Complete the table for each function. Then answer the questions that follow.
a=
; b =
; c =
; d =
;
e =
; f =
; g =

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:(8 + 5i)(3 + 2i) - (4 + i)(4 - i)[/tex]

[tex]\qquad \sf  \dashrightarrow \:[( 8 \sdot3) + (8 \sdot2i) + (5i \sdot3) + (5i \sdot2i)] -[( 4 \sdot4) + (4 \sdot - i) + (i \sdot4) + (i \sdot - i)][/tex]

[tex]\qquad \sf  \dashrightarrow \:[24+ 16i + 15i+ 10i {}^{2} ] -[16 - 4 i+ 4i - i {}^{2} ][/tex]

[tex]\qquad \sf  \dashrightarrow \:[24+ 31i+ 10 {}{( - 1)} ] -[16 - ( - 1){}^{} ][/tex]

[tex]\qquad \sf  \dashrightarrow \:[24+ 31i - 10 {}{} ] -[16 + 1{}^{} ][/tex]

[tex]\qquad \sf  \dashrightarrow \:[14+ 31i {}{} ] -[17{}^{} ][/tex]

[tex]\qquad \sf  \dashrightarrow \: - 3+ 31i {}{} [/tex]

I hope you understood the procedure ~

The perimeter of the composite shape is: (3π + 12)mm

A semicircle is a part of a circle cut through its diameter.

Analysis:

perimeter of a semicircle = πr

where r = 6/2 = 3mm

perimeter of a semicircle = π(3)  = 3π

perimeter of incomplete rectangle = L+2B, L = 6mm, B = 3mm

perimeter of rectangle = 6mm +2 x 3= 12mm

perimeter of shape = (3π+12)mm

In conclusion, the perimeter of the rectangle is (3π+12)mm

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Answer: Choice A)  x ≥ -3

Reason:

The graph has a closed filled in circle at -3, which means we include this value. So we'll have "or equal to" as part of the inequality sign.

We'll also have "greater than" because we're shading to the right.

Hence, we have "greater than or equal to".

Put another way, x = -3 or x > -3 are two possibilities.

If the endpoint at -3 was an open hole, then we'd exclude the endpoint and go for x > -3 instead of x ≥ -3

Answer:

X≥-3

Step-by-step explanation:

Inequalities represent a range of values, rather than a single value.

Let us consider the inequality

x > - 3

This would mean can be any value greater than -3, not including -3.

This is represented by a line starting from -3 and extending indefinitely (marked by an arrow head). Note that at -3, there is a small empty circle which represents that -3 is not included.

In case the inequality was

x > -3

It would mean that -3 has also been included.

In case you can't draw on the number line, you can also show the range just above the number.

If hose A takes x hours to fill the pool, hose B will take x+3 hours to fill the pool. So, each hour, A will fill [tex]\bf{\dfrac{1}{x}}[/tex] parts of the pool and B will fill [tex]\bf{\dfrac{1}{x+3}}[/tex] parts. Since using both hoses fills the pool completely, you have to:

                                                          [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ 1= \frac{1}{x}+\frac{1}{x}+\frac{1}{x+3}+\frac{1}{x+3} } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2}{x}+\frac{2}{x+3} } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2x+2x+6}{x(x+3)} } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+3x=4x+6\ \Longrightarrow\ \ 0=x^2-x-6=(x-3)(x+2) } \end{gathered}$}[/tex]

Hose A takes 3 hours to fill the pool and Hose B takes 6 hours.

The height of the kite will be 53.32 feet above the ground.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

The height of the kite above the ground will be calculated as:-

[tex]Sin\theta = \dfrac{perpendicular}{Hypotenuse}[/tex]

[tex]Sin(29)=\dfrac{H}{110}[/tex]

H = Sin(29)  x  110

H  = 53.32 feet

The hand of the boy is 3.5 above the ground so the total height H(t) of the kite above the ground will be:-

H(t)  = 53.232  +  3.5

H(t)  = 56.28 feet.

Therefore the height of the kite will be 53.32 feet above the ground.

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Answer:

Step-by-step explanation:

\text{What function uses the \color{green}{\textbf{O}PPOSITE} and the \color{#EB0000}{HYPOTENUSE}?}

What function uses the OPPOSITE and the HYPOTENUSE?

\text{\Large \underline{S}\color{green}{O}\color{#EB0000}{H}-CAH-TOA}

S

​

OH-CAH-TOA

\text{sin }\color{purple}{29}=\frac{\color{green}{\text{opposite}}}{\color{#EB0000}{\text{hypotenuse}}}=\frac{\color{green}{x}}{\color{#EB0000}{110}}

sin 29=

hypotenuse

opposite

​

=

110

x

​

\text{sin }29=

sin 29=

\,\,\frac{x}{110}

110

x

​

\frac{\text{sin }29}{1}=

1

sin 29

​

=

\,\,\frac{x}{110}

110

x

​

110\text{ sin }29=

110 sin 29=

\,\,x

x

Cross multiply.

x=53.329058...

x=53.329058...

Type into calculator.

\text{Add 3.5, the distance from the ground to his hand:}

Add 3.5, the distance from the ground to his hand:

53.329058...+3.5=

53.329058...+3.5=

\,\,56.829058...

56.829058...

\approx

≈

\,\,56.8

56.8

Round to the nearest tenth.

\text{The kite is 56.8 feet above the ground.}

The kite is 56.8 feet above the ground.

The approximate length of arc QR to nearest tenth is 9.9cm

The formula for calculating the length of an arc is expressed as:

L = r theta

where

r is the radius of an arc = 20cm/2 = 10cm

theta = 180 - 123 = 57 degrees

Determine the length of an arc

L = 10(57π/180)
L = 57π/18
L = 9.94cm

Hence the approximate length of arc QR to nearest tenth is 9.9cm

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Answer:

9.9

Step-by-step explanation:

Population density=Total population/Total area

#Chicago

Population density

#Los angeles

Population density

Difference

The population density of Chicago is 3741.9 greater than Los Angele's population density.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics,  notably algebra, data management, and geometry.

As per the given information in the question,

The population density is the ratio of the total population to the total area.

Total population of Chicago = 2,707,120

The land area of Chicago = 227.635

Then, the population density of Chicago will be:

= 2,707,120/227.635

= 11892.37

Total population of Los Angeles =  3,819,702

The land area of Los Angeles = 468.670

Then, the population density of Los Angeles will be:

= 3,819,702/468.670

= 8150.08

Then, the difference between Chicago and Los Angeles will be:

= 11892.37 - 8150.08

= 3741.9

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Step-by-step explanation:

remember a few things :

a × -1 = -a

-a × -1 = a

-1 × -1 = 1

1 × a = a

therefore,

-1 × -1 × a = 1 × a = a

and finally

c × (a + b) = c×a + c×b

so, we can say

(1 - 5) = -1 × -1 × (1 - 5) =

= -1 × (-1×1 + -1×-5) = -1 × (-1 + 5) =

= -1 × (5 - 1) = -(5 - 1)

We calculate the module:

[tex]|z|\: = \: \sqrt{( - 3) ^{2} \: + \: {4}^{2} } [/tex]

[tex]|z| \: = \: \sqrt{9 \: + \: 16} [/tex]

[tex]|z| \: = \: \sqrt{25} [/tex]

[tex] \boxed{|z| \: = \: 5}[/tex]

We calculate the angle formed by "z":

[tex] \arctan( \frac{4}{ - 3} ) \: = \: \underline{0.92729521 \: \text{rad}}[/tex]

We pass it to degrees:

[tex]0.92729521 \: \times \: \frac{180}{\pi} [/tex]

[tex] \frac{166.91313924}{\pi} [/tex]

[tex] \frac{166.91313924}{3.14159265}[/tex]

[tex] \boxed{ 53.13°}[/tex]

Now we use this formula to transform it into a trigonometric form:

[tex] \boxed{z \: = \: |z| \times \: ( \cos( \alpha) \: + \: i \: \times \: \sin( \alpha))}[/tex]

[tex] \boxed{ \bold{z \: = \: 5 \times \: ( \cos( 53.13°) \: + \: i \: \times \: \sin( 53.13°))}}[/tex]

[tex] \boxed{ \bold{z \: = \: 5 \times \: ( \cos( 53.13°) \: + \: i \: \times \: \sin( 53.13°))}}[/tex]

Answer:

160 million

Step-by-step explanation:

According to the ILO as of 2021, there's an estimated 160 million children working right now, so i don't know what answer you should put :/

Answer:

D 215 million

Step-by-step explanation:

Answer:

it think it is B. Digital payments are more common than ever.

Step-by-step explanation:

"Significant gains have been recorded, however, in the share of consumers using two or more digital payments methods, which jumped from 45 percent last year to 58 percent in 2020 "

Hope This Helped

Answer:

see the attachment photo!

Answer:

94 cm^2 (cm squared bc it's surface area)

Step-by-step explanation:

so we know...

length = 5

height = 3

width = 4

there are two of the same sides in a rectangular prism

5x3 = 15

4x3 = 12  

4x5 = 20

15 + 12 + 20 = 47 x 2 = 94

Answer:

[tex]x=-2,y=6[/tex]

Step-by-step explanation:

We can add these 2 equations together to eliminate [tex]x[/tex] from the equation, leaving us to solve for [tex]y[/tex].

[tex](4x+8y) + (-4x+y) = (40) + (14)\\9y = 54\\\boxed{y = 6}[/tex]

Now we can solve for [tex]x[/tex] through substituting [tex]y[/tex].

[tex]4x+8y=40\\4x+8(6)=40\\4x+48=40\\4x=-8\\\boxed{x=-2}[/tex]

We can check our answers by substituting [tex]x[/tex] and [tex]y[/tex] into one of the equations and seeing if the equation is true.

[tex]-4x+y=14\\-4(-2)+6=14\\8+6=14\\14=14[/tex]

LHS = RHS so our answers are correct.

Step-by-step explanation:

sum of interior angle sum of each angle

1) 720 120

2)360 90

3)540 108

(2)

a) a=360-90-90-122

a=58

b) b=360-100-95-35

b=130

c) c=720-140-110-110-125-139

c=105

d) 2d=540-80-90-90

2d=280

d= 140

3) 5(360/5)

=360

4) y=90+90-122

y=58

x=360-117-66-58

x=119

Answer:

The value of x in the figure is 3.5

Step-by-step explanation:

When we look at the figure, we see that AB and BC, are connected, to make a longer side of a triangle. We can also see that BC is dilated from AB. When dilating, we multiply or divide by a number, to get the extended or shortened length. (Just keep multiplication and division in mind)                    To get x, we can do the same that we did to get 2, from 4. From AB to BC it goes from 4 to 2.

To get 2 from 4, you must divide 4 by 2. So when we do the same thing to 7, we should get x.

7 / 2 = 3.5

The value of x in the figure is 3.5

[tex]\\ \rm\dashrightarrow \dfrac{4}{2}=\dfrac{7}{x}[/tex]

[tex]\\ \rm\dashrightarrow 2=\dfrac{7}{x}[/tex]

[tex]\\ \rm\dashrightarrow x=\dfrac{7}{2}[/tex]

[tex]\\ \rm\dashrightarrow x=3.5[/tex]

5(3x+2)-2(4x-1)

= 15x+10-8x+2

= 7x+12

The histogram includes data from a voluntary response sample which is not representative of the population.

A histogram is a chart that represents numerical data using bars. The dataset is split into intervals, each interval is represented by a bar, and the number of variables in each interval makes up the frequency for that interval.

From the histogram attached, we can see that there is a huge gap from around 17000 miles to 32500 miles.

Now, when we have this kind of gap it means that the histogram includes data from a voluntary response sample which is not representative of the population.

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Answer:

Step-by-step explanation:

1. So there is two bread options but let's ignore that due every option being the same for both bread options.

2. So if you look there are three meat options meaning there is a one in three chance logical chance someone picks turkey (note when I say logical I mean that doesn't mean that this will be true in real life) and there is a one in two logical chance someone picks Swiss cheese.

3. So with a one in three chance logical meat option and a one two chance cheese option and.

4. Now knowing this it is simple math at this point as simple as [tex]\frac{1}{3}[/tex] x [tex]\frac{1}{2}[/tex]

5. 1 x 1 = 1 and 3 x 2 = 6

6. leading to [tex]\frac{1}{6}[/tex]

Answer:

3

Step-by-step explanation:

2r=d

d/2=r

Using linear functions, it is found that it will take 7 hours for Michael to deliver as many newspapers as Franklin.

A linear function is modeled by:

y = mx + b

In which:

The linear functions that give the amounts for Franklin and Michael after h hours are given by:

They will be equal when:

F(h) = M(h)

Hence:

26 + 9h = 5 + 12h

3h = 21

h = 7

It will take 7 hours for Michael to deliver as many newspapers as Franklin.

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Answer:

  35.4 million

Step-by-step explanation:

We assume the description "increases by 10% per day" means the base of the percentage is the previous day's number of streams. Then the sequence of streams on consecutive days is a geometric sequence with a first term of 20 million and a common ratio of (1 +10%) = 1.10.

__

The n-th term of a geometric sequence is ...

  an = a1×r^(n-1) . . . . . where a1 is the first term, and r is the common ratio

The sequence of streams on consecutive days is then ...

  an = 20×1.10^(n-1) . . . . millions of streams on day n

For n = 7, the number of streams is ...

  a7 = 20×1.10^(7 -1) ≈ 35.4 . . . . million streams

There will be about 35.4 million streams on the seventh day.

Answer:

Cube with a side length of 2/5 cm: 8/125 cm^3

Rectangular prism with a length, width, and height of 3/5 cm, 4/5 cm, and 3/5 cm, respectively: 36/125cm^3

Rectangular prism with a length, width, and height of 1/5 cm, 2/5 cm, and 3/5 cm, respectively: 6/125 cm^3.

Cube with a side length of 1/5 cm: 1/125 cm^3

Step-by-step explanation:

For the first one, cubes have equal sides, we would do 2/5*2/5*2/5, which is 8/125 cm^3.

Next we have a rectangular prism. For this, we will just multiply all of the sides with each other which is 3/5*4/5*3/5 which is 36/125 cm^3

Now we have another rectangular prism. Again, we will multiple all of the sides with one another: 1/5*2/5*3/5, which is 6/125 cm^3.

Lastly, there is a cube with a side length of 1/5 cm. We know that cubes have equal sides, so it would be 1/5*1/5*1/5, which is 1/125 cm^3.

I hope this helped.

Answer:

b=17.75 ft

Step-by-step explanation:

We will answer this using Pythagorean Theorem.
Since the bottom of a ladder is 3 feet from the wall, and the ladder is 18 ft long, the ladder is the hypotenuse. Knowing pythagorean theorem (a^2+b^2=c^2), we can plug it in.
3^2 + b^2 = 18^2

9+b^2=324

b^2=315

b=17.75 ft

A random sample  is a sample in which the chosen elements are removed from the population once they are chosen.

A sample is a smaller group of the population that has the desired elements of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.

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Answer:

triagle

Step-by-step explanation:

it is tringle because because this pattern other is tall and other is short it gona be isocelese triagle

Answer:

[tex]2x+16y[/tex]

Add  [tex]12y[/tex] and [tex]4y[/tex].

[tex]2x+16y[/tex]

Answer:

2x + 16y

Step-by-step explanation:

The y terms can be added together. 12y + 4y is 16y. The 2x has to just stay the way it is because it could only be added to another x term and there aren't any. So you are left with 2x + 16y

Answer:

Equation 75 X .45 = P

P = 33.75

The equivalent expression of [tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex] is [tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]

The expression is given as:

[tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex]

Collect like terms

[tex]-\dfrac65+\dfrac{4}{15}+\dfrac13v-\dfrac23v[/tex]

Evaluate the like terms (take LCM)

[tex]\dfrac{-6 * 3 + 4}{15}+\dfrac{v - 2v}3[/tex]

Evaluate the like expressions

[tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]

Hence, the equivalent expression of [tex]-\dfrac65-\dfrac23v+\dfrac{4}{15}+\dfrac13v[/tex] is [tex]-\dfrac{15}{15}-\dfrac{v}3[/tex]

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