a swimming pool is 10 feet and 14 feet long. A
concrete border was poured that was 3 feet wide
around the pool. Find the perimeter of the
concrete walk.

[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 ~

Using it's concept, it is found that the probability that a person chosen at random from this group has brown or green eyes is of [tex]\frac{13}{25}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that the group has 20 + 6 + 17 + 7 = 50 people, of which 20 + 6 = 26 have brown or green eyes, hence the probability is given by:

p = 26/50 = 13/25.

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Answer:

[tex]h(x) = \frac{1}{4} x[/tex]

Step-by-step explanation:

To find the inverse of a function, the steps are:

In this case, since h(x) is the inverse function of f(x), we can replace x with h(x) in step 3.

_____

f(x)= 4x

Let y= f(x) [tex]\textcolor{steelblue}{\text{ - step 1}}[/tex]

y= 4x

Divide both sides by 4:

[tex] \frac{1}{4} y = x[/tex]

[tex]x = \frac{1}{4} y \: \: \: \textcolor{steelblue}{\: \text{ - step 2}}[/tex]

Replace x with h(x) and y with x:

[tex]\bf{h(x) = \frac{1}{4} x} \: \: \: \textcolor{steelblue}{\: \text{ - step 3}}[/tex]

Additional:

For a similar question on inverse functions, do check out the following!

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

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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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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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.

Answer:

Equation 75 X .45 = P

P = 33.75

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:

=> Expand by applying the FOIL method

[tex]2x\cdot \:3x+2x\left(-8\right)-7\cdot \:3x-7\left(-8\right)[/tex]

=> combine like terms

[tex]6x^2-37x+56[/tex]

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

= 15x+10-8x+2

= 7x+12

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

Both lines are parallel because: A. both lines have a slope of 4/3.

The slope of a line = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

The slope of parallel lines are the same, while the slope of perpendicular lines are negative reciprocals.

Slope of AB = 4 units/3 units = 4/3

Slope of CD = 4 units/3 units = 4/3

Both lines have the same slope, therefore, they are parallel to each other.

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The asked sum of multiples of five from 10 to 75, inclusive, is 595.

To find the sum of multiples of five from 10 to 75, inclusive, we can use the formula for the sum of an arithmetic series:

Sum = (n/2) * ([first term] + [last term])

Following the given case, the first term (a) is 10, the last term (l) is 75, and the common difference (d) between consecutive terms is 5 (since we are considering multiples of five).

The number of terms (n) can be calculated as:

n = (last term - first term) / common difference + 1

Let's calculate the number of terms first:

n = (75 - 10) / 5 + 1

n = 65 / 5 + 1

n = 13 + 1

n = 14

Now, we can determine the sum of the multiples of five:

Sum = (14/2) * (first term + last term)

Sum = 7 * (10 + 75)

Sum = 7 * 85

Sum = 595

Therefore, the asked sum of multiples of five from 10 to 75, inclusive, is 595.

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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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Answer: 19.7

Step-by-step explanation:

By the Pythagorean theorem,

[tex](BD)^{2}=8^{2}+18^{2}\\\\(BD)^{2}=388\\\\BD=\sqrt{388} \approx \boxed{19.7}[/tex]

Any time we have a single positive tile pair up with a single negative tile, those two tiles cancel out.

Three positive tiles and three negative tiles will pair up and cancel out. We're left with two positive tiles only. This represents the number 2.

In other words, 5 + (-3) = 5 - 3 = 2

Answer:

a) k = 10              b) k = 7.5

Step-by-step explanation:

( 5k+ 20 ) + ( 7k + 40 ) = 180

12k + 60 = 180

12k = 120

k = 10

40 + ( 12k + 10) + 180 - ( 8k + 80 ) = 180

50 + 12k + 180 - 8k - 80 = 180

50 + 12k -8k - 80 = 0

50 + 4k - 80 = 0

30 = 4k

k = 7.5

Answer:

Step-by-step explanation:

The total number of counters in the bag is 5 + 3 = 8.

and only 5 are red.

Then

the probability of obtaining a red counter is :

[tex]= \frac{5}{8} = 0.625[/tex]

Answer:

The ans of first one is 0/8 = 0

and 6÷0 = undefined....hope this helps:)

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]

Answer:

slope = 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 9 ) and (x₂, y₂ ) = (- 4, 2 )

m = [tex]\frac{2-9}{-4-3}[/tex] = [tex]\frac{-7}{-7}[/tex] = 1

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:

Translation: please help it's due today

Would love to help but there is no question to answer

Answer:

2

Step-by-step explanation:

2 can go into 12,2, and 84

To obtain the greatest common divisor of (g.c.d) we must do it in simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

  [tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 2 \ \ \ 84}\\ \ 6 \ \ \ 1 \ \ \ 42 \end{matrix}\right|\begin{matrix} 2\\ \: \end{matrix} \end{gathered}$}[/tex]

As we can see the number 2, is the only common prime number.

The greatest common factor of 12, 2, and 84 is 2.

Answer:

b =22

Step-by-step explanation:

The formula to calculate the area of a trapezoid:

1/2*(a+b)*h : (a: base, b: base, h: height)

The formula to calculate the area of a triangle:

1/2*a*h (a: base, h: height)

All inputs are given for trapezoid so let's first find the area of trapezoid then we can find the value of b:

1/2*(10+12)*7 = 77 cm^2 is the area of trapezoid

now for the area of triangle:

1/2*b*7 = 77 (it was given that the areas are equal)

first we multiply both sides by 2

7*b = 154 now divide both sides by 7

b = 22