at

(3.5, -5).

The point of inflection is where the graph begins to change direction. This is at (2, 1).

Therefore, the 2nd option is correct.

Answer:

b

Step-by-step explanation:

forgive me if im wrong, its been a long time since ive done these. it doesnt seem like theres any complex numbers so it shoild be all real #

Answer:

A. x >= 0

Step-by-step explanation:

The domain of a function is the set of values that are the x-coordinates of all the points f the function.

This function starts at x = 0 and goes on forever with greater values of x.

Answer: A. x >= 0

Answer:

52

Step-by-step explanation:

140 - 13 = 127

127 - 75 = 52

Check your work:

75 + 13 + 52

= 140

52

Step-by-step explanation:

75 + 13=88

140 - 88=52

75 + 13 + 52=140

hope it helps stay safe and have a good day =D

Answer:

Option D is correct.

The only partial representations of the given information are the table and the graph.

This is because, on their own, they do not provide the corresponding value of y for every given x.

Step-by-step explanation:

Complete Question

Four representations of the same data are shown below.

- Verbal Description

Shay pays a $4 monthly fee in addition to the data and minutes charges on her cell phone bill, x.

- Equation

y = x + 4

- Table

- Graph

Cell Phone Bill

Which two representations are considered to be only partial representations?

A) the equation and the verbal description

B) the verbal description and the graph

C) the table and the equation

D) the graph and the table

Solution

A complete representation would give the total amount Stay pays in a month, given the number of minutes. There would be no domain of x (minutes charges on her phone) where there is a solution, that the complete representation wouldnt give the corresponding y (total amount of money she would pay.

Taking each of the representations one at a time.

- Verbal Description

The verbal description alone explains the subject matter to us in details. With the explanation from the verbal description, the value of y is always just there to obtain.

- Equation

y = x + 4

The equation too, alone, will give the value of y for every given value of x. So, it is also a complete representation of the subject matter all on Its own.

- Table

Although, the values of the table aren't all presented above, but it is evident that the table, no matter how long, can only give the corresponding values of y given x, to an extent. A table, on its own, would not give all the values of y, for every value of x, one can think of. Unless one of the other methods of representation has already been given, the table alone is a partial representation of the subject matter.

- Graph

Just like the table is absent Too, the graph too cannot be attached, to avoid question deletion due to violating community guidelines. But the graph Too, on its own just shows a straight line graph of y and x, over a limited range of values. It stops after that and on its own, the graph wouldn't be able to outrightly represent the subject matter as we don't know if the relationship is linear forever, or not, from just seeing a graph of y against x over a very limited range.

Hence, it is evident that the table and the graph represent partial representations of the subject matter because, on their own, they do not provide the corresponding value of y for every given x.

Hope this Helps!!!

Answer:

D, C, A, B

Step-by-step explanation:

Find common factor:

60 is the common denominator

2/5=24/60

2/3=40/60

1/4=15/60

1/10=6/60

Answer:

A. 2/5 = 0.4

B. 2/3 = 0.66

C. 1/4 = 0.25

D. 1/10 = 0.1

Arranging them in the box we have

D , C , A , B

Since D is the smallest followed by C followed by A followed by B which is the largest

Hope this helps

Answer:

Answer: Choice C)  

Stretched vertically, flipped over x axis, shifted 7 units down

Step-by-step explanation:

The graph of g(x) is graph of f(x) reflected along the y - axis. Its magnitude is also multiplied by 2.

A cubic function is of the form f(x) = ax³ + bx² + cx + d, where a, b, c, and d are constants and a ≠ 0. It has a degree of 3 and has 3 possible roots.

We have the following functions -

f(x) = x³

g(x) = -2x³

The graph of g(x) is graph of f(x) reflected along the y - axis. Its magnitude is also multiplied by 2. Refer to the graph attached.

Therefore, the graph of g(x) is graph of f(x) reflected along the y - axis. Its magnitude is also multiplied by 2.

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Answer:

3

Step-by-step explanation:

Answer:

D. 44 dm³

Step-by-step explanation:

Volume of cuboid equals:

a × h

4 × 11

= 44

The volume of the shape is 44 dm³.

Answer:

  O True

Step-by-step explanation:

If we substitute (x, y) = (0, 0) into both inequalities, we have ...

  0 < 2·0 +4   ⇒   0 < 4 . . . true

  0 > -2·0 -2   ⇒   0 > -2 . . . true

The point (0, 0) satisfies both inequalities, so is contained in the solution set.

Answer:

Graph using graphing calc or desmos.

Step-by-step explanation:

Answer:

your graph is below. i have algebra 2 on flvs.

Answer:

m∠QPR = 20°

Step-by-step explanation:

Step 1: Find x

4x + 27 + 9x - 115 = 107

13x - 88 = 107

13x = 195

x = 15

Step 2: Find m∠QPR

9(15) - 115

135 - 115

m∠QPR = 20°

Solution: 25 × $9.85= $246.25 purchase price

25 × $11.22 = $280.5 sale price

$280.5 – $246.25 = $34.25 profit in dollars

$34.25 ÷ $246.25 = 0.139 = 13.9% ROI

Purchase price of the share is equals to 246.25dollars.

Profit percentage is equals to 13.9 percentage ( nearest tenth).

" Purchase price is defined as the total amount paid to buy any product."

Formula used

Profit = Selling price - Purchase price

Profit percentage = [tex]\frac{profit}{cost price} (100)[/tex]

According to the question,

Total number of shares = 25

Purchase price of one share =  9.85 dollars

Selling price of 1 share = 11.22 dollars

Therefore,

Purchase price of 25 shares = (9.85 × 25 )dollars

                                               = 246.25 dollars

Selling price of 25 shares = (11.22 × 25) dollars

                                           = 280.5 dollars

Selling price > Purchase price

Therefore,

Profit = Selling price - Purchase price

         = 280.5 - 246.25

         = 34.25 dollars

Substitute the value in the formula we get,

Profit percentage = [tex]\frac{34.25}{246.25} (100)[/tex]

                              = 13. 9 percentage ( nearest tenth)

Hence, purchase price of the share is equals to 246.25dollars.

Profit percentage is equals to 13.9 percentage ( nearest tenth).

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Answer:

6

Step-by-step explanation:

rearrange the numbers from smallest to biggest:

-19, -14, -9, -3, 6, 8, 14, 19, 20

the set of data the question requires is the middle data. there are 9 sets of data. the middle data = (9 + 1) ÷ 2 = 5

find the fifth piece of data from the rearranged order.

ans: 6

Answer:

6

Step-by-step explanation:

gotchu G

Answer: true

Step-by-step explanation:

Answer:

e can treat 7 friends

Step-by-step explanation:

2f+10=24

2f=24-10=14

f=14/2=7

Answer:

They have 23 dimes

Step-by-step explanation:

Let x be the number of dimes

1 dime = 0.1 dollar

x dimes = 0.1x dollars

They found there were 14 more quarters than dimes.

No. of quarters = x+14

1 quarter = 0.25 dollar

(x+14) quarter =0.25 (x+14)

The number of nickels was 8 less than 4 times the number of dimes.

So, No. of nickels= 4x-8

1 nickel = 0.05 dollar

(4x-8) nickel = 0.05(4x-8) dollar

The total value of the nickels, dimes, and quarters was $15.75.

So,0.1x+0.25 (x+14)+ 0.05(4x-8)=15.75

x=23

Hence they have 23 dimes

Answer:

It is 49

Step-by-step explanation:

Divide 98 by 2 to get semicircle radius.

Answer:

49 meters

Step-by-step explanation:

The radius is half of the diameter

98 divided by 2 is 49 which is the radius of the semicircle

Answer:

aₙ=  n²-6

Step-by-step explanation:

The sequence:

- 5, -2, 3, 10, 19, ...

The difference between terms:

3, 5, 7, 9

The next term would be: 19+11= 30

Let's work out the formula:

aₙ= a₁+n²-1= -5+ n²-1= n²-6

Let's test this formula for 5th and 6th terms:

So the nth term is:

Answer:

71

Step-by-step explanation:

4, 7, 12, 21, 38, ...

next term:

nth term:

Answer:

840

Step-by-step explanation:

Let x be the total earning.

3/4 × x = 630

x = 630 × 4/3

x = 840

The worker’s total earning for the month is 840.